Computer Vision
Chapter 9
Texture
Presented by 王夏果 and 傅楸善教授
Cell phone: 0937384214
E-mail: r94922103@ntu.edu.tw
Digital Camera and Computer Vision Laboratory
Department of Computer Science and Information Engineering
National Taiwan University, Taipei, Taiwan, R.O.C.
Introduction
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What does texture mean? Formal approach
or precise definition of texture does not exist!
Texture discrimination techniques are for the
part ad hoc.
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Definition of Texture
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Non-local property, characteristic of region
larger than its size
Repeating patterns of local variations in
image intensity which are too fine to be
distinguished as separated objects at the
observed resolution
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Definition of Texture (cont.)
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For humans, texture is the abstraction of
certain statistical homogeneities from a
portion of the visual field that contains a
quantity of information grossly in excess of
the observer’s perceptual capacity
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Texture Analysis Issues
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Pattern recognition: given texture region,
determine the class the region belongs to
Generative model: given textured region,
determine a description or model for it
Texture segmentation: given image with
many textured areas, determine boundaries
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Statistical Texture-Feature
Approaches
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Autocorrelation function
Spectral power density function
Edgeness per unit area
Spatial gray level co-occurrence probabilities
Graylevel run-length distributions
Relative extrema distributions
Mathematical morphology
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Image Texture Analysis
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Give a generative model and the values of its
parameters, one can synthesize
homogeneous image texture samples
associated with the model and the given
value of its parameters.
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Image Texture Analysis (cont.)
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Verification: verify given image textures
sample consistent with model
Estimation: estimate values of model
parameters based on observed sample
examples of model-based techniques
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Some Model-Based Techniques
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Autoregressive, moving-average, time-series
models (extended to 2D)
Markov random fields
Mosaic models
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Texel
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Texture element, basic textural unit of some
textural primitives qualitatively evaluated
image texture properties
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Some Texture Features
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Fineness
Coarseness
Contrast
Directionality
Roughness
Regularity
Smoothness
Granulation
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Some Texture Features (cont.)
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Randomness
Lineation
Mottled
Irregular
Hummocky
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Take a Break
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Texture and Scale
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For any textural surface, there exists a scale
at which, when the surface is examined, it
appears smooth and textureless. (see from
infinite distance)
As resolution increases, the surfaces appears
as a fine texture and then a coarse one, and
for multiple-scale textural surface the cycle of
smooth, fine, and coarse may repeat.
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Texture and Scale (cont.)
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Thus, texture cannot be analyzed without
frame of reference on scale or resolution.
Texture is a scale-dependent phenomenon.
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Characterizing Texture
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Characterize gray level primitive properties
Characterize spatial relationships between
them
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First-Order Gray-Level Statistics
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Statistics of single pixels
E.g. Histogram, mean, median, variance
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Second-Order Gray-Level
Statistics
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The combined statistics of gray levels of pairs
of pixels in which each two pixels in a pair
have a fixed relative position
E.g. co-occurrence
Gray level spatial dependence: characterize
texture by co-occurrence
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Co-Occurrence Matrix
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The gray level co-occurrence can be
specified in a matrix of relative frequencies Pij
with which two neighboring pixels separated
by distance d occur on the image, one with
gray level i and the other with gray level j
Symmetric matrix
Function of angle and distance between
pixels
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2)
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Co-Occurrence Matrix (cont.)
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Probability of horizontal, d pixels apart pixels
P(i, j, d, 0°) =
#{[(k, l), (m, n)] | k-m = 0, |l-n| = d, I(k, l) = i, I(m,n) = j}
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Probability of 45°, d pixels apart pixels
P(i, j, d, 45°) =
#{[(k, l), (m, n)] | (k-m = d, l-n = -d) or (k-m = -d, l-n = d),
I(k, l) = i, I(m,n) = j}
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Co-Occurrence Matrix (cont.)
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Probability of 90°, d pixels apart pixels
P(i, j, d, 90°) =
#{[(k, l), (m, n)] | |k-m| = d, l-n = 0, I(k, l) = i, I(m,n) = j}
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Probability of 135°, d pixels apart pixels
P(i, j, d, 135°) =
#{[(k, l), (m, n)] | (k-m = d, l-n = d) or (k-m = -d, l-n = -d),
I(k, l) = i, I(m,n) = j}
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0
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Co-Occurrence Matrix (cont.)
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Matrix symmetric: P(i, j, d, a) = P(j, i, d, a)
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Take a Break
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Matrix with Highest Entropy
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When all entries in Pij are equal
Image where no preferred gray-level pairs
exist features calculated from the cooccurrence matrix
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Generalized Gray Level Spatial
Dependence Models for Texture
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Simple generalization: consider more than
two pixels at a time
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Generalized Co-Occurrence
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Strong texture measures take into account
the co-occurrence between texture primitives.
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Texture Primitive
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Connected set of pixels characterized by
attribute set
Simplest primitive: pixel with gray level
attribute
More complicated primitive: connected set of
pixels homogeneous in level, characterized
by size, elongation, orientation, and average
gray level
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Spatial Relationship
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We have a list of primitives, their center
coordinate, and their attributes after the
primitives have been constructed.
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Spatial Relationship (cont.)
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Autocorrelation Function
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Texture relates to the spatial size of the gray
level primitives on an image
Gray level primitives of larger size are
indicative of coarser texture
Gray level primitives of smaller size are
indicative of finer texture
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Autocorrelation Function (cont.)
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Autocorrelation function describes the size of
gray level primitives
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Autocorrelation Function (cont.)
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Autocorrelation Function (cont.)
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Autocorrelation Function (cont.)
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If the gray level on image is relatively large:
texture is coarse, autocorrelation drops off
slowly with distance
If the gray level on image is relatively small:
texture is fine, autocorrelation drops off
quickly with distance
Periodic
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Take a Break
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Digital Transform Methods and
Texture
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In the digital transform method of texture
analysis, the digital image is typically divided
into a set of non-overlapping small square
subimages
The vectors is reexpressed in a new
coordinate system
Fourier transform uses the complex sinusoid
basic set, Handamard transfer uses the
Walsh function basic set, …..
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Texture Energy
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The image is first convolved with a variety of
kernels
Then each convolved image is processed
with a nonlinear operator to determine the
total textural energy in each pixel’s
neighborhood
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Texture Edgeness
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Autocorrelation function and digital transform
both reference texture to spatial frequency
Texture Edgeness: conceive texture in terms
of edgeness per unit area
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Texture Edgeness (cont.)
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Use small neighborhood to detect microedge
Use large neighborhood to detect macroedge
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Vector Dispersion
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Divide the texture into mutually exclusive
neighborhoods
A sloped plane fit to the gray levels is
performed for each neighborhood
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Relative Extrema Density
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Count the number of extrema per unit area
for a texture measure
One dimension, along a horizontal scan
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Relative Extrema Density (cont.)
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Relative minimum:
g(i) ≦ g(i+1) and g(i) ≦ g(i-1)
Relative maximum:
g(i) ≧ g(i+1) and g(i) ≧ g(i-1)
Pixels in a constant run: both minimum and
maximum
Center a square window around each pixel,
and count the number of extrema pixels
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Mathematical Morphology
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Granularity of a binary image F:
# F  Hd
G (d )  1 
#F
#F: number of elements in F
H d : disk structuring element of diameter d
 G(d) measures the proportion of pixel
participating in grains of size smaller than d
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Mathematical Morphology (cont.)
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Scale-k volume of the blanket around a gray
level intensity surface I:
V (k )   ( I k H )(r, c)  ( Ik H )(r, c)
( r ,c )
⊕k: k-fold dilation
Θk: k-fold erosion
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Autoregression Models
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Doing linear estimates of a pixel’s gray level
with the gray levels in the neighborhood
For coarse texture, coefficient will be similar
For fine texture, coefficient will vary widely
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Autoregression Models
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Next gray value aN+1 : linear combination of
synthesized data and noise value
ak : given starting sequence
bk : randomly generated noise image
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Autoregression Models (cont.)
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Two-dimensional autoregression model:
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Autoregression Models (cont.)
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Easy to use the estimator in a node that
synthesized textures from any initially given
linear estimator
Sufficient to capture everything in a texture
But the textures it can characterize are likely
to consist mostly of microtextures
Microtexture: gray level primitives are small,
spatial interaction between primitives is local
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Take a Break
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Discrete Markov Random Fields
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Assumption: the texture field is stochastic
and stationary and satisfies a conditional
independence assumption
When the distributions are Gaussian, each
pixel’s value is a combination of the value in
its neighborhood plus a noise term
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Discrete Markov Random Fields
(cont.)
h: coefficients, computed from texture image with
least-square method
u: joint set of possible correlated Gaussian
random variables
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Random Mosaic Models
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Constructing steps:
1. Provide a mean of tessellating a plane into
cells
2. Assign a property value to each cell
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Structural Approaches to Texture
Models
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Pure structural model: primitives in regular
repetitive spatial arrangements
To describe the texture, describe the
primitives and the placement rules
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Texture Segmentation
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Each region has homogeneous texture, and
each pair of adjacent regions is differently
textured
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Synthetic Texture Image
Generation
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Fractals: shapes that exhibit recursive selfsimilarity
Every fractal can be recursively subdivided
into smaller non-overlapping shapes, each of
which is a scale-down version of the whole,
either in a deterministic sense or in a
statistical sense
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Shape from Texture
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Use image texture gradients to estimate
surface orientation of the observed 3D object
Assumption: no depth changes and no
texture changes in observed texture area,
and no subtextures
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Shape from Texture (cont.)
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Unknown plane where texture observed
Ax + By + Cz + D = 0
where A2  B 2  C 2  1
From perspective projection, 3D point
(x, y, z) with projection (u, v)
x
u f
z
y
v f
z
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Shape from Texture (cont.)
 Df
z
Au  Bv  Cf
•Solving z, …., use similar triangle geometry
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Summary
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Texture: in terms of primitives and spatial
relationships
Qualitatively, shape from texture can work
Quantitatively, the techniques are generally
not dependable
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