SHAPE AND LUMINANCE CUES FOR THE VISUAL
PERCEPTION OF GLOW
MINJUNG KIM
A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES
IN PARTIAL FULFILMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
MASTER OF ARTS
GRADUATE PROGRAM IN PSYCHOLOGY
YORK UNIVERSITY
TORONTO, ONTARIO
AUGUST 2011
SHAPE AND LUMINANCE CUES FOR THE
VISUAL PERCEPTION OF GLOW
by Minjung Kim
a thesis submitted to the Faculty of Graduate Studies of
York University in partial fulfilment of the requirements
for the degree of
MASTER OF ARTS
c 2011
Permission has been granted to: a) YORK UNIVERSITY LIBRARIES to lend or sell copies of this dissertation in paper, microform or electronic formats, and b)
LIBRARY AND ARCHIVES CANADA to reproduce,
lend, distribute, or sell copies of this thesis anywhere in
the world in microform, paper or electronic formats and
to authorise or procure the reproduction, loan, distribution or sale of copies of this thesis anywhere in the world
in microform, paper or electronic formats.
The author reserves other publication rights, and neither
the thesis nor extensive extracts for it may be printed or
otherwise reproduced without the author’s written permission.
SHAPE AND LUMINANCE CUES FOR THE VISUAL
PERCEPTION OF GLOW
by Minjung Kim
By virtue of submitting this document electronically, the author certifies that this
is a true electronic equivalent of the copy of the thesis approved by York University
for the award of the degree. No alteration of the content has occurred and if there
are any minor variations in formatting, they are as a result of the conversion to
Adobe Acrobat format (or similar software application).
Examination Committee Members:
1. Dr. Laurie Wilcox
2. Dr. Richard Murray
3. Dr. Keith Schneider
4. Dr. Laurence Harris
Abstract
We investigated the role of three-dimensional shape cues on glow perception, a novel
research area, and tested the hypothesis that real-life glowing objects are bright in
valleys and dark on peaks (bright-means-deep).
Experiment 1. We simulated the bright-means-deep relationship using a novel technique called diffuse countershading. We found that countershaded stimuli appeared
to glow and that higher countershading weights yielded stronger glow.
Experiment 2. We disrupted the bright-means-deep relationship of countershaded
stimuli by inverting or randomizing their depths under stereoscopic viewing. This
did not reduce the perceived degree of glow.
Experiment 3. Participants judged the relative depths of probed locations on countershaded stimuli. These judgments were fairly accurate, suggesting that the visual
system can infer depth from the bright-means-deep pattern.
We find that the bright-means-deep relationship only partially captures the perceptual cues to glow, but that it may be important in physically generating glow.
iv
Acknowledgements
I am deeply grateful for my supervisor and mentor, Dr. Richard Murray, without
whom this thesis could not have been completed. Thank you very much for your
boundless patience, ceaseless understanding, and—most of all—your amazing sense
of humour. Science should be fun.
v
Table of Contents
Abstract
iv
Acknowledgements
v
Table of Contents
vi
List of Figures
x
1 Introduction
1
2 Background
7
2.1
2.2
Lightness-Based Approaches . . . . . . . . . . . . . . . . . . . . . .
7
2.1.1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
2.1.2
The Anchoring Theory of Lightness . . . . . . . . . . . . . .
11
2.1.3
Lightness-Based Glow and Shape . . . . . . . . . . . . . . .
14
Blur-Based Approaches . . . . . . . . . . . . . . . . . . . . . . . . .
15
2.2.1
15
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vi
2.2.2
The Glare Illusion
. . . . . . . . . . . . . . . . . . . . . . .
18
2.2.3
Blur-Based Glow and Shape . . . . . . . . . . . . . . . . . .
22
3 Experiment 1: Can we induce perceived glow by simulating a
bright-means-deep relationship?
24
3.1
Experiment 1A . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
3.1.1
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
3.1.2
Results and Discussion . . . . . . . . . . . . . . . . . . . . .
33
Experiment 1B . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
3.2.1
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
3.2.2
Results and Discussion . . . . . . . . . . . . . . . . . . . . .
49
General Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
3.3.1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
3.3.2
Luminance Histogram Skewness as a Predictor of Glow . . .
58
3.3.3
Final Remarks
59
3.2
3.3
. . . . . . . . . . . . . . . . . . . . . . . . .
4 Experiment 2: Can we reduce perceived glow by destroying an
existing bright-means-deep relationship?
64
4.1
Experiment 2A . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
4.1.1
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
4.1.2
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
vii
4.2
4.3
Experiment 2B . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
4.2.1
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
4.2.2
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
5 Experiment 3: Can we accurately perceive 3D shape from glow
(shape-from-glow)?
83
5.1
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
5.1.1
Participants . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
5.1.2
Stimuli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
5.1.3
Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
5.2
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
5.3
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
6 Conclusion
94
6.1
Diffuse Countershading and Perceived Glow . . . . . . . . . . . . .
94
6.2
Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
6.2.1
Varieties of Glow . . . . . . . . . . . . . . . . . . . . . . . .
97
6.2.2
Glow, Glowability, and Material Properties . . . . . . . . . . 100
6.2.3
Glow and Colour . . . . . . . . . . . . . . . . . . . . . . . . 101
6.2.4
Glow as a Pre-Attentive Feature . . . . . . . . . . . . . . . . 103
viii
References
107
ix
List of Figures
1.1
The Mach bent-card illusion . . . . . . . . . . . . . . . . . . . . . .
3
1.2
The importance of shape for perceived glow . . . . . . . . . . . . .
5
2.1
Depiction of glow in paintings . . . . . . . . . . . . . . . . . . . . .
8
2.2
The anchoring theory of lightness on glow perception . . . . . . . .
12
2.3
Glow in a complex object
. . . . . . . . . . . . . . . . . . . . . . .
15
2.4
Glow from contrast-reversed shadows . . . . . . . . . . . . . . . . .
16
2.5
Example of bloom . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
2.6
Depiction of glow in line drawings . . . . . . . . . . . . . . . . . . .
18
2.7
The glare illusion . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
2.8
Luminance gradients for glow and depth . . . . . . . . . . . . . . .
23
3.1
Example of glow in real life . . . . . . . . . . . . . . . . . . . . . .
25
3.2
Objects under diffuse lighting . . . . . . . . . . . . . . . . . . . . .
26
3.3
Experiment 1A: sample stimuli . . . . . . . . . . . . . . . . . . . .
30
x
3.4
Experiment 1A: response matrix . . . . . . . . . . . . . . . . . . . .
35
3.5
Experiment 1A: Thurstone scaling . . . . . . . . . . . . . . . . . . .
40
3.6
Experiment 1A: Thurstone scaling predictability . . . . . . . . . . .
42
3.7
Experiment 1B, Condition 1: mean luminance control . . . . . . . .
46
3.8
Experiment 1B, Condition 2: maximum Weber contrast control . .
47
3.9
Experiment 1B, Condition 1: mean luminance ratio does not predict
participant response . . . . . . . . . . . . . . . . . . . . . . . . . .
50
3.10 Experiment 1B, Condition 2: contrast ratio does not predict participant response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
3.11 Experiment 1B, Condition 1: countershading weights predict participant response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
3.12 Experiment 1B, Condition 2: countershading weights predict participant response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
3.13 Number of pixels contributing to glow does not decrease with increasing countershading weights . . . . . . . . . . . . . . . . . . . .
57
3.14 Diffuse countershading with low-skew stimulus . . . . . . . . . . . .
60
3.15 Diffuse countershading with medium-skew stimulus . . . . . . . . .
61
3.16 Diffuse countershading with high-skew stimulus . . . . . . . . . . .
62
4.1
71
Experiment 2A: sample stimuli . . . . . . . . . . . . . . . . . . . .
xi
4.2
Experiment 2A: destroying the bright-means-deep relationship does
not reduce perceived glow . . . . . . . . . . . . . . . . . . . . . . .
74
4.3
Experiment 2A: response time analysis . . . . . . . . . . . . . . . .
75
4.4
Experiment 2B: stimuli . . . . . . . . . . . . . . . . . . . . . . . . .
77
4.5
Experiment 2B: results . . . . . . . . . . . . . . . . . . . . . . . . .
80
5.1
Shape-from-shading . . . . . . . . . . . . . . . . . . . . . . . . . . .
84
5.2
Experiment 3: T-junctions can provide strong depth cues . . . . . .
88
5.3
Experiment 3: sample stimulus . . . . . . . . . . . . . . . . . . . .
89
5.4
Experiment 3: participants can make accurate depth judgments . .
91
6.1
Aurora . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
6.2
A ‘glowable’ object . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.3
Glow and saturation . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.4
Asperity scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.5
Glow and colour in natural settings . . . . . . . . . . . . . . . . . . 104
6.6
Glow and colour in art . . . . . . . . . . . . . . . . . . . . . . . . . 105
xii
1
Introduction
What are the perceptual cues that signal the presence of glow in a scene? Glow, or
self-luminosity, is associated with high luminance—and so, we might naı̈vely expect
that the visual system signals glow whenever an extremely luminous surface patch
is present in a scene. This is not the case, however. For example, we can create
illusions of glow in paintings and photographs, where the paint depicting glow is not
the most luminous surface patches in the scene. Therefore, the visual perception of
glow must involve a psychological explanation beyond simple luminance detection.
Previous research on glow confirms above the observation. It has been shown,
for example, that glow percepts in simple stimuli are modulated by the perceived
areas of surface patches, in addition to their physical luminance values (Bonato &
Gilchrist, 1999). Indeed, recent neuroimaging evidence demonstrated that glowing stimuli, compared to non-glowing stimuli with equivalent mean luminance and
contrast levels, generated more activation near colour-processing areas (Leonards,
Troscianko, Lazeyras and Ibanez, 2005). Overall, there exists strong evidence that
1
the human visual system has sophisticated mechanisms for distinguishing glowing
surfaces from non-glowing surfaces of equal luminance.
However, existing research has largely neglected the potentially important role
of three-dimensional shape on perceived glow. This is surprising, because the important role of 3D shape perception in lightness processing has long been recognized
in classic demonstrations such as the Mach bent-card illusion (Fig. 1.1). The card
is set up with the central edge towards the viewer (convex), and with the light
source illuminating the left face such that it has a higher luminance than the right
face. When viewed binocularly, the left and the right faces appear to be of approximately the same lightness, due to lightness constancy. When viewed monocularly,
and we force ourselves to see the card as pointing away from us (concave), the left
face appears to be painted a lighter shade of grey than the right. This is because,
according to the concave interpretation of the bent card, the left face is under the
same illumination as the right face and yet has a higher luminance—and therefore,
the visual system interprets the left face as having a higher reflectance.
For an example of how shape influences glow, consider Figure 1.2. We first
render a randomly generated blobby object and a smooth sphere as Lambertian, or
matte, surfaces (top row; for a description of Lambertian surfaces, see Experiment
3, Introduction). We then take the shading pattern of the sphere and texture-map
it onto the corresponding points of the blob, as though the sphere were shrink2
Figure 1.1: The Mach bent-card illusion (Mach, 1885/1959). For this illusion,
we take a plain, rectangular piece of cardboard and bend it in half. We then
set up the card with the central edge towards the viewer (convex), and with the
light source illuminating the left face. When viewed binocularly, the left and the
right faces appear to be of the same lightness. When viewed monocularly, and we
force ourselves to see the card as pointing away from us (concave), the left face
appears to be painted a darker shade of grey than the right. This phenomenon
shows the influence of shape on lightness. Adapted from Gilchrist (2006).
3
wrapped onto the shape of the blob. The resulting object appears translucent,
and even appears to glow (bottom row). This percept of glow must arise from the
interaction between the 3D shape and luminance, as neither the blob nor the sphere
appears to glow on its own; it is the specific way in which the shape of the blob is
shaded with the luminance of the sphere that causes the glow percept.
In this thesis, we propose and examine what we call the bright-means-deep hypothesis: we hypothesize that, in at least some complex glowing objects, concavities
are bright and convexities are dark (‘bright-means-deep’), and that the visual system is sensitive to the particular bright-means-deep correlation between the shape
and the luminance of an object. If, indeed, this hypothesis is supported, then we
should find that either mimicking or disrupting the shape-luminance relationship
of an object will either increase or decrease the perception of glow. In addition,
we should find that the visual system is able to make depth discriminations using
glowing objects by assuming that brighter points are placed deeper than darker
points.
We begin by reviewing previous studies on glow, then describe three experiments
that examined the bright-means-deep hypothesis. In the first experiment, we asked
if glow can be induced in complex objects by manipulating the 3D shape and
luminance profiles of objects. In the second experiment, we examined whether
interfering with the bright-means-deep relationship between shape and luminance
4
+
shape
luminance
=
Figure 1.2: The importance of shape for perceived glow. Top row. The blob
and the sphere are both Lambertian. Bottom row. Texture-mapping the shading
pattern of the sphere onto the shape of the blob drastically changes the perceived
material of the blob; the blob now appears to glow. The illusion is particularly
strong when viewed on a monitor rather than on paper, as LCDs have larger
dynamic range than ink on paper.
5
can reduce the perceived degree of glow. In the final experiment, we examined
whether the visual system is able to recover reliable shape information from glowing
objects, even though their shape and luminance relationships are very different from
those of non-glowing objects.
Together, our experiments demonstrate that, to perceive glow, the visual system
relies on the ways in which the shape and luminance of an object interact—but that
this interaction is only partially captured by the bright-means-deep relationship.
Our experiments identify an important research area, and contribute some of the
first investigations on 3D shape and glow.
6
2
Background
Although the important role of perceived depth on perceived surface lightness has
been examined extensively (e.g., Mach, 1885/1959, Fig. 1.1; Kardos, 1934, and
Koffka, 1915, in Gilchrist, 2006, p.53), the influence of perceived depth on glow has
received limited attention. In this section, we review current theories of glow, and
suggest they can be classified as one of two broad categories that we call lightnessbased and blur-based approaches.
2.1
2.1.1
Lightness-Based Approaches
Overview
Lightness-based approaches posit that lightness constancy is a critical factor for
glow perception, and that a surface patch appears to glow when its luminance
exceeds an illumination-dependent luminance threshold. Even a moderately luminous surface patch may appear to glow in dim light; however, an equally luminous
surface patch may not appear to glow in bright light.
7
Contrast-based accounts, as in Arnheim (1974), are examples of lightness-based
approaches. Arnheim (1974) presented a set of observations on factors that strengthen
perceived glow in images, remarking that paintings with strong apparent glow generally depict dark scenes accented with relatively bright paint (e.g., Fig. 2.1). This
work, however, only considered 2D image-based properties (i.e., pixel luminances),
without accounting for possible role of 3D shape.
Figure 2.1: In art, glow is sometimes depicted by contrasting bright patches
with the overall low illumination (Rembrandt van Rijn, 1638).
Ullman (1976) experimentally demonstrated that a high-contrast scene does
not necessarily yield a perception of glow. He proposed a new model of glow detection based on intensity gradient ratios, which were used to approximate reflectance
ratios. These terms are explained below.
8
Suppose that we have a pair of non-glowing surface patches, P0 and P1 . The
reflectance at these patches, R0 and R1 , is a function of surface pigmentation,
and describes the proportion of incident light that is reflected from the surface
patches. Under identical lighting conditions, a surface patch with high reflectance
appears lighter than one with a low reflectance. Assuming that illumination is
approximately uniform with a value of I, and also that P0 and P1 are facing the
light source, the luminance at these points are (Horn, 1986)
L0 = I R 0
(2.1)
L1 = I R 1
(2.2)
where L0 and L1 correspond to P0 and P1 , respectively. Moreover,
R0
L0
=
L1
R1
For two non-glowing patches, we expect that the luminance ratio,
to the reflectance ratio,
R0
.
R1
(2.3)
L0
,
L1
is equivalent
While obtaining R0 and R1 is extremely difficult—a
general solution to this problem has yet to be found in either human or computer
vision research—Ullman (1976) proposed that the reflectance ratio may be approximated by the intensity gradient ratio,
S0
,
S1
where the intensity gradients are the
first-order derivatives of luminance at P0 and P1 . Then,
L0
S0
=
L1
S1
9
(2.4)
L0 − L1
S0
=0
S1
(2.5)
=G
Equation 2.5 is called the Source-, or S-, operator, and is expected to return G = 0
for two non-glowing surface patches. Suppose now that P0 is a glowing surface
patch whereas P1 is a non-glowing surface patch. The luminance at P0 is
L0 = I R 0 + g
where g represents the luminance contribution from glow, g > 0. Then,
S0
L0 − L1
=g
S1
(2.6)
(2.7)
=G
Therefore, if G = 0, both surface patches are non-glowing, and if G = g, g > 0,
P0 is glowing. In practice, G may not only have to be positive but also exceed a
pre-defined luminance threshold, as noisy input luminances may lead to spurious
G > 0. However, Ullman did not specify how the luminance threshold should be
chosen, beyond that it should illumination-dependent.
The strength of Ullman’s method is that it only requires simple arithmetic operations on input luminances (subtraction and division), and that it is also specific
enough to be implemented on a computer vision system. Indeed, Ullman reported
that the S-operator was effective in detecting glow in simple, Mondrian-type stimuli
consisting of grey square patches on a flat plane.
10
However, it is not clear how the S-operator applies to more complex scenes with
3D shapes. Suppose, e.g., that some of the surface patches were randomly reoriented such that they no longer faced the light source. In this situation, luminance
variations from shading and from reflectance would be conflated, and S-operator
would need to be modified to account for the role of 3D shape.
2.1.2
The Anchoring Theory of Lightness
Gilchrist and Bonato published an extensive series of studies (Bonato & Gilchrist,
1994, 1999; Gilchrist & Bonato, 1995; Gilchrist et al., 1999) framed in terms of
Gilchrist’s anchoring theory of lightness perception (Gilchrist, 2006; Gilchrist et al.,
1999, Chapters 9-11). According to the anchoring theory, every scene has some
reference luminance value that serves as the anchor; all other luminances are compared to this anchor value for lightness estimation. Glow is perceived if a surface
patch exceeds the luminance of the anchor by a factor of 1.7 (Bonato & Gilchrist,
1999), and a perceptually fluorescent, or fluorent (Evans, 1959), white is perceived
if a surface patch is more luminous than the anchor but does not exceed the 1.7
threshold.
To a first approximation, the anchor is the highest luminance in the scene.
However, its precise value depends on the perceived area of the brightest surface
patch relative to other surface patches (Bonato & Gilchrist, 1999; Li & Gilchrist,
11
Figure 2.2: As the area of the dark patch increases with respect to the area of
the light patch, the light patch begins to glow. The numbers below the discs, as
well as the labels ‘A’ and ‘B’, were added for this thesis, and were not part of
the original figure. Adapted from Li and Gilchrist (1999).
12
1999). For example, consider a Ganzfeld composed of two homogeneous regions A
and B such that A is five times as luminous as B. When A occupies at least 50% of
the visual field (Fig. 2.2, discs 1 through 3), white is anchored to A and B appears
correspondingly grey. Suppose that we begin increasing B’s area (Fig. 2.2, discs 4
and 5), and continue until B occupies a larger region of space than A. As B’s area
increases, it appears brighter and begins to appear white; meanwhile, A begins to
generate a percept beyond white (Li & Gilchrist, 1999), and when finally A appears
at least 1.7 times as bright as white, A begins to glow (Bonato & Gilchrist, 1999).
The anchoring theory of lightness incorporates an important role of scene structure, whereby shape and depth cues segment a scene into regions of similar illumination, or frameworks (Gilchrist et al., 1999). For example, the adjacent faces of
a cube may belong to different frameworks, as light may illuminate one face but
not the others. While the role of frameworks with respect to lightness constancy in
general has been extensively studied, however, it is unclear as to how the anchoring
theory would explain the role of shape and depth in complex glowing objects. Thus
far, studies on glow have been limited to easily segmented stimuli, such as rectangular surface patches (Bonato & Gilchrist, 1994, 1999), centre-surround displays
(Bonato & Gilchrist, 1999; Gilchrist & Bonato, 1995), Mondrian-patterned boxes
(Bonato & Gilchrist, 1994, 1999), and Ganzfelds (Li & Gilchrist, 1999).
In contrast, consider Figure 2.3, which is a photograph of a translucent, backlit
13
Venus de Milo. Does the entire statue belong to a single framework, or should
it be segmented into multiple frameworks? On one hand, Figure 2.3 appears to
be lit from a single source, so perhaps it belongs to a single framework. On the
other hand, some parts of the statue appear to glow more strongly than others,
implying different regions of illumination, so perhaps it should be segmented into
multiple frameworks. If so, should each ridge or valley be considered to be a
separate framework? Anchoring theory has not yet addressed these problems that
are associated with glow in complex shapes.
2.1.3
Lightness-Based Glow and Shape
In a theoretical paper, Langer (1999) posited that the visual system may perceive
glow when surface patches in a concavity appear to be brighter than its surroundings. Consider, for example, Figure 2.4: the top figure depicts a scene composed
of white blocks, arranged such that an area is cast in shadow. The shadowed area
is concave with respect to the rest of the scene geometry, and when the image is
contrast-reversed, as in the bottom figure, the concavity appears to glow. Langer
noted that, in the contrast-reversed image, the pattern of brightness around the
concavity mimics the type of lighting pattern that would be expected if a real light
source were placed within the concavity. However, Langer did not explore in detail
the perceptual aspects of this apparent glow in concavities.
14
Figure 2.3: Glow in a complex object. Here, glow is perceived to emanate from
within the statue of Venus de Milo. Does the statue belong to a single framework,
or to multiple? If multiple, how should it be segmented? Chen, Lensch, Fuchs
and Seidel (2007).
2.2
2.2.1
Blur-Based Approaches
Overview
Blur-based approaches rely on bloom, which is the halo of light surrounding some
glowing objects (Fig. 2.5). Although the precise cause of bloom is under debate,
most researchers agree that it is likely due to the scattering of light at the cornea,
the lens, and the retina (Spencer, Shirley, Zimmerman & Greenberg, 1995); this
15
Figure 2.4: Glow from contrast-reversing shadows. Top. Some blocks are
arranged such that an area is cast in shadow. Bottom. Contrast-reversed version
of the top image. The shadowed region in the top image appears to glow in the
bottom image. Adapted from Langer (1999).
scatter can be characterized by a point-spread function (PSF), and can be thought
of as a blurring of the input image such that even an infinitesimally small point
light source projects onto the retina as a 2D shape such as a disc.
The human visual system seems to recognize bloom as a cue for detecting light
sources. Artists are recommended, for example, to draw halo-like rays to indicate
radiance (Beckman, Nilsson & Paulsson, 1994; Fig. 2.6). Indeed, studies have
16
Figure 2.5: A real-life example of bloom. All imperfect imaging systems are
prone to bloom, including camera lenses. Here, bloom is the most apparent
around the edges of the stained glass windows (Pemberton, 2006).
found that filtering images with a blurring kernel—either using a physiologically
accurate PSF that characterizes the human eye (Spencer et al., 1995), or some
approximation thereof (Yoshida, Ihrke, Mantiuk & Seidel, 2008)—can enhance the
perceived brightness of images by 20% to 35% (Yoshida et al., 2008). Yoshida et al.
(2008) report, for example, that convolving the input image with a Gaussian kernel
is almost as effective as a physiologically-based PSF in inducing glow, and is computationally less intensive as the Gaussian kernel is spatially separable. However,
17
the authors also note that the PSF is less likely to distort the size and shape of the
light source than the Gaussian.
Figure 2.6: An example of glow depicted in graphic art. Although (a) is a simple
black-and-white line drawing with only a few rays for bloom, the radiance of the
candle is still successfully conveyed. In comparison, (c) appears quite dull without
bloom. Note, also, that simply having rays present is not sufficient; attaching
the halo to the flame, as in (b), fails to trigger the psychological recognition of
glow. Adapted from Beckman et al. (1994).
2.2.2
The Glare Illusion
A related effect is the glare illusion (Zavagno, 1999, Zavagno & Caputo, 2001,
Zavagno, Annan & Caputo, 2004, Zavagno & Caputo, 2005; similar to the ‘sun
18
Figure 2.7: The glare illusion. Top row. Luminance gradients induce the
appearance of glow, whereas solid squares do not. Bottom row. The glare illusion
persists even when the gradients are placed on a grey background, yielding a
percept of ‘grey glow.’ According to some lightness-based approaches to glow,
glow requires that the luminance of the glowing patch exceeds the luminance of
white; the existence of grey glow provides a strong counterexample. Adapted
from Zavagno and Caputo (2001; 2005).
19
illusion’ reported by Kennedy, 1976). To create this illusion, four luminance gradients, which vary smoothly from black to white, are arranged around a central
white square such that the white edges of the luminance gradients are adjacent to
the central square (Zavagno & Caputo, 2001, Fig. 2.7, top left). The luminance
gradients greatly enhance the perceived brightness of the central square, such that
the central square appears to glow; this illusory brightness enhancement is stronger
than in other perceptually similar illusions, such as the brightness enhancement in
the Kanizsa triangle (Zavagno, 1999). Zavagno and Caputo (2001) explained the
glare illusion in terms of bloom, emphasizing the role of blurry edges on 2D images.
This model, therefore, is also structure-blind, addressing only luminance variations
on the 2D plane without any contribution of shape or depth.
The glare illusion provides compelling evidence that the anchoring theory of
lightness does not present a complete account of glow. For example, they show
that a perceptually grey square—which is less luminous than white—can appear
to glow (Zavagno, 1999; Zavagno & Caputo, 2001; Fig. 2.7, bottom row), and
that luminances eliciting percepts of glow can be lower than those eliciting the
perception of white. These findings demonstrate that at least some perception of
glow is independent from the anchoring of white (Zavagno et al., 2004; Zavagno &
Caputo, 2005).
It is therefore interesting that Ullman (1976) predicted, but did not expound
20
upon, the possibility of grey glow. Consider, again, Equation 2.5:
S0
G = L0 − L1
S1
(2.8)
The model predicts glow percepts at pixels where G is positive and above some
threshold, which occurs when L0 is sufficiently larger than L1 SS01 . This means
that, even if L0 is small on an absolute scale, it should be possible to perceive glow
if L0 sufficiently dwarfs L1 SS10 —i.e., glow is possible even when an object is less
bright than its surroundings.
In the glare illusion (Fig. 2.7), S0 is the intensity gradient of the central square;
since the square is constant in luminance, S0 is equal to zero. Similarly, S1 is the
intensity gradient of the luminance gradients on the side; S1 has some real, non-zero
value. Therefore, L1 SS01 is always equal to zero for any stimulus with a luminance
gradient, and therefore will yield a glow percept for even small values of L0 —i.e.,
grey glow.
Beyond Ullman’s (1976) prediction, the disparity between the lightness-based
approaches and the blur-based approaches has not been resolved. One possible
explanation for this apparent contradiction is that glow processing is multi-faceted,
and that the two streams of research are examining different types of glow. This
leaves open the possibility that there exist completely unexamined forms of glow,
and further supports the notion that the perception of glow is an area ripe for
investigation.
21
2.2.3
Blur-Based Glow and Shape
Leonards, Benton and Scott-Samuel (2008) used the glare illusion (Fig. 2.7) to
examine the relationship between perceived depth and glow. This work was motivated by the observation that luminance gradients may be interpreted as shading
patterns (Leonards et al., 2008); for example, Fig. 2.8 (left) may appear to be a
cross receding in depth.
Luminance gradients were overlaid on backgrounds of varying luminances (Fig.
2.8). Participants judged whether the luminance gradients appeared to glow (glow
judgment) or appeared to be in front or behind the background (depth judgment).
In general, Leonards et al. found that the threshold background luminance required
to elicit glow percepts was lower than the threshold for depth percepts, and concluded that glow and depth are likely processed by separate mechanisms. However,
the researchers did not identify the precise mechanisms, and—more importantly—
did not investigate whether perceived shape may actually contribute to the percept
of glow.
22
Figure 2.8: Luminance gradients for glow and depth. Participants made judgments on whether the luminance gradients appeared to glow (glow judgment)
or appeared to be in front or behind the background (depth judgment). The
arrowed annotations are part of the original figure, and can be ignored for this
thesis. Adapted from Leonards et al. (2008).
23
3
Experiment 1: Can we induce perceived glow
by simulating a bright-means-deep relationship?
How might 3D shape influence glow perception? Consider a translucent object with
an internal light source. Assuming constant material thickness, the most luminous
surface patches of this object are the most closely located to the internal source of
glow, and hence, are located in valleys; conversely, the darkest surface patches are
located the furthest away from the light source, and are found on peaks. That is,
the deeper the surface patch, the brighter it is: brightness and depth are positively
correlated in an approximate ‘bright-means-deep’ relationship (see, e.g., Fig. 2.3,
Fig. 3.1).
Note that the bright-means-deep relationship is the inverse of the dark-meansdeep relationship found between depth and brightness for non-glowing objects under
diffuse light (Langer & Bülthoff, 2000, Fig. 3.2). Under diffuse lighting conditions
(e.g., on a cloudy day), light is received more or less uniformly from all directions,
and therefore, the luminance of a surface patch is determined by how much of the
24
Figure 3.1: A real-life example of glow. Regions with bright valleys appear to
glow, whereas regions with dark valleys do not. Joseph and O’Connell (2010).
light source is visible from the patch: for example, a surface patch on a peak is
bright, as it is exposed to the whole sky, and a surface patch in a valley is dark,
since much of the sky is occluded. In computer graphics, this dark-means-deep
shading pattern under purely diffuse lighting is approximated with a technique
called ambient occlusion, because diffuse (ambient) light is prevented from reaching
surface patches in valleys due to occlusion (Zhukov, Iones & Kronin, 1998).
In our first experiment, we induced the percept of glow by inverting the darkmeans-deep relationship between brightness and depth in diffusely illuminated ob-
25
Figure 3.2: Langer and Bülthoff (2000) analyzed the shading patterns found
on diffusely lit objects, and found that they roughly follow a ‘dark-means-deep’
pattern: surface patches on peaks tend to be bright, and those in valleys tend
to be dark. The arrowed annotations are from the original figure, and can be
ignored for this thesis. Adapted from Langer and Bülthoff (2000).
jects, thus creating the bright-means-deep relationship found in some glowing objects. We call this technique diffuse countershading, as the technique involves modulating the luminance of an image in a manner opposite to the shading pattern of
a diffusely illuminated object. Langer (1999) also suggested that a bright-meansdeep relationship may be characteristic of glowing objects, but did not explore
the relevance of the bright-means-deep relationship to the perception of glow in
psychophysical experiments.
26
The full description of our stimulus generation can be found under Stimuli, below. Briefly, we generated images with diffuse countershading as follows. We rendered objects with complex, wavy surfaces under purely direct and purely diffuse
lighting, and then contrast-reversed the diffuse image to obtain the countershaded
image (Fig. 3.3). Akin to a photographic negative, the countershaded image preserves shape information, only affecting the relative values of the pixel luminance.
The final stimulus was a weighted sum of the direct, the diffuse, and the countershaded components; we call this the (diffusely) countershaded image (Fig. 3.3).
We hypothesized that images with large countershaded components will appear
to glow, as the diffusely countershaded component will induce the bright-meansdeep relationship between brightness and depth that is characteristic of some glowing objects. We evaluated two hypotheses:
Hypothesis 1.1: Diffusely countershaded images can appear to glow.
Hypothesis 1.2: The perceived degree of glow increases with increasing amounts
of diffuse countershading.
27
3.1
Experiment 1A
3.1.1
3.1.1.1
Methods
Participants.
Six participants between the ages of 18 and 40 volunteered for the study; five were
naı̈ve to the purpose of the experiment, and one was the author (MK). One of the
naı̈ve participants was stereoblind (MS), but was not excluded from the study as the
experiment did not examine stereoscopic depth cues. Otherwise, all participants
had normal or corrected-to-normal vision.
3.1.1.2
Stimuli.
Object meshes were generated as follows. A torus can be parameterized as
x(θ, φ) = (R + r cos(φ)) cos(θ)
(3.1)
y(θ, φ) = (R + r cos(φ)) sin(θ)
(3.2)
z(θ, φ) = r sin(φ)
(3.3)
Here, R is the major radius, defined as the distance from the centre of the whole
torus to a point at the centre of the tube, and r is the minor radius, defined as the
radius of a cross-section of the tube. θ and φ are angles ranging from 0◦ to 360◦ .
We made the torus bumpy by modulating its minor radius with low-pass noise.
28
The bumpy torus was parameterized as
x(θ, φ) = (R + (1 + n(θ, φ)) r cos(φ)) cos(θ)
(3.4)
y(θ, φ) = (R + (1 + n(θ, φ)) r cos(φ)) sin(θ)
(3.5)
z(θ, φ) = (1 + n(θ, φ)) r sin(φ)
(3.6)
r and R had a ratio of 1:2. Here, n(θ, φ) is the modulating noise function. It is 2D,
low-pass-filtered white noise with a sharp upper cut-off frequency of 20 cycles over
the range [0◦ , 360◦ ] and a standard deviation of 0.10. We generated a wire mesh
torus by obtaining 550 samples from Equations 3.4, 3.5, and 3.6, at θ and φ evenly
distributed between 0◦ and 360◦ .
The meshes were used to render shapes with a medium grey Lambertian surface (50% reflectance) on a completely black background in RADIANCE (Ward &
Shakespeare, 1998; Fig. 3.3). 550 different samples of these randomly generated
object shapes were used in Experiment 1A.
Objects were rendered under purely direct lighting, and separately under purely
diffuse lighting. The purely direct and purely diffusely lit stimuli were used to
generate the final stimulus, but were not themselves seen by participants during
the experiment. For the directly lit images, the light source was simulated as an
infinitely distant disk subtending 1◦ of the sky. The disk was randomly positioned
29
Figure 3.3: Glow by diffuse countershading. The glow stimulus is a weighted
sum of the direct, diffuse, and countershaded images. Top row. The object
is rendered under purely direct and purely diffuse lighting. The purely diffuse
component is contrast-reversed to generate the countershaded image. Bottom
three rows. The stimulus is generated at multiple countershading weights ranging
from 0.0 to 10.0.
30
on the arc along 60◦ slant and ±15◦ tilt, where 0◦ slant points towards the camera
along the optical axis and tilt is coded so that 0◦ is overhead. For the diffusely lit
images, the light source was simulated as a uniformly lit sphere covering the whole
sky except for the small portion visible behind the object. The direct and diffuse
light source luminances were chosen so that, under either light source alone, a white
surface patch would have a maximum luminance of 200 cd/m2 .
After rendering the directly lit and the diffusely lit stimuli, the countershaded
stimuli were generated as follows. First, we obtained the countershaded image:
C = max(F ) − F
(3.7)
where F is the luminance of the diffuse image and max(F ) is the maximum luminance present in the diffuse image. C is the countershaded luminance, with
the brightest pixel of F mapped to zero, and the darkest pixel of F mapped to
max(F ) − min(F ). The final stimulus, S, was a weighted sum of the direct, the
diffuse, and the countershaded images, such that
S = D + 0.2F + wC
(3.8)
where D, F , and C were the directly lit image, the diffusely lit image, and the
countershaded image, respectively. D + 0.2F was a rendering of the torus under a
typical lighting condition consisting of a point and an ambient light source (Phong,
1975; Shreiner & Khronos Group, 2009). The constant w was the countershading
31
weight, and ranged from 0.0 to 10.0 in steps of 1.0. This can be conceptualized
as starting out with a Lambertian object (w = 0.0), and gradually increasing the
contribution of countershaded component. The average image-wise contribution of
the countershaded component can be calculated as follows:
contribution =
w
1.2 + w
(3.9)
So, at a weight of 1.0, the countershaded image contributed almost 50% of the
luminance, and at 5.0 and higher, more than 80% of the luminance.
The final rendered images were 800×800 pixels, and were viewed from a distance
of 1.67 m. The images subtended 6.71◦ × 6.71◦ of visual angle. The monitor refresh
rate was 60 Hz, and the monitor resolution was 1920×1200 pixels, where each pixel
was 0.00026 cm × 0.00026 cm. The colour look-up table of the LCD monitor was
linearized prior to the experiment.
3.1.1.3
Procedure.
Before the experiment began, participants were instructed on the task. To describe
glow, the following phrases were used: “is radiant,” “is emitting light,” or “is not
just bright because of an external light source.”
In each trial, participants were simultaneously presented with a pair of randomly
selected torus shapes with different diffuse countershading weights. With a key
press, participants indicated the object that appeared to glow more strongly. The
32
key press ended the trial, and the subsequent trial began immediately, without any
pause or feedback.
Since we tested 11 countershading weights, there were 11 ×
10
2
= 55 possible
pairwise comparisons. We ran 10 trials per pair, for a total of 550 trials for the
entire experiment. To minimize fatigue, the experiment was divided into five blocks.
We employed a randomized design, displaying all possible pairwise comparisons in
the same block.
3.1.2
3.1.2.1
Results and Discussion
Glow Response Probabilities.
For each of the 55 possible pairwise comparisons, we calculated the proportion of
trials in which the participants chose the stimulus with the higher diffuse countershading weight w, thus generating a response matrix for each participant (Fig. 3.4).
The response matrix is arranged such that diffuse countershading weights increase
from top to bottom, and from left to right.
The pale yellow cells correspond to the perfect response of always choosing the
stimulus with the higher w, whereas the medium green cells correspond to 50%
chance. Rates lower than chance are depicted with deep green. The main diagonal
corresponds to same-weight comparison trials; although we did not have any trials
33
with same-weight comparisons, we expect that comparing two stimuli with identical
w would only lead to chance-level responses. Note also that the matrix is symmetric
across the main diagonal, as comparing stimuli with w = 3.0 and w = 5.0, for
example, is equivalent to comparing stimuli with w = 5.0 and w = 3.0.
Our main finding is that participants were more likely to choose the stimulus
with higher countershading weight when comparing stimuli pairs with very different
countershading weights. All six participants were more likely to choose stimuli with
w > 0.0 over stimuli with w = 0.0, as can be seen by the largely pale and yellow
leftmost column of the response matrix. By contrast, participants were almost as
likely to choose either the higher- or the lower-weight stimulus when stimuli with
similar w weights were compared. This pattern is tested statistically in the next
section.
3.1.2.2
Thurstone Scaling Analysis.
For each pairs of countershading weights, we analyzed the participant responses using Thurstone scaling analysis for data with binary preferences, which is a method
of constructing scales for psychological quantities (Thurstone, 1927a,b). This technique allowed us to examine how the countershading weights corresponded to psychological units of glow, measured as a psychological distance in a signal detectionlike framework.
34
100
90
80
proportion correct
70
60
50
40
0
20
10
2
3
4
5
6
7
8
9
10 0
1
2
3
4
5
6
7
8
9
10
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
MK
VM
10
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
30
1
0
MD
MS
10
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
0
10
TP
0
AC
1
2
3
4
5
6
7
8
9
10 0
1
10
2
3
4
5
6
7
8
9
10
Figure 3.4: Response matrices from Experiment 1A. For each participant, 11
diffuse countershading weights, ranging from 0.0 to 10.0 in steps of 1.0, were
tested. Participant MK was the author, and participant MS was stereoblind.
35
Suppose that we have a psychological scale of glow, ranging from zero glow
to extremely strong glow. Percepts on this scale are probabilistically generated
and can be represented as normal random variables. This means that, on average,
we expect a stimulus to generate a specific level of perceived glow, but that on
a trial-to-trial basis, the same stimulus may yield a range of different levels of
glow. Furthermore, the distance between any pair of glow percepts is measured
in standard deviations (SD), following from the assumption that the percepts are
normally distributed. If glow percepts are separated by a small distance (e.g., 0.0 or
1.0 SD), then participants are about equally likely to choose either stimulus. If glow
percepts are separated by a large distance (e.g., 3.0 or 4.0 SD), then participants
are much more likely to choose one of the two stimuli.
We can formalize this framework as follows. Let i and j be independent normal
random variables representing a pair of glow stimuli I and J, such that
i ∼ N (µi , σi 2 )
(3.10)
j ∼ N (µj , σj 2 )
(3.11)
where µ is the mean and σ 2 is the variance of the normal distribution. Then, the
discriminability between i and j can be treated as a single random variable dij ,
dij ∼ N (µi − µj , σi 2 + σj 2 )
(3.12)
Following convention (Thurstone, 1927a,b), we assume that glow percepts are equally
36
variable (σi = σj = 1). Therefore,
dij ∼ N (µi − µj , 2)
(3.13)
Using Thurstone’s Law of Comparative Judgment (Thurstone, 1927a,b), we convert
response probabilities into discriminability values using Φ−1 (x), the inverse normal
cumulative distribution function:
dij = Φ−1(pij )
p
σi 2 + σj 2
√
= Φ (pij ) 2
(3.14)
−1
where pij is proportion of trials in which participants choose i in favour of j, obtained from response matrices (Fig. 3.4).
Since we obtained 55 possible pairs of countershading weight combinations, and
a response probability for each pair, we have 55 different discriminability estimates.
By contrast, the number of parameters in our Thurstone model is much smaller.
We have 11 glow parameters to model, but use one degree of freedom by fixing
the w = 0.0 percept as the zero point of the glow scale (Thurstone, 1927b). With
55 estimates and 10 unknowns, we have an overconstrained system, meaning that
estimates could be inconsistent with each other—e.g., dik could yield a different
value depending on whether it was calculated directly from pik or from dij + djk .
Therefore, we obtained the final discriminability values by choosing the estimates
that maximized the log-likelihood.
37
The maximum-likelihood fit was determined as follows. Let wi , i = 1, 2, ...11,
represent the 11 countershading weights, and let gi represent the 11 internal glow
levels corresponding to each wi . The probability of choosing a stimulus with countershading wi over wj can be obtained by rearranging Equation 3.14,
gi − gj
√
pij = Φ
2
dij
=Φ √
2
(3.15)
where dij = gi −gj is the discriminability between two stimuli and Φ(x) is the normal
cumulative distribution function. The maximum-likelihood estimates of the glow
parameters, gi , were obtained by maximizing the following likelihood function:
11 Y
11
Y
gi − gj
√
L=
Bin kij , nij , Φ
2
i=1 j=1
(3.16)
Or, equivalently, the log-likelihood function:
log(L) =
11 X
11
X
i=1
gi − gj
√
log Bin kij , nij , Φ
2
j=1
(3.17)
Here, Bin(k, n, p) is the binomial probability mass function, which returns the
probability that a Bernoulli random variable with success probability p yields k
successes out of n trials. With respect to our model, nij represents the number of
trials on which participants compared stimuli with countershading weights wi and
wj , ordered such that wi > wj , and kij represents the number of trials on which
participants chose the higher-weight stimulus. The origin of the glow scale was fixed
to g = 0.0, corresponding to the stimulus with countershading weight w = 0.0.
38
The maximum log-likelihood fit—or equivalently, the minimum negative loglikelihood fit—was obtained from the f minsearch function in MATLAB 2009
(Mathworks, 2009). To avoid local minima, we repeated the function minimization 20 times, starting from different random initial estimates each time, and chose
the glow values gi with the overall best log-likelihood estimate.
The results of this analysis for all six subjects can be found in Figure 3.5.
On the x-axis, we show the countershading weights. On the y-axis, we show the
psychological strength of glow (gi ) in standard deviation units. If countershading
had no effect on perceived glow whatsoever, the graphed line would be constant at
0.0 SD; this is not the case. Rather, we see that countershading induced a percept of
glow in all participants, and increasing the countershading weight led to an increase
in the strength of perceived glow (Fig. 3.5). Indeed, we found an extremely strong
effect of countershading: for most of the participants, w = 5.0 was enough to induce
a glow of 3.0 SD or higher, or equivalently, to generate a glow percept 98% of the
time. Note that the strength of perceived glow appears to increase rapidly at low
countershading weights (w = 0.0 to w = 4.0), then plateaus by w = 6.0 or w = 7.0
for all participants. This is probably because the effectiveness of countershading
reaches a point of diminishing return for purely physical reasons: using Equation
3.9, we see that when we increase the weight from 1.0 to 2.0, the contribution of
the countershaded image increases by 17%, but that when we increase the weight
39
from 9.0 to 10.0, the contribution only increases by 1%.
25
Participants
MK
MS
VM
TP
MD
AC
perceived glow (SD)
20
AC
15
TP
10
VM
MK
MD
5
MS
0
0
1
2
3
4
5
6
7
8
9
10
countershading weights (w)
Figure 3.5: Thurstone scaling analysis from Experiment 1A. The analysis revealed that diffuse countershading yields extremely strong glow percepts. On the
x-axis, we have the countershading weights. On the y-axis, we have the glow responses, in standard deviation (SD) units. The dotted line at 0.0 SD represents
chance response. For most of the participants, w = 5.0 was enough to induce a
glow of 3.0 SD or higher—i.e., when provided with a pair of stimuli, one with
w = 5.0 and one with 0.0, participants choose the higher-weight stimulus 98% of
the time. Participant MK was the author, and participant MS was stereoblind.
40
We evaluated the goodness of the model fit. For all of the 55 model-predicted
discriminabilities, dij , we obtained the model-predicted response probabilities, p̂ij
(Eq. 3.15). We calculated the Pearson correlation between the model-predicted
response probabilities p̂ij and the actual response probabilities pij ; the results are
summarized in (Fig. 3.6). For all six participants, we found that the modelpredicted probabilities are very good predictors of the actual probabilities, with
correlation coefficients ranging from ρ(53) = 0.81, p < .0001, to ρ(53) = 0.95, p <
.0001 (Fig. 3.6).
Overall, the results of Experiment 1A may be summarized as follows:
Result 1.1: Hypothesis 1.1 was supported. We have found that adding a diffusely
countershaded component to the image of an otherwise ordinarily lit object can
induce a percept of glow.
Result 1.2: Hypothesis 1.2 was supported. Increasing the weight of the countershading component increased the perceived strength of glow.
3.2
Experiment 1B
Diffuse countershading can change the mean luminance and contrast of the stimulus.
This raises the possibility that countershading may not induce perceived glow via
the bright-means-deep relationship, but simply by manipulating low-level image
properties like luminance and contrast. In Experiment 1B, we deliberately varied
41
0.0
1.0
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
VM
ρ = 0.95
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
1.0
actual response probability
0.2
MK
ρ = 0.84
MD
ρ = 0.87
1.0
MS
ρ = 0.81
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
1.0
TP
ρ = 0.90
1.0
AC
ρ = 0.88
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
0.0
model-predicted response probability
Figure 3.6: Evaluation of model-fit glow strengths from Experiment 1A. For all
six participants, the model-fit glow strengths accurately predicted the obtained
responses, with correlation coefficients ranging from ρ = 0.81 to ρ = 0.95. For
all participants, p < .0001. Participant MK was the author, and participant MS
was stereoblind.
42
stimulus luminance and contrast to test this possibility.
3.2.1
3.2.1.1
Methods
Participants.
Six participants between the ages of 18 and 40 volunteered for the study; five
were naı̈ve to the purpose of the experiment, and one was the author (MK). All
had normal or corrected-to-normal vision. Of the naı̈ve participants, only AC had
previously participated in Experiment 1A. Participants CP later participated in
Experiment 2.
3.2.1.2
Stimuli.
General. Randomly generated objects were rendered under purely direct and purely
diffuse lighting using the same RADIANCE set-up as in Experiment 1A. In this
experiment, we used countershaded stimuli with countershading weight w = 5.0
and non-countershaded stimuli with w = 0.0. These values were selected because,
in Experiment 1A, participants almost always perceived the w = 5.0 stimulus as
glowing more than the w = 0.0 stimulus (Fig. 3.5).
The equipment set-up was identical to that of Experiment 1A, except that the
monitor was placed 1.46 m from the participant. To maintain approximately the
43
same stimulus size, the stimuli were reduced to 512 × 512 pixels, or 5.16◦ × 5.16◦ .
Condition 1. Mean luminance control. In this condition, we randomized mean
luminance and held contrast constant, to examine whether luminance variations
influenced on participants’ glow judgments. The mean stimulus luminances were
set to one of five levels, ranging from from a minimum of 25.0 cd/m2 to a maximum
of 100.0 cd/m2 , increasing by a factor of
√
2 per step. We chose the mean luminances
on a geometric scale, rather than on a linear scale, in order to ensure that the five
luminance levels were roughly equally discriminable (Wallach, 1963).
The maximum Weber contrast of each stimulus in the luminance control condition was set to a constant value. The Weber contrast, c, of a pixel located at (i, j)
is defined as follows:
c=
L − L̄
L̄
(3.18)
Here, L is the luminance of the pixel at (i, j), and L̄ is the mean luminance of the
torus; pixels belonging to the background were excluded from L̄ calculations. The
Weber contrast of the pixel, c, may be either positive or negative, depending on
whether the pixel luminance higher or lower than the image mean. We took the
maximum Weber contrast of an image to be
cmax = max(|c|)
(3.19)
We calculated the average maximum Weber contrasts of non-countershaded
44
stimuli (cc = 1.71) and countershaded stimuli with w = 5.0 (cs = 2.45). All stimuli
in the mean luminance condition were scaled to have a maximum Weber contrast
at the geometric mean of the above two values (c =
p
(cc cs ) = 2.05).
Sample stimuli, at each of the five levels, are shown in Figure 3.7.
Condition 2. Maximum contrast control. In this condition, we randomized maximum Weber contrast and held luminance constant, to examine whether contrast
had a large effect on participants’ glow judgments. The maximum contrasts were
scaled to one of five levels, ranging from a minimum contrast of 0.85 to a maximum
of 3.42, with the middle level set to cc = 1.71. As with Condition 1, the levels
were chosen on a geometric scale, increasing by a factor of
√
2 per step. The mean
luminance of each stimulus in the contrast control condition was set to 100 cd/m2 .
Sample stimuli, at all five levels, are shown in Figure 3.8.
3.2.1.3
Procedure.
General. The procedures of this experiment were identical to those in Experiment
1A, except that same-luminance and same-contrast comparisons were allowed. Each
condition consisted of 200 blocks, with 40 trials assigned to each of the five possible luminance ratio or contrast ratio comparisons (explained in detail below). To
minimize fatigue, the experiment was divided into five blocks. We employed a
randomized design, displaying all possible pairwise comparisons in the same block.
45
Figure 3.7: Experiment 1B, Condition 1: mean luminance control. Top half.
Sample glow stimuli (w = 5.0) at each of the five mean luminance levels. Bottom
half. Sample control stimuli (w = 0.0) at each of the five mean luminance levels.
46
Figure 3.8: Experiment 1B, Condition 2: maximum Weber contrast control.
Top half. Sample glow stimuli (w = 5.0) at each of the five maximum Weber
contrasts. Bottom half. Sample control stimuli (w = 0.0) at each of the five
maximum Weber contrasts.
47
Condition 1. On each trial, participants simultaneously viewed a countershaded
stimulus (w = 5.0) and a non-countershaded stimulus (w = 0.0), and indicated by
a key press which appeared to glow more. A luminance ratio was chosen randomly
√
√
from the following set: 1:1, 1: 2, 1:2, 1:2 2, and 1:4. Two luminances were
√
√
chosen randomly from the set, 25 cd/m2 , 25 2 cd/m2 , 50 cd/m2 , 50 2 cd/m2 , and
100 cd/m2 , so as to produce the required luminance ratio. The two luminances were
randomly assigned to the countershaded and non-countershaded stimuli. Note that
a consequence of using five fixed luminance levels was that when the desired ratio
√
was, say, 1: 2, there were four possible luminance pairs, but when the desired ratio
was 1:4, the only possible luminances were 25 cd/m2 and 100 cd/m2 .
Condition 2. On each trial, participants simultaneously viewed a countershaded
stimulus (w = 5.0) and a non-countershaded stimulus (w = 0.0), and indicated by
a key press which appeared to glow more. A contrast ratio was chosen randomly
√
√
from the following set: 1:1, 1: 2, 1:2, 1:2 2, and 1:4. Two contrasts were chosen
randomly from the set, 0.85, 1.21, 1.71, 2.42, and 3.42, so as to produce the required
contrast ratio. The two contrasts were randomly assigned to the countershaded
and non-countershaded stimuli. As in Condition 1, a consequence of using five
√
fixed contrast levels was that when the desired ratio was, say, 1: 2, there were
four possible contrast pairs, but when the desired ratio was 1:4, the only possible
contrasts were 0.85 and 3.42.
48
3.2.2
Results and Discussion
During debriefing, participant CP reported that he or she responded based on the
absolute brightness of the stimuli, rather than whether the stimuli appeared to
glow. This was confirmed in the analysis, and therefore, CP’s data were omitted
from subsequent analyses.
The trials were aggregated by luminance or contrast ratios. For each mean luminance ratio, we calculated the proportion of trials in which the higher-luminance
stimulus was chosen over the lower-luminance stimulus as glowing. Similarly, for
each maximum contrast ratio, we calculated the proportion of trials in which the
higher-contrast stimulus was chosen over the lower-contrast stimulus as glowing.
The results are plotted in Figure 3.9 and Figure 3.10. The dotted grey line at
50% represents chance, i.e., the expected pattern of results if participants did not
make glow judgments based on luminance or contrast. In Condition 1, we found that
all participants except CP, chose between higher and lower luminance stimuli with
equal probability, even when one stimulus was four times as luminous as the other.
As well, in Condition 2, we found that all participants except CP chose between
higher or lower contrast stimuli with equal probability, even when one stimulus was
as high in contrast as the other. These results demonstrate that luminance- and
contrast-based cues had little influence on participants’ glow judgments.
49
probability of choosing higher luminance stimulus (%)
1:1
1:�2
1:2
1:2�2
4:1 1:1
1:�2
1:2
1:2�2
4:1
100
100
80
80
60
60
40
40
20
20
AC
0
MK
0
100
100
80
80
60
60
40
40
20
20
GP
0
SME
0
100
100
80
80
60
60
40
40
20
20
0
CW
1:1
1:�2
1:2
1:2�2
4:1 1:1
CP
1:�2
1:2
1:2�2
4:1
0
mean luminance ratios
Figure 3.9: Experiment 1B, Condition 1. Mean luminance ratio does not predict participant response. The only exception is participant CP, who responded
based on absolute brightness of the image, rather than whether or not it appeared to glow. The dotted grey line represents the pattern of results expected
if participants had not made glow judgments based on luminance or contrast.
50
probability of choosing higher contrast stimulus (%)
1:1
1:�2
1:2
1:2�2
4:1 1:1
1:�2
1:2
1:2�2
4:1
100
100
80
80
60
60
40
40
20
20
AC
0
MK
0
100
100
80
80
60
60
40
40
20
20
GP
0
SME
0
100
100
80
80
60
60
40
40
20
20
0
CW
1:1
1:�2
1:2
1:2�2
4:1 1:1
CP
1:�2
maximum Weber contrast ratios
1:2
1:2�2
4:1
0
Figure 3.10: Experiment 1B, Condition 2. Maximum contrast ratio does not
predict participant response. The only exception is participant CP, who responded based on absolute brightness of the image, rather than whether or not it
appeared to glow. The dotted grey line represents the pattern of results expected
if participants had not made glow judgments based on luminance or contrast.
51
We see a different pattern of results when we re-plot the data as a function
of the proportion of trials in which the countershaded stimulus was chosen over
the non-countershaded stimulus (Fig. 3.11, 3.12). The dotted grey line along the
diagonal represents the expected pattern of results if participants had made glow
judgments based on luminance or contrast, rather than countershading. To see
why luminance- or contrast-based responses predict a diagonal line, consider the
following example. In the 1:4 luminance ratio comparison, the trial consists of a
countershaded, low-luminance stimulus (Fig. 3.7, first torus in top half) and a
control, high-luminance stimulus (Fig. 3.7, last torus in bottom half). Therefore,
if participants had always chosen the higher luminance stimulus, the probability
of choosing the countershaded stimulus would be 0%. In the 4:1 luminance ratio
comparison, the trial consists of a counterhsaded, high-luminance stimulus (Fig.
3.7, last torus in top half) and a control, low-luminance stimulus (Fig. 3.7 first
torus in bottom half). Therefore, if participants had always chosen the higher
luminance stimulus, the probability of choosing the countershaded stimulus would
be 100%.
All participants, except for CP, overwhelmingly chose the countershaded stimulus over the control stimulus at all luminance and contrast ratio comparisons. These
results confirm that, even when mean luminance and contrast vary substantially,
diffuse countershading is an effective method of inducing glow.
52
probability of choosing countershaded stimulus (%)
1:4
1:2�2
1:2
1:�2
1:1
�2:1
2:1
2�2:1
4:1 1:4
1:2�2
1:2
1:�2
1:1
�2:1
2:1
2�2:1
4:1
100
100
80
80
60
60
40
40
20
20
AC
0
MK
0
100
100
80
80
60
60
40
40
20
20
GP
0
SME
0
100
100
80
80
60
60
40
40
20
20
0
CW
1:4
1:2�2
1:2
1:�2
1:1
�2:1
2:1
2�2:1
4:1 1:4
CP
1:2�2
1:2
1:�2
1:1
�2:1
2:1
2�2:1
4:1
0
mean luminance ratios
Figure 3.11: Experiment 1B, Condition 1. Countershading weights predict
participant response. The only exception is participant CP, who responded based
on absolute brightness of the image, rather than whether or not it appeared to
glow. The dotted grey line along the diagonal represents the expected pattern
of results if participants had made glow judgments based on luminance, rather
than based on countershading.
53
probability of choosing countershaded stimulus (%)
1:4
1:2�2
1:2
1:�2
1:1
�2:1
2:1
2�2:1
4:1 1:4
1:2�2
1:2
1:�2
1:1
�2:1
2:1
2�2:1
4:1
100
100
80
80
60
60
40
40
20
20
AC
0
MK 0
100
100
80
80
60
60
40
40
20
20
GP
0
SME 0
100
100
80
80
60
60
40
40
20
20
CW
0
1:4
1:2�2
1:2
1:�2
1:1
�2:1
2:1
2�2:1
4:1 1:4
CP 0
1:2�2
1:2
1:�2
1:1
maximum Weber contrast ratios
�2:1
2:1
2�2:1
4:1
Figure 3.12: Experiment 1B, Condition 2. Countershading weights predict
participant response. The only exception is participant CP, who responded based
on absolute brightness of the image, rather than whether or not it appeared to
glow. The dotted grey line along the diagonal represents the expected pattern of
results if participants had made glow judgments based on contrast, rather than
based on countershading.
54
3.3
3.3.1
General Discussion
Overview
We examined whether apparent glow can be induced by mimicking the brightmeans-deep relationship, which characterizes some complex glowing objects, and
we introduced diffuse countershading as a means to achieve this manipulation.
We found diffuse countershading to be an effective method of inducing glow, even
when we controlled for simple low-level image properties such as mean luminance
or maximum Weber contrast.
How well do existing theories of glow explain the effectiveness of diffuse countershading? We consider the lightness-based and blur-based approaches in turn.
Lightness-based approaches posit that a surface patch appears to glow when
its luminance exceeds a context-dependent luminance threshold. According to
Gilchrist’s (1999) anchoring theory of lightness, the luminance threshold must be
1.7 times the anchored luminance of white (Bonato & Gilchrist, 1999). Furthermore, the total area of surface patches exceeding the anchored luminance must be
small, following the area rule (Gilchrist et al., 1999).
Suppose that our stimuli had the highest anchored luminance possible while still
inducing glow—i.e., we met only the minimal requirements for glow. This means
that only the pixel with the highest luminance in the stimulus (Lmax ) met the 1.7
55
threshold, thus the luminance of the anchor was Lanchor =
Lmax
.
1.7
The anchoring
theory of lightness predicts that very few pixels would have luminances greater than
Lanchor .
For the stimuli from Experiment 1A, we calculated the proportion of pixels
with luminances above Lanchor ; the result of the analysis is shown in Figure 3.13.
Ignoring w = 0.0 (no countershading, hence no glow), above-anchor pixels ranged
from 7% (w = 2.0) to 19% (w = 10.0), comprising a non-negligible area of the
stimuli; this is contrary to what the anchoring theory would predict. If we relaxed
our assumption about minimal glow, we would expect an even larger proportion of
above-anchor pixels.
Furthermore, in accordance with the area rule, the anchoring theory would
predict that participants should have found stimuli with fewer high-luminance pixels
to glow more—i.e., participants should have found w = 2.0 to glow more than
w = 10.0. This is not what we found in the Thurstone analysis (Fig. 3.5), where
increasing countershading weights increased participant glow response. Therefore,
such lightness-based approaches are unable to explain the effectiveness of diffuse
countershading.
What about blur-based approaches? Blur-based approaches posit that smooth
luminance gradients provide cues to glow; for example, a suitably blurred white
disc appears to glow more than a sharply defined white disc. However, blur-based
56
100
90
pixels above anchor (%)
80
70
60
50
40
30
20
10
0
0
1
2
3
5
4
6
7
8
9
10
countershading weights
Figure 3.13: Proportion of pixels with luminances above Lanchor =
Lmax
1.7 .
The
x-axis shows countershading weights and the y-axis shows the proportion of pixels whose luminances exceeded Lanchor . Each point is an average of 550 torus
samples.
approaches cannot account for why even simple contrast-reversal can yield a strong
sense of glow, as in Langer (1999, Figure 2.4) or in the countershaded component
of our stimuli (Figure 3.3, top right). Any luminance gradients present in the
countershaded component are also present in the diffusely lit component (Figure
3.3, top centre), but just with the opposite polarity; blur-based approaches cannot
57
predict perceived glow in the countershaded component as it is neither more nor
less blurred than the diffusely lit component.
It could be argued that—because the experiment stimuli are actually weighted
sums of directly lit, diffusely lit, and countershaded components—the luminance
gradients on the stimuli are not identical to the luminance gradients generated by
contrast-reversal alone. However, we note that the stimuli with the strongest glow
percepts consist almost entirely of the countershaded component; for example, at
w = 10, the countershaded component contributes 89% of the luminance on average.
Therefore, it appears that blur-based approaches are unable to completely account
for the effectiveness of diffuse countershading.
3.3.2
Luminance Histogram Skewness as a Predictor of Glow
Interestingly, the effectiveness of countershading seems to be correlated with the
luminance distribution of the diffusely lit image—which is a distinctly 2D, imagebased statistic. Countershading relies on contrast-reversal, which sets the luminances of bright pixels to be dark, and vice versa. In terms of a the luminance
distribution histogram, this means that the histogram becomes mirrored through
the y-axis—e.g., a diffuse image with a positively skewed luminance histogram will
yield a countershaded image with a negatively skewed histogram (Fig. 3.14, 3.15,
3.16, right column). On average, therefore, we expect that images with highly
58
asymmetric histograms benefit greatly from countershading whereas those with
fairly symmetric histograms do not. For example, Figure 3.14, which has a roughly
symmetric luminance histogram for the diffusely lit image, has a low absolute skewness of 0.15. When diffuse countershading is applied to it, it appears to be a fairly
uninteresting surface with extremely bright points, but it does not yield a sense of
glow radiating, as in Figure 3.16, which has an absolute skewness of 1.42. Figure
3.15 has an intermediary absolute skewness of 0.32, and so, its percept appears to be
somewhere between that of Figure 3.14 and Figure 3.16. This covariation between
skewness of the luminance histogram and perceived glow suggests the interesting
possibility that we may be able to predict the maximum amount of glow boost that
can be induced by countershading.
3.3.3
Final Remarks
We conclude this section with two final remarks. First, although we found that
diffuse countershading is an effective method for inducing glow, we have not conclusively demonstrated that perceived depth causally affects the perceived glow
of an object. Indeed, the bright-means-deep hypothesis implies that both the
luminance-based (‘bright’) and geometry-based (‘deep’) components are important
to perceived glow, and so, we need to be able to show that manipulating either
one should create or destroy glow. Therefore, in Experiment 2, we manipulate the
59
abs(skewness) = 0.15
diffuse
countershaded
final stimulus
Figure 3.14: Diffuse countershading with a low-skew stimulus. Top and middle rows. The left column depicts the diffusely and countershaded images, and
the right column depicts their luminance histograms. Bottom row. The final
stimulus, generated using Equations 3.7 and 3.8 with w = 5.0.
60
abs(skewness) = 0.32
diffuse
countershaded
final stimulus
Figure 3.15: Diffuse countershading with a medium-skew stimulus. Top and
middle rows. The left column depicts the diffusely and countershaded images,
and the right column depicts their luminance histograms. Bottom row. The final
stimulus, generated using Equations 3.7 and 3.8 with w = 5.0.
61
abs(skewness) = 1.42
diffuse
countershaded
final stimulus
Figure 3.16: Diffuse countershading with a high-skew stimulus. Top and middle rows. The left column depicts the diffusely and countershaded images, and
the right column depicts their luminance histograms. Bottom row. The final
stimulus, generated using Equations 3.7 and 3.8 with w = 5.0.
62
geometry-based components to examine directly whether or not bright-means-deep
relationship can influence the perceived degree of glow.
Second, diffuse countershading is a physically unrealistic approximation to glow:
lighting effects such as interreflections are not modelled, for example, in spite of
the fact that countershaded stimuli in this experiment appear to be reasonably
realistic objects, with globally coherent shape. How accurate is this impression of
perceived shape in countershaded objects, given that their shading patterns are so
unlike those of most real-life objects? In Experiment 3, we experimentally confirm
the goodness of these shape percepts by examining how well the visual system
performs depth discrimination tasks using countershaded stimuli.
63
4
Experiment 2: Can we reduce perceived glow
by destroying an existing bright-means-deep
relationship?
Previous research has demonstrated that depth cues influence surface lightness
perception. For example, Mach’s classic bent-card illusion shows that the visual
system is able to account for convex-concave relations to discount illumination when
estimating surface lightness (Mach, 1885/1959, Gilchrist, 2006, p.25; Fig. 1.1).
According to the bright-means-deep hypothesis, stimuli that are bright in valleys
and dark on peaks appear to glow. This implies that, as with the Mach bentcard illusion, correctly recognizing the convex-concave relationship of an object is
important to the perception of glow; therefore, we might expect that modifying the
perceived shape of an object should affect whether it appears to glow.
In Experiment 1, we found that at least some types of glow are generated by
the bright-means-deep relationship. What happens, then, when we take a glowing
64
object and modify its shape, such that valleys are no longer bright and peaks are
no longer dark? The bright-means-deep hypothesis predicts that this type of shape
modification should significantly reduce the perceived glow of the object.
In Experiment 2, we examined this prediction. In the first condition, we replicated Experiment 1 to ensure that diffuse countershading could induce convincing
percepts of glow in the new stimuli (see description under Stimuli, below). In the
second condition, we examined whether inverting the disparity of a glowing object,
and hence inverting the bright-means-deep relationship, can reduce perceived glow;
we call this manipulation depth inversion. In the third condition, we examined
whether changing the shape of a glowing object, and hence altering the brightmeans-deep relationship in random ways, can reduce perceived glow; we call this
depth randomization.
Hypothesis 2.1: As in Experiment 1, participants will find the countershaded
stimuli to glow more than the non-countershaded, Lambertian stimuli (Condition
1).
Hypothesis 2.2: Inverting the 3D shape of a glowing stimulus will significantly
reduce the degree of perceived glow (Condition 2).
Hypothesis 2.3: Randomizing the 3D shape of a glowing stimulus will significantly reduce the degree of perceived glow (Condition 3).
65
4.1
Experiment 2A
4.1.1
4.1.1.1
Methods
Participants.
Six participants between the ages of 18 and 40 volunteered for the study; five were
naı̈ve to the purpose of the experiment, and one was the author. All had normal
or corrected-to-normal vision. Three of the naı̈ve participants also participated
in other glow experiments; the remaining two naı̈ve participants were new to the
experiment.
4.1.1.2
Stimuli.
General. The stimuli were created by first generating disparity maps Z(x, y) and
Z 0 (x, y), then rendering a luminance map L(x, y) based only on Z 0 (x, y), and finally
texture-mapping L(x, y) onto Z(x, y), 0 ≤ x ≤ 1, 0 ≤ y ≤ 1. The resulting
stimulus was a surface (x, y, Z(x, y)) with luminance L(x, y), such that the depth
and luminance were determined by Z(x, y) and Z 0 (x, y), respectively. The main
experimental manipulation consisted of choosing Z(x, y) and Z 0 (x, y) such that
they were either congruent (Z(x, y) = Z 0 (x, y)) or incongruent (Z(x, y) 6= Z 0 (x, y)).
The generation of Z(x, y) and L(x, y) is described in detail below.
The disparity map Z(x, y) for each stimulus was a square sample of 2D low-pass
66
filtered Gaussian white noise, with a sharp upper cut-off frequency of 8 cycles per
square width (or equivalently, height). The maximum amplitude of the noise was
equal to the square width.
The luminance map L(x, y) was an image of a square, depth-modulated surface
patch, created using diffuse countershading (Eq. 3.7, 3.8). The directly lit image
D and the diffusely lit image F were rendered in RADIANCE, and depicted a
square, medium grey (50% reflectance), Lambertian surface patch that was depthmodulated with Z 0 (x, y). Z 0 (x, y) was a sample of noise with the same statistical
properties as Z(x, y) described above. The countershaded image C was generated
from F using Equation 3.7, then added to D and F in a weighted sum using
Equation 3.8.
For D, the light source was simulated as an infinitely distant disk subtending
1◦ of the sky. The disk was randomly positioned on the arc along 60◦ slant and
±15◦ tilt, where 0◦ slant points towards the camera along the optical axis and tilt is
coded so that 0◦ is overhead. For F , the light source was simulated as a uniformly
lit sphere covering the whole sky except for the small portion visible behind the
object. The direct and diffuse light source luminances were chosen so that, under
either light source alone, a white surface patch would have a maximum luminance
of 200 cd/m2 .
To create a stronger sense of depth, we applied a marble-like reflectance pattern
67
to the stimulus by multiplying it pointwise by a sample R(x, y) from the RADIANCE marble.cal texture. Thus, the luminance map was
L(x, y) = R(x, y) · (D(x, y) + 0.2 F (x, y) + w C(x, y))
(4.1)
We applied the marble texture using the above equation rather than use the built-in
RADIANCE texture-mapping routines, because the countershaded component C
was the contrast-reversed version of F —so, if F depicted a marble texture with dark
lines, then C would depict a texture with bright lines. Therefore, we had to first
generate the untextured countershaded image, and then modulate its luminance by
the marble texture to ensure that the resulting image would show dark lines.
Also to provide strong cues, stimuli in all conditions sinusoidally oscillated
about their vertical axes with an amplitude of 5◦ and a period of 1.54 s, and were
stereoscopically presented using the Stereographics CrystalEyes 3 apparatus for
Stereo3D viewing, with a simulated interocular distance of 6 cm. The stimuli were
displayed on a Philips 107B5 CRT monitor placed 1.36 m away from the participants’ eyes, subtending 276 × 276 pixels, or 2.95◦ × 2.95◦ . The monitor refresh rate
was 85 Hz, and the monitor resolution was 1280 × 960 pixels, where each pixel was
0.00023 cm × 0.00023 cm. The colour look-up table of the monitor was linearized
prior to the experiment. For sample stimuli, see Figure 4.1.
Condition 1. Countershaded vs. Lambertian. Condition 1 tested whether countershading was effective at creating a percept of glow, even though specifics of
68
the stimuli have been modified from Experiment 1, such that they were marbletextured, oscillating, and stereoscopically displayed.
Participants viewed a pair of stimuli with luminance map L(x, y); one of the
pairs was rendered with w = 5.0 (countershaded) and the other was rendered with
w = 0.0 (no countershading; Lambertian). The value of 5.0 was chosen because, at
this setting, all participants in Experiment 1A perceived glow of 3.0 SD or higher—
meaning that participants chose a stimulus with w = 5.0 over one with w = 0.0 at
least 98% of the time.
Each luminance map was texture-mapped onto the same disparity map used to
generate the luminance map (Z(x, y) = Z 0 (x, y)). Thus the countershaded stimuli
followed the bright-means-deep relationship.
Condition 2. Depth-normal vs. depth-inverted. In this condition, participants
viewed a pair of stimuli with luminance map L(x, y), both rendered with w = 5.0.
In one stimulus, the luminance map was texture-mapped on to the same disparity
map used to generate the luminance map (Z(x, y) = Z 0 (x, y)), and in the other,
the luminance map was texture-mapped onto the depth-reversed version of that
map (Z(x, y) = −Z 0 (x, y)). Thus the two stimuli presented the same luminance
pattern, but the former showed a bright-means-deep pattern and the latter showed
a dark-means-deep pattern.
Condition 3. Depth-normal vs. depth-randomized. In this condition, partic69
ipants viewed a pair of stimuli with luminance map L(x, y), both rendered with
w = 5.0. In one stimulus, the luminance map was texture-mapped on to the same
disparity map used to generate the luminance map (Z(x, y) = Z 0 (x, y)), and in the
other, the luminance map was texture-mapped onto a new, independently sampled
disparity map. Thus the two stimuli presented the same luminance pattern, but
the former showed a bright-means-deep pattern and the latter showed statistically
independent luminance and depth.
4.1.1.3
Procedure.
Before the experiment began, participants were instructed on how to perform the
experiment task. To describe glow, the following phrases were used: “is radiant,”
“is emitting light,” or “is not just bright because of an external light source.”
In addition, participants were instructed to avoid over-analyzing the task, and to
respond using their perceptual “gut feelings” to avoid prolonged trials. We then
checked for the participants’ stereoscopic vision by asking whether or not they see
perceived depth in a simple stereoscopic display.
Each trial began with a fixation dot on the screen for 100 ms. A pair of stimuli
were then presented stereoscopically against a black background. Participants then
indicated, with a key press, which of the two stimuli appeared to glow more strongly.
The following trial began immediately afterwards, without any feedback.
70
luminance
depth
countershaded
normal
Lambertian
Lambertian
normal
depth-normal
countershaded
normal
depth-inverted
countershaded
inverted
depth-normal
countershaded
normal
countershaded
randomized
countershaded
stimuli
vs.
vs.
vs.
depth-randomized
Figure 4.1: Sample stimuli of all three conditions in Experiment 2A. To provide
strong shape cues, all stimuli were presented stereoscopically, were textured with
marble-like patterns, and sinusoidally oscillated ±5◦ . Note that the images above
are not stereoscopic pairs, but are monocular examples of the stimuli seen during
the experiment.
71
The stimuli stayed on the computer screen until participant response, and participants were allowed as much time as possible to respond. This was because,
due to individual variability in stereoacuity, some participants might not have been
able to experience a strong sense of stereoscopic depth from a short, fixed stimulus
presentation. To prompt the observers to respond, we played a non-intrusive ‘click’
sound after 2.0 s of stimulus presentation.
Participants saw all three conditions interleaved within a single session, and as
such, followed the same general procedure. There were 400 trials total: 200 trials
of Condition 1, 100 trials of Condition 2, and 100 trials of Condition 3.
4.1.2
Results
See Figure 4.2 for a summary. Participants’ glow response rates were analyzed
in each of the three conditions. As expected, diffuse countershading was found
to be extremely effective in the new stimuli, yielding a glow response rate with
M = 95%, SD = 9%, which is significantly above the chance level of 50% (t(5) =
12.21, p < 0.0001). This means that participants chose the countershaded stimuli
over the non-countershaded stimuli 95% of the time, and supports the conclusions
of Experiment 1.
Contrary to our expectations, however, we found that neither depth inversion
nor depth randomization resulted in a significant reduction of perceived glow—
72
that is, participants did not reliably choose the depth-normal stimuli as glowing
more. The mean glow response rate of the depth inversion condition was M =
63%, SD = 17%, which is not significantly different from chance level (t(5) =
1.84, p = 0.13)—i.e., participants chose depth-normal and depth-inverted stimuli
about equally often. The mean glow response rate of the depth randomization
condition was M = 57%, SD = 13%, which is not significantly different from
chance level (t(5) = 1.30, p = 0.25)—i.e., participants depth-normal and depthrandomized stimuli about equally often.
We also analyzed the participant response times. We found that, in a majority of
the trials, participants typically responded within 1 s of stimulus onset, and almost
always responded within 2 s, suggesting that we could have used a fixed stimulus
duration if needed (Fig. 4.3).
Result 2.1: Hypothesis 2.1 was supported. Diffuse countershading was found to
generate strong percepts of glow in randomly generated blobby surfaces.
Result 2.2: Hypothesis 2.2 was not supported. Inverting the depth of a glowing
stimulus did not significantly reduce the degree of perceived glow.
Result 2.3: Hypothesis 2.3 was not supported. Randomizing the depth of a
glowing stimulus did not significantly reduce the degree of perceived glow.
73
response consistent with
bright-means-deep pattern (%)
100
***
90
80
70
60
50
40
30
20
10
0
countershaded
vs. Lambertian
depth-normal vs.
depth-inverted
depth-normal vs.
depth-randomized
Figure 4.2: Results of Experiment 2A. In Condition 1, participants chose the
countershaded stimuli over the Lambertian stimuli as the more glowing stimulus
on 95% of trials, in line with the results of Experiment 1. However, contrary to
our hypothesis, neither depth inversion (Condition 2) nor depth randomization
(Condition 3) significantly reduced the degree of perceived glow. The condition
means are depicted as orange bars, and the individual subject means are depicted
as grey circles (n = 6); the dotted line at 50% represents chance. Note the large
individual variability in Conditions 2 and 3.
74
0
2
4
6
8
10
0
2
4
6
8
MK
300
300
200
200
100
100
0
number of trials
10
MD
YM
MC
0
300
300
200
200
100
100
0
0
CO
DS
300
300
200
200
100
100
0
0
2
4
6
8
10
0
2
reaction times (s)
4
6
8
10
0
Figure 4.3: Response time analysis. Participants typically responded within 2
seconds of stimulus presentation.
75
4.2
Experiment 2B
Given the surprising results of Experiment 2A, we repeated the experiment at a
much lower countershading weight of w = 1.2 to confirm that depth manipulations
do not significantly affect glow judgments across different stimuli configurations. As
well, in order to encourage response time consistency across trials and participants,
stimuli were replaced with a blank screen after 1.2 s of presentation.
4.2.1
4.2.1.1
Methods
Participants
Six participants between the ages of 18 and 40 volunteered for the study; five were
naı̈ve to the purpose of the experiment, and one was the author. All had normal
or corrected-to-normal vision. Three of the naı̈ve participants also participated in
other experiments; the remaining two naı̈ve participants were new to the experiment.
4.2.1.2
Stimuli
The stimuli were generated using the same method as in Experiment 2A, except
that the countershading weight, w, was set to 1.2 rather than 5.0 for all stimuli
except for the Lambertian stimuli in Condition 1. The value of 1.2 was chosen
76
because, when w = 1.2, the countershaded image contributes 50% of the final
stimulus luminance (Eq. 3.9). Sample stimuli can be seen in Figure 4.4.
luminance
depth
countershaded
normal
Lambertian
Lambertian
normal
depth-normal
countershaded
normal
depth-inverted
countershaded
inverted
depth-normal
countershaded
normal
countershaded
randomized
countershaded
stimuli
vs.
vs.
vs.
depth-randomized
Figure 4.4: Experiment 2B stimuli. These were generated as in Experiment 2A,
except that the countershading weight was set to w = 1.2 rather than w = 5.0.
77
4.2.1.3
Procedure
The procedure was identical to that of Experiment 2A, except that the stimuli
were replaced with a blank screen after 1.2 s of presentation, in order to encourage
response time consistency across trials and observers. The duration of 1.2 s was
chosen in part because we found that participants tended to respond within 1 s
of stimulus onset (Fig. 4.3), and also in part to be consistent with the stimulus
presentation duration of 1.2 s in Experiment 3.
4.2.2
Results
The results of Experiment 2B were similar to those of Experiment 2A. See Figure
4.5 for a summary of results. In Condition 1, we found that diffuse countershading induced a percept of glow in most participants, M = 82%, SD = 34%, with
marginal non-significance (t(5) = 2.29, p = .07). In Conditions 2 and 3, we failed
to find evidence of reduced glow; the mean glow response rate for Condition 2 was
M = 46%, SD = 15% (t(5) = −0.66, p = 0.54), and the mean glow response rate
for Condition 3 was M = 44%, SD = 18% (t(5) = −0.78, p = .47).
The non-significant result in Condition 1 is likely due to an extreme outlier increasing the overall variability of the data. With the outlier excluded, we found that
the results of Condition 1 are precisely in line with the earlier results of Experiment
78
2A, with M = 96%, SD = 5% (t(4) = 21.65, p < .0001), showing a statistically significant effect of countershading on participant glow response. Excluding the outlier
data did not affect the results of either Condition 2, M = 45%, SD = 8% (t(4) =
−0.66, p = 0.54) or Condition 3, M = 44%, SD = 9% (t(4) = −0.71, p = 0.52).
Note that, in Figure 4.5, the condition means are calculated without the outlier,
but the outlier data are plotted for reference.
4.3
Discussion
We began with the hypothesis that disrupting the bright-means-deep pattern should
reduce perceived glow, but failed to find evidence in support of this hypothesis. For
both high glow (Experiment 2A) and low glow (Experiment 2B) objects, we found
that neither depth inversion nor depth randomization yielded significant reduction
in glow percepts, which seems to show that perceived depth may not have a crucial
role in glow processing. This is surprising, given what we know about the visual
system’s sensitivity to the perceived 3D shape of an object when making surface
lightness judgments (Mach, 1885/1959).
What could explain these results? One possibility is that there is individual variability in how depth and luminance cues are integrated to form percepts of glowing
objects. In both Experiments 2A and 2B, there was great individual variability in
participant glow response rates: some participants showed significant reduction in
79
response consistent with
bright-means-deep pattern (%)
100
90
*
80
70
60
50
40
30
20
10
0
countershaded
vs. Lambertian
depth-normal vs.
depth-inverted
depth-normal vs.
depth-randomized
Figure 4.5: Results of Experiment 2B confirm the results of Experiment 2A:
disrupting the bright-means-deep pattern of glowing objects does not strongly
affect perceived glow of the object. The statistical non-significance of Condition
1 is driven entirely by the outlier near the bottom of the y-axis (dotted circle).
The condition means, calculated without the outlier, are depicted as orange bars
(n = 5); the individual subject means are depicted as grey circles. The dotted
line at 50% represents chance. Note the large individual variability in Conditions
2 and 3, even after the outlier is discarded.
80
perceived glow, whereas some showed none at all, with extreme outliers on either
side of the chance line (Fig. 4.2). Therefore, we may find some small effects of shape
manipulation if we repeated the experiment using participant-specific thresholds for
glow percepts. We could, for example, define the threshold countershading weight
as the level of countershading at which the participant identifies the countershaded
stimulus as the glowing stimulus 75% of the time. We could then generate stimuli
at the specific threshold countershading weight for each participant, and evaluate
the effects of depth manipulations at these thresholds. At threshold level of glow
perception, depth manipulations may be more likely to affect perceived glow.
While Experiment 2B examined the effects of depth manipulation on low-glow
stimuli, the null result does not necessarily rule out the need to examine individual
countershading thresholds. In Experiment 2B, we used a countershading weight of
w = 1.2—which, while low, still was large enough to yield a glow percept strong
enough that most participants in Condition 1 still obtained glow response rates
nearing 100%. This suggests that even a weight of 1.2 is already much higher than
the threshold weight for most people, and implies that luminance-based cues may
already override shape-based cues at this point.
Another possibility is that the stimuli appeared extremely unnatural, and participants simply were not perceiving the shape correctly. This relates to the above
point that different individuals may rely on stereopsis cues to greater or lesser ex81
tents, and participants with particularly low reliance on stereopsis cues may have a
harder time perceiving depth correctly. Even for participants with strong reliance
on stereopsis, it is possible that the physically unrealistic countershading generated
incoherent percepts that that were difficult to interpret as a meaningful shape. We
examined this possibility in Experiment 3, where we investigated whether or not it
is possible obtain reliable shape information from countershaded glow pattern.
Finally, it may be that depth cues are not as important to perceiving glow as we
predicted. Image-based cues have, in the past, been shown to be sufficient for perceiving complex structures such as 3D shape (see, e.g., shape-from-shading, Horn,
1970; shape-from-specularities, Fleming, Torralba & Adelson, 2004b); perhaps glow
in complex objects can also be detected based on image-based cues only.
82
5
Experiment 3: Can we accurately perceive 3D
shape from glow (shape-from-glow)?
Shape-from-shading is the recovery of 3D shape from shading patterns in a single 2D
image. By assuming certain relationships between shape and luminance, the visual
system is able to recover 3D shape structure from simple 2D luminance variations
(Fig. 5.1).
In Experiment 3, we examined whether the visual system can recover shape
information from the luminance pattern of glowing objects, or shape-from-glow.
According to the bright-means-deep hypothesis, the shading patterns of a glowing
object can be approximated by a bright-means-deep relationship between shape and
luminance—i.e., peaks are dark and valleys are bright. However, the bright-meansdeep relationship is so unlike the shading found in common scenes, it is not at all
clear how standard approaches to shape-from-shading would recover the shape of
a glowing object.
Compare the bright-means-deep relationship to the standard shape-from-shading
83
Figure 5.1: Shape-from-shading. By assuming certain relationships between
shape and luminance, the visual system is able to recover the 3D shape structure
from simple 2D luminance variations (Strazza, c. 1850).
model under collimated light. Standard shape-from-shading is formulated in terms
of surface normals and the light source position, and is formalized in Lambert’s
cosine law (Horn, 1986):
I=




L α cos(θ), if θ < 90◦



0,
(5.1)
if θ ≥ 90◦
where L is the light intensity, α is the surface albedo, and θ is the angle between
the surface normal and the light source direction. A surface point that is oriented
84
directly towards the light source (θ = 0◦ ) receives the maximal amount of light,
therefore the luminance at the surface point is limited only by its albedo and by
the lighting intensity (I = L α); a surface point oriented at 90◦ or more receives no
light at all (θ ≥ 90◦ ), and therefore has zero luminance (I = 0); and a surface point
oriented somewhere in-between (0◦ ≤ θ < 90◦ ) receives some in-between quantity of
light, and therefore has some in-between level of shading (0 < I ≤ L). This means
that, according to Lambert’s law, a surface patch that is near a peak and is facing
the light source must be bright; according to the bright-means-deep hypothesis, we
expect that a surface patch near a peak is dark.
Note that even the non-classical Langer and Bülthoff (2000) model for shapefrom-shading under diffuse lighting predicts that the visual system should misinterpret glowing images. According to Langer and Bülthoff (2000), shading under diffuse lighting can approximately be characterized as a dark-means-deep relationship—
i.e., peaks are bright and valleys are dark. A naı̈ve generalization of the dark-meansdeep model, then, would predict that glowing objects would appear inside-out, with
all convex-concave shape relationships inverted. For these reasons, we might wonder
how well human observers will be able to perceive the shapes of glowing objects.
In this experiment, we employed a relative depth probe task (Langer & Bülthoff,
2000; Todd, 2004) to determine whether, given two surface points on a glowing surface, participants can accurately judge the relative depths of the probes. We also
85
assessed a control condition, in which participants judged the relative depths of
probes on non-glowing objects under typical lighting consisting of a direct component and an ambient component. In both conditions, performance was measured in
terms of accuracy rates, i.e., the percentage of trials in which participants correctly
identified the nearer probe. We evaluated three specific hypotheses:
Hypothesis 3.1: Participants will perform significantly above chance (50%) in
the glow condition.
Hypothesis 3.2: Participants will perform significantly above chance (50%) in
the no-glow condition.
Hypothesis 3.3: The mean performance in the glow condition will not be significantly different from the performance in the no-glow condition.
5.1
5.1.1
Methods
Participants
Six participants between the ages of 18 and 40 volunteered for the study; five
were naı̈ve to the purpose of the experiment and one was the author. All had
normal or corrected-to-normal vision. All participants had previously participated
in Experiment 1 or 2.
86
5.1.2
Stimuli
We used the stimuli generated in Experiment 1, but with two probes—a red and
a yellow—placed on the surface of the stimulus to indicate the surface points to
compare. The diffuse countershading weights were set to w = 5.0 for the glow
condition, and to 0.0 for the no-glow condition. As in Experiment 1, the light
source was randomly positioned somewhere on the arc along 60◦ slant and ±15◦
tilt, where 0◦ slant represents the angle relative to the optical axis and tilt is coded
so that 0◦ is overhead.
Probe locations were carefully selected to prevent subjects from relying on shape
cues other than glow or shading. Following Langer and Bülthoff, contour cues were
avoided by placing probes far from junctions, which are known to provide strong
depth cues (e.g., T-junctions; Fig. 5.2). See Figure 5.3 for a typical stimulus
marked with red and yellow probes. The edge (contour) map on the right-side of
the figure show that, near the probe locations, there are no junctions and only
few edges present; indeed, the stimulus image on the whole is sparse in contour
information, especially away from the centre. Furthermore, to prevent participants
from mentally tracing the contours, the stimuli were only presented for 1200 ms,
which was too short for subjects to attend to regions far from the probe points (see
Procedure, below). Participants were forced to rely on shading cues, as it would
87
have been difficult for participants to make rapid and accurate depth judgments
based on line contours alone.
Figure 5.2: T-junctions occur at occlusions, and therefore can provide strong
depth cues. As such, we avoided placing probes near T-junctions in our stimuli.
Adapted from Todd (2004).
As our stimuli were untextured and were not presented stereoscopically, participants could not base their responses on texture or binocular disparity cues.
5.1.3
Procedure
Each trial began with a blank screen with a fixation dot, followed by the onset of two
circular probes (one red and one yellow). Subjects then had 600 ms to foveate on
the probes. A stimulus was then shown behind the probes, and subjects indicated
which of the two surface points marked by the probes appeared to be closer in
88
Figure 5.3: Top. Sample stimulus. Bottom. Binary edge map of the countershaded image, obtained using the Sobel edge detector implemented in the MATLAB R2009b Image Processing Toolbox with default parameter values (Mathworks, 2009). Although edges are present in this image, they do not provide
much contour information and it is difficult to determine depth relations based
on them—especially when the image is cropped to the neighbourhood local to
the probes.
89
depth. To prevent subjects from mentally tracing the stimulus contours, the screen
was blanked after 1200 ms of stimulus presentation, following Langer and Bülthoff.
Subjects responded with a key press, which ended the trial and immediately began
the following trial. Subjects were not provided feedback.
For five of the six participants, we had 320 trials × 2 conditions (glow, no
glow), for a total of 640 trials segmented into 5 blocks. For the sixth participant,
the experiment software unexpectedly quit after 573 trials (288 glow trials and 285
no-glow trials). For all participants, we interleaved the glow and no-glow stimuli in
the same block.
5.2
Results
See Figure 5.4. Participants’ accuracy rates in depth judgments were analyzed for
the glow and the no-glow stimuli. For both glow and no-glow conditions, participants performed significantly better than chance level (50%): the mean accuracy
rate for the glow condition was M = 61%, SD = 9% (t(5) = 2.92, p = .03),
and the mean accuracy rate for the no-glow condition was M = 75%, SD = 7%
(t(5) = 8.37, p < .001). As well, we found that participants were significantly
better at depth judgments in the no-glow condition than in the glow condition,
M = 14%, SD = 4% (t(5) = 8.34, p < .0001).
Result 3.1: Hypothesis 3.1 was supported. Participants were significantly better
90
*
100
percent correct (%)
90
80
70
*
**
60
50
40
30
20
10
0
glow
no glow
Figure 5.4: Results of experiment 3. Participants can make accurate depth
judgments based on glow information. The individual subject means are depicted
in grey circles (n = 6); the dotted line at 50% represents chance response.
than chance at discriminating the relative depths of glow stimuli.
Result 3.2: Hypothesis 3.2 was supported. Participants were significantly better
than chance at discriminating the relative depths of no-glow stimuli.
Result 3.3: Hypothesis 3.3 was not supported. Contrary to our original prediction, we found that participants were significantly worse at depth discrimination
with glowing stimuli than with no-glow stimuli.
91
5.3
Discussion
We examined whether participants can make accurate depth judgments based on
the shading patterns of a glowing object. We found that, although depth judgments
were more accurate with regular Lambertian objects, participants could still make
accurate depth judgments with glowing objects.
This is remarkable, as standard approaches to understanding shape-from-shading
rely on Lambert’s cosine law (Horn, 1986; Zhang et al., 1999) and shape-fromshading under diffuse illumination describes shading as an approximately ‘darkmeans-deep’ pattern (Langer & Bülthoff, 2000). Neither of these can explain shapefrom-glow. The fact that we can perceive the 3D shape of glowing objects makes it
conceivable that 3D shape may have a role in glow perception. Indeed, our results
suggest that there may exist different mechanisms (priors) for perceiving shape
under different circumstances, which lead to possible topics for further research.
Note that the stimuli in the current experiment were not generated by simulating physically realistic glow processes in detail. They were generated via diffuse
countershading, which can induce perceived glow (Experiment 1A), but may be
lacking some properties of shading found in real-life glowing objects. It may be
informative to repeat the experiment with images of physically accurate glow, either by using high-dynamic range photographs of real-life glowing objects or by
92
rendering a glowing object using a 3D rendering software.
In the future, the robustness of shape-from-glow should be examined. How well
would participants perform depth discrimination tasks on the undulated surfaces
from Experiment 2, for example? Perhaps the null result in Experiment 2 can, in
part, be accounted for by strongly conflicting cues between stereoscopic depth cues
and shape-from-glow depth cues, meaning that participants in Experiment 2 did
not have strong, accurate depth percepts.
93
6
Conclusion
6.1
Diffuse Countershading and Perceived Glow
We set out to investigate the relevance of 3D shape to the perception of glow. Based
on the observation that glowing objects are often bright in concavities and dark at
convexities, we proposed the bright-means-deep hypothesis, and predicted that the
visual system is sensitive to the bright-means-deep relationship between shape and
luminance of glowing objects.
In Experiment 1, we introduced a novel technique called diffuse countershading, which we used to mimic the bright-means-deep relationship in glowing objects.
The countershaded component of a diffusely countershaded object was obtained by
contrast-reversing the luminance pattern of a diffusely lit Lambertian object. We
found that diffuse countershading was an extremely effective method of generating apparent glow (Experiment 1A), and that participant glow responses were not
driven by low-level image properties such as mean luminance and contrast (Experiment 1B). These results are consistent with the bright-means-deep hypothesis.
94
In contrast, the results of Experiment 2 provided evidence against the brightmeans-deep hypothesis. We interfered with the bright-means-deep relationship of
an already glowing object by modifying its depth, and investigated whether this
disruption reduced the perceived degree of glow. Surprisingly, we found that neither
depth inversion nor depth randomization reduced the perceived degree of glow,
which suggests that perceived shape does not play as critical a role as expected.
Furthermore, we found that the results hold across both high (Experiment 2A)
and low (Experiment 2B) countershading weights, suggesting that countershadinggenerated glow is robust across a wide range of stimulus parameters. These results
are inconsistent with the bright-means-deep hypothesis.
In Experiment 3, we examined whether the visual system can correctly make
depth judgments based on glowing patterns. The results showed that it is possible
to obtain strong and accurate impressions of depth from countershaded objects, or
shape-from-glow, which suggests that human shape-from-shading mechanisms are
much more flexible than can be accounted for by classical theories of shape-fromshading (Horn, 1986; Zhang et al., 1999). These results are consistent with the
bright-means-deep hypothesis in that the ability to accurately discern depth on a
glowing object is a necessary precondition for the bright-means-deep hypothesis to
be a plausible explanation of glow perception.
What could explain these seemingly contradictory results across the experi95
ments? We suggest two possible explanations.
One possibility is that the results of Experiment 2 were confounded due to
competing depth cues from stereopsis and from shading. While stereopsis is known
to be a strong cue to depth, the results of Experiment 3 suggest that luminancebased depth cues in glowing stimuli can also be quite strong. This potential cue
conflict may explain the large individual variability obtained in Experiment 2, as
participants may have placed different weights on stereoscopic and luminance-based
depth cues, yielding vastly different depth percepts. To examine this possibility,
further studies are needed. For example, participants’ depth percepts could be
directly examined using the two-probe method in Experiment 3.
Another possibility is that, contrary to the bright-means-deep hypothesis, imagebased, depth-blind mechanisms may be sufficient to explain the perception of glowing objects. Diffuse countershading is an effective method of creating perceived glow
because it mimics some aspects of physical glow processes at a broad, statistical
level without modelling the underlying physics. Yet, the bright-means-deep correlations may be perceptually irrelevant in that the visual system relies on other,
possibly image-based, features to detect glow. This would account for both the
positive results of Experiment 1, and the negative results of Experiment 2.
However, the implications of our studies are limited by the fact that, while
diffuse countershading is an effective approximation to glow, it is not physically
96
accurate—and as a result, subtle but critical nuances in shading may be lost. Given
that we used diffuse countershading as a method of generating glow in Experiments
2 and 3, we should allow for the possibility that a more physically realistic method
may have yielded different results.
Our results show that the bright-means-deep relationship may play an important
role in the physical process of generating glow, but that it only partially captures
perceptual cues to glow. Future studies should more directly examine the role of
shape on glow, either by studying the shape and luminance statistics of real-life
glowing objects, or by using a physically realistic method of rendering glow.
6.2
Future Directions
As the perception of glow is still an under-studied area, some fundamental questions
as to the nature of glow have yet to be addressed. For example, are there multiple
cues to glow? Are some material types more conducive to glow than others? In
this section, we highlight a few topics of further study and suggest ideas for future
investigations.
6.2.1
Varieties of Glow
Just as the visual system integrates several different cues to estimate, say, the
motion of an object (e.g., retinal motion, occlusion cues, shadow cues), there may
97
be several different types of information that provide reliable evidence that a surface
is glowing.
Consider, again, the lightness-based versus blur-based models of glow. Lightnessbased models posit that a glowing surface patch must be more luminous than a
white patch; yet, research has shown that a grey patch, which is less luminous
than white, can appear to glow (Zavagno, 1999; Zavagno & Caputo, 2001, 2005).
Conversely, blur-based models posit that smooth luminance gradients provide perceptual cues to glow; yet, it has been found that glow can be generated without
luminance gradients (Bonato & Gilchrist, 1999; Li & Gilchrist, 1999). These inconsistencies may be reconciled if we accept that the studies investigated different
cues to glow.
In fact, other types of cues may exist. Consider, for example, the distinction
between an object with a glowing surface, or surface glow, versus an object with
an internal source of glow, or volume glow. This distinction is important, because
the physical processes involved in generating each can be very different. In surface
glow, the surface itself emits light, and any scattering of light occurs outside of the
glowing object. In volume glow, the light is emitted from within the object, and
scatters as it diffuses through the material.
The glow of stars, for example, could be considered to be surface glow as the
stars appear fairly flat points. In contrast, the glow in Figure 2.3 could be considered
98
to be volume glow, as there is a strong sense of light emanating from within. We
propose that previous studies on glow examined surface glow (Fig. 2.7, the glare
illusion), whereas the glow in the Experiment 1 stimuli examined volume glow (Fig.
3.3). Note that some types of glow, such as the glow of an aurora (Fig. 6.1), are
difficult to categorize into either surface or volume glow.
Figure 6.1: Aurora. Would this be considered to be surface glow or volume
glow? From NASA Astronomy Picture of the Day, December 19, 2009 (Hansen,
2009).
99
6.2.2
Glow, Glowability, and Material Properties
When we study glow, we should make a clear distinction between studying an object
that is currently in the state of glowing and an object that could potentially glow
under the right illumination (glowable), as the former is an effect of illumination
and the latter is a surface material property. For example, Figure 6.2 is glowable
in that it is currently not glowing, but could conceivably glow under backlighting.
Figure 6.2: A ‘glowable’ object. Although the above object does not currently
glow, it seems conceivable that it could appear to glow under the right kind of
illumination. Adapted from Fleming & Bülthoff (2005).
Glowability is associated with the transmittance of light through an object’s
100
surface; this is a distinctly non-Lambertian property, and hence, studies of glowability should examine non-Lambertian materials. Translucent materials, such as
wax or alabaster, are prime examples. Although our understanding of translucency
has vastly improved in recent decades (Jensen, Marschener, Levoy & Hanrahan,
2001), the interaction between translucency and glow has not not been investigated
beyond the observation that translucent materials whose luminances positively correlate with saturation can appear to possess a warm glow (Fleming & Bülthoff, 2005;
Fleming et al., 2004a, Figure 6.3).
As well, surfaces populated by fine hairs, such as velvet or the skin of a peach,
can appear to transmit light—and hence, be glowable—due to a radiometric phenomenon called asperity scattering. The hairs form a pseudo-layer of ‘cloud cover’
above the solid surface of the object, and scatter light in a non-Lambertian way
(Koenderink & Pont, 2003, see Fig. 6.4). Again, the interaction between asperity
scattering and glow has not been investigated.
6.2.3
Glow and Colour
Consider Figures 6.5 and 6.6. Although the greyscale images are approximately
matched in luminance with the colour images (ITU-R Recommendation BT.601
for converting RGB to luminance; International Telecommunications Union, 2011),
they do not appear to glow as strongly. This demonstration implies that the visual
101
Figure 6.3: Glow and saturation. Left. Saturation and luminance are positively
correlated. Right. Saturation and luminance are negatively correlated. Fleming
reports that most observers find the left image to glow more strongly than the
right image (Fleming & Bülthoff, 2005; Fleming et al., 2004a). Note that this
figure is best viewed on a monitor rather than on paper, as LCDs have larger
dynamic range than ink on paper. Adapted from Fleming and Bülthoff (2005).
system is sensitive to chromatic cues to glow.
Even though we intuitively associate glow with specific colours, such as with the
warm yellow of ember or the cool green of fireflies, the connection between colour
and glow has not been formally studied. Are certain hues more likely to appear
to glow? For a given hue, is it possible to induce glow by increasing or decreasing
saturation? Fleming and Bülthoff (2005) previously observed that objects whose
102
Figure 6.4: Asperity scattering. Left. A red sphere with asperity scattering
rendered in blue. Right. A red sphere rendered without any asperity scattering.
The presence of asperity scattering, as in velvet, can induce glow. Note that this
figure is best viewed on a monitor rather than on paper, as LCDs have larger
dynamic range than ink on paper. Adapted from Koenderink & Pont (2003).
luminance positively correlated with saturation are tend to induce percepts of glow
(Fig. 6.3), but did not investigate this further, leaving open possible topics of future
research.
6.2.4
Glow as a Pre-Attentive Feature
Given that lighting-related phenomena such as convexity from shading (Ramachandran, 1988), 3D orientation from shading (Enns & Rensink, 1990), and cast shadows
(Rensink & Cavanagh, 2004), are processed pre-attentively, it is possible that glow
103
Figure 6.5: Glow and colour in natural settings. Left. Original photographs
in colour. Right. Although the greyscale version is approximately matched in
luminance (International Telecommunications Union, 2011), the greyscale images
do not appear to glow as strongly as the colour images. From top to bottom,
photographs adapted from Argerich (2011), Kaplan (2011), and Ayiomamitis
(2009).
104
Figure 6.6: Glow and colour in art. Top. Original painting in colour. Bottom.
Although the greyscale version is approximately matched in luminance (International Telecommunications Union, 2011), the greyscale image does not appear to
glow as strongly as the colour image. Adapted from Monet (1872).
105
is also processed rapidly and without the aid of attention.
As far as we know, only one study to date has examined the possibility of glow
as a pre-attentive feature (Correani, Scott-Samuel & Leonards, 2006). In a visual
search task, participants either searched for a glowing target item among nonglowing distractor items, or vice versa. The glowing items were generated using the
glare illusion (Zavagno, 1999; Zavagno & Caputo, 2001, 2005; see Fig. 2.7). Glowing
items exhibited both pop-out (Wolfe & Horowitz, 2004) and search asymmetry
(Treisman & Souther, 1985), with glowing items found more quickly among nonglowing items, and vice versa. As such, the glowing items passed the two classic
criteria for determining whether a property is processed pre-attentively (Correani
et al., 2006, Experiment 1); however, control conditions did not conclusively rule
out the possibility that luminance gradients were driving the pre-attentive effect,
rather than glow per se (Correani et al., 2006, Experiments 2-4). Therefore, further
investigation is required.
Although our experiments identified an important research area and provide
some of the first investigations on 3D shape and glow, it is evident that we have
barely touched on the set of possible research topics. Understanding glow better in
complex stimuli will bring us a step closer to formulating a comprehensive theory
of glow perception, and will help us develop perceptually motivated algorithms for
detecting and rendering glow.
106
References
Argerich, L. (2011). Dawn of the planets [Photograph]. Retrieved July 10, 2011
from http://apod.nasa.gov/apod/ap110507.html. NASA Astronomy Picture of
the Day, May 7, 2011.
Arnheim, R. (1974). Art and visual perception: psychology for the creative eye.
Berkeley, CA: University of California Press, second edition.
Ayiomamitis, A. (2009). Sunrise over the parthenon [Photograph]. Retrieved July
10, 2011 from http://apod.nasa.gov/apod/ap090621.html. NASA Astronomy
Picture of the Day, June 21, 2009.
Beckman, C., Nilsson, O., & Paulsson, L.-E. (1994). Intarocular light scattering in
vision, artistic painting, and photography. Applied Optics, 33(21), 4749–4753.
Bonato, F. & Gilchrist, A. (1994). The perception of luminosity on different backgrounds and in different illuminations. Perception, 23, 991–1006.
doi:10.1068/p230991.
Bonato, F. & Gilchrist, A. (1999). Perceived area and the luminosity threshold.
Perception & Psychophysics, 61(5), 786–797.
Chen, T., Lensch, H. P. A., Fuchs, C., & Seidel, H.-P. (2007). Untitled photograph of Venus de Milo [Photograph]. Retrieved January 18, 2011 from
http://www.inf.mpg.de/˜lensch/proj/3DScanTranslucent.
Correani, A., Scott-Samuel, N. E., & Leonards, U. (2006). Luminosity—a perceptual “feature” of light-emitting objects? Vision Research, 46, 3915–3925.
Enns, J. T. & Rensink, R. A. (1990). Influence of scene-based properties on visual
search. Science, 247, 721–723.
Evans, R. M. (1959). Fluorescence and gray content of surface colors. Journal of
the Optical Society of America, 49(11), 1049–1059.
107
Fleming, R. W. & Bülthoff, H. H. (2005). Low-level image cues in the perception of
translucent materials. ACM Transactions on Applied Perception, 2(3), 346–382.
doi:10.1145/1077399.1077409.
Fleming, R. W., Jensen, H. W., & Bülthoff, H. H. (2004a). Perceiving translucent
materials. In Proceedings of ACM Symposium on Applied Perception in Graphics
and Visualization (pp. 127–134). Los Angeles, CA, USA: ACM.
Fleming, R. W., Torralba, A., & Adelson, E. H. (2004b). Specular reflections and
the perception of shape. Journal of Vision, 4, 798–820.
Gilchrist, A. (2006). Seeing Black and White. Toronto, Canada: Oxford University
Press.
Gilchrist, A. & Bonato, F. (1995). Anchoring of lightness values in center-surround
displays. Journal of Experimental Psychology: Human Perception and Performance, 21(6), 1427–1440. doi:10.1037/0096-1523.21.6.1427.
Gilchrist, A., Kossifydis, C., Bonato, F., Agostini, T., Cataliotti, J., Li, X., Spehar,
B., Annan, V., & Economou, E. (1999). An anchoring theory of lightness perception. Psychological Review, 106(4), 795–834. doi:0.1037/0033-295X.106.4.795.
Hansen, B. G. (2009). Aurora shimmer, meteor flash [Photograph]. Retrieved June
20, 2011 from http://apod.nasa.gov/apod/ap091219.html. NASA Astronomy
Picture of the Day, December 19, 2009.
Horn, B. K. P. (1970). Shape from shading: a method for obtaining the shape of
a smooth opaque object from one view. PhD thesis, Massachussetts Institute of
Technology.
Horn, B. K. P. (1986). Robot Vision. Boston, MA, USA: The MIT Press.
International Telecommunications Union (2011). ITU-R Recommendation BT.601.
Technical report, International Telecommunications Union, R00-SG06. Retrieved
July 14, 2011 from http://www.itu.int/rec/R-REC-BT.601-7-201103-I/en. Section 2.5.1.
Jensen, H. W., Marschner, S. R., Levoy, M., & Hanrahan, P. (2001). A practical
model for subsurface light transport. In L. Pocock (Ed.), SIGGRAPH ’01: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive
Techniques (pp. 511–518). New York, NY, USA: ACM.
108
Joseph, S. & O’Connell, K. (2010). Untitled photograph of clouds at nasa’s
kennedy space center [Photograph].
Retrieved January 17, 2011 from
http://mediaarchive.ksc.nasa.gov/detail.cfm?mediaid=45510.
Kaplan, D. (2011). Moon and Venus over Switzerland [Photograph]. Retrieved July
10, 2011 from http://apod.nasa.gov/apod/ap110202.html. NASA Astronomy
Picture of the Day, February 2, 2011.
Kennedy, J. M. (1976). Sun figure: an illusory diffuse contour resulting from an
arrangement of dots. Perception, 5, 479–481.
Koenderink, J. & Pont, S. (2003). The secret of velvety skin. Machine Vision and
Applications, 14, 260–268. doi:10.1007/s00138-002-0089-7.
Langer, M. S. (1999). When shadows become interreflections. International Journal
of Computer Vision, 34(2/3), 193–204.
Langer, M. S. & Bülthoff, H. H. (2000). Depth discrimination from shading under
diffuse lighting. Perception, 29, 649–660. doi:10.1068/p3060.
Leonards, U., Benton, C., & Scott-Samuel, N. (2008). Gradient-induced depth and
glow: similar processes? Perception, 37, 21. ECVP Abstract Supplement.
Leonards, U., Troscianko, T., Lazeyras, F., & Ibanez, V. (2005). Cortical distinction
between the neural encoding of objects that appear to glow and those that do
not. Cognitive Brain Research, 24, 173–176.
Li, X. & Gilchrist, A. (1999). Relative area and relative luminance combine to
anchor surface lightness values. Perception & Psychophysics, 61(5), 771–785.
doi:10.3758/BF03206896.
Mach, E. (1885). The analysis of sensations. New York, NY, USA: Dover Publications, Inc., 1959 edition.
Mathworks (2009). MATLAB version 7.9.0 [Software]. Natick, MA, USA: The
MathWorks, Inc.
Monet, C. (1872). Impression, soleil levant [Painting]. Retrieved July 14, 2011 from
http://en.wikipedia.org/wiki/File:Claude Monet, Impression, soleil levant, 1872.jpg.
Pemberton, D. S. (2006).
Untitled photograph of bloom around the
stained glass windows in Old Saint Paul’s Cathedral, in Wellington, New Zealand [Photograph].
Retrieved March 8, 2011 from
http://commons.wikimedia.org/wiki/File:Old saint pauls 1.jpg.
109
Phong, B. T. (1975). Illumination for computer generation pictures. Graphics and
Image Processing, 18(6), 311–317.
Ramachandran, V. S. (1988). Perception of shape from shading. Nature, 331,
163–166.
Rembrandt
van
Rijn
(1638).
The
wedding
of
Samson
[Painting].
Retrieved
January
17,
2011
from
http://www.backtoclassics.com/gallery/rembrandtvanrijn/the wedding of samson/.
Rensink, R. A. & Cavanagh, P. (2004). The influence of cast shadows on visual
search. Perception, 33, 1339–1358.
Shreiner, D. & Khronos Group (2009). OpenGL Programming Guide: The Official
Guide to Learning OpenGL, Versions 3.0 and 3.1. Upper Saddle River, NJ, US:
Addison-Wesley Professional, 7th edition.
Spencer, G., Shirley, P., Zimmerman, K., & Greenberg, D. P. (1995). Physicallybased glare effects for digital images. In S. G. Mair & R. Cook (Eds.), SIGGRAPH ’95: Proceedings of the 22nd Annual Conference on Computer Graphics
and Interactive Techniques (pp. 325–334). New York, NY, USA: ACM.
Strazza, G. (c. 1850). The veiled virgin [Sculpture]. Retrieved July 3, 2011 from
http://en.wikipedia.org/wiki/File:Veiled virgin 400.jpg. First known recorded
report of statue in 1856.
Thurstone, L. L. (1927a). A law of comparative judgment. Psychological Review,
34, 273–286.
Thurstone, L. L. (1927b). Psychophysical analysis. American Journal of Psychology, 38, 368–389.
Todd, J. T. (2004). The visual perception of 3D shape. Trends in Cognitive Sciences,
8(3), 151–121.
Treisman, A. & Souther, J. (1985). Search asymmetry: a diagnostic for preattentive
processing of separable features. Journal of Experimental Psychology: General,
114(3), 285–310.
Ullman, S. (1976). On visual detection of light sources. Biological Cybernetics, 21,
205–212. doi:10.1007/BF00344165.
Wallach, H. (1963). The perception of neutral colors. Scientific American, 208(1),
107–116.
110
Ward, G. & Shakespeare, R. (1998). Rendering with RADIANCE: the art and
science of lighting visualization. San Mateo, CA, USA: Morgan Kaufmann.
Wolfe, J. M. & Horowitz, T. S. (2004). What attributes guide the deployment of
visual attention and how do they do it? Nature Reviews Neuroscience, 5, 1–7.
Yoshida, A., Ihrke, M., Mantiuk, R., & Seidel, H.-P. (2008). Brightness of the
glare illusion. In S. Creem-Regehr & K. Myszkowski (Eds.), Proceedings of ACM
Symposium on Applied Perception in Graphics and Visualization (pp. 83–90).
Los Angeles, CA, USA: ACM.
Zavagno, D. (1999). Some new luminance-gradient effects. Perception, 28, 835–838.
doi:10.1068/p2633.
Zavagno, D., Annan, V., & Caputo, G. (2004). The problem of being white: testing
the highest luminance rule. Vision, 16(3), 149–159.
Zavagno, D. & Caputo, G. (2001). The glare effect and the perception of luminosity.
Perception, 30, 207–222.
Zavagno, D. & Caputo, G. (2005). Glowing greys and surface-white: the
photo-geometric factors of luminosity perception. Perception, (pp. 261–274).
doi:10.1068/p5095.
Zhang, R., Tsai, P.-S., Cryer, J. E., & Shah, M. (1999). Shape from shading: a
survey. IEEE Transactions on Pattern Analysis and Machine Intelligence, 21(8),
690–706.
Zhukov, S., Iones, A., & Kronin, G. (1998). An ambient light illumination model.
In G. Drettakis & N. Max (Eds.), Rendering Techniques ’98 (pp. 45–55). Vienna:
Eurographics Workshop on Rendering.
111