International Journal of Emerging Technologies and Engineering (IJETE)
Volume 1 Issue 1 January 2014, ISSN 2348 – 8050
CONGLOMERATION OF REFLECTION SEPARATION METHODS
P.Santhana Kumari and Professor Mr.K.Madhan Kumar.
Abstract
Reflection arises when the photograph of an object is
taken, which is placed behind the glass. The object
also has other reflection problem like surface
reflection. Reflection is the major problem, it can
be eliminated by using many algorithms. Yet they
have some disadvantages. The recently used
constrained optimization technique will overcome
those drawbacks. It formulates the reflection
separation as a energy minimization function
.Energy function is derived from Baye’s rule for a
maximum a posteriori (MAP) estimate. This
appraisal discusses all the existing methods used in
reflection separation and their performance analysis.
Keywords— Independent Component Analysis,
Specular to Diffuse Mechanism, Sparsity Prior and
Maximum a posteriori Estimation.
I. INTRODUCTION
The subject of reflection severance occurs
obviously in our everyday life when a preferred
scene restrains another scene reflected off a
transparent or semi-reflective medium. Common
examples include photographs of scenes taken
through windows or photographs of objects which
are placed inside glass showcases found in retail
store and museum settings. The aim is to solve this
problem of reflection by post processing the images.
The image with reflection consist of two layers, they
are background layer and reflection layer. The
background layer is the image of the object and the
reflection layer is the unwanted scene which is
reflected in the glass. To reduce the effect of
reflection, the polarizer filter is placed in front of the
camera. But this will not completely eliminate the
reflection. Because the polarization depends on the
angle of incidence, the polarizer partially eliminates
the reflection. So in this the image of an object is
taken in same view point but in different polarization
angles, which is done by adjusting the polarizer
which is placed in front of the camera. To
accomplish this goal, a simple assumption is made
that the reflection and background layers are
mutually exclusive. The object also has the other
reflection problem explicitly surface reflection. In
this surface reflection comprise two components
they are diffuse and specular components. In [1] the
two components are separated by independent
component analysis. And in [2] the specular and
diffuse components are analyzed based on color
ratio. And here the normalization for both input
image and diffuse pixels are taken into account. [3]
is based solely on colors. The intensity logarithmic
differentiation of an input image and specular free
image is compared. Specular to diffuse mechanism
used in both [2] and [3]. In [4] the sparsity prior
approach is made that is optimized by iterative
reweighted least squares approach. In [5] the image
gradients classified into background layer gradients
and reflection layer gradients using the information
from the multiple input images. Then formulate this
reflection separation problem as a constrained
optimization problem where the reflection layer, the
background layer and the “matte” that determines
the mixing coefficients of the both layers. Fig
.1.shows the general block diagram of image
dispensation. In general the image of an object is
captured by the camera in which the polarizer is
present. By means of adjusting the polarizer multiple
polarized images are captured. Initially these input
images are read and subsequently the images are
converted into pixels or image gradients using
derivative methods. Again these images are
processed for reflection separation .It can be done by
ICA, specular to diffuse mechanism and
optimization formulation techniques. After that the
preferred reflection separated image is obtained,
which is then displayed in the monitor.
Fig.1.The general block diagram of image
dispensation.
II.LITERATURE REVIEW
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International Journal of Emerging Technologies and Engineering (IJETE)
Volume 1 Issue 1 January 2014, ISSN 2348 – 8050
A.
INDEPENDENT
ANALYSIS
COMPONENT
Shinji Umeyama et… al. [1] used a new separation
technique of diffuse and specular reflections based
on Independent Component Analysis. This can be
realized by observing surface reflection through a
polarizer with several point of references. A stable
separation algorithm was given based on
dichromatic reflection model. In this method the
separation results seem very good in spite of several
approximations introduced such as the unpolarized
diffuse reflection and the distant light source. They
are significantly better than the naive separation only
by a polarizer but the specular reflection cannot be
eliminated completely simply by using a polarizer.
Independent Component Analysis (ICA) is a
nonlinear data analysis method , when some
mixtures of probabilistically independent source
signals are observed, ICA recovers the original
source signals from the observed mixtures without
knowing how the sources are mixed. Since both the
original signals and the mixing coefficients are
unknown, this estimation seems impossible at the
first sight.
An ICA algorithm for reflection component
separation:
By rotating the polarizer, a series of M
surface reflection images are captured. The images
are scanned and vectorized into row vector xj. the
observation matrix X is composed of these row
vectors.
x1
x2
X= ⋮
xM
The problem of separation of diffuse and specular
reflections is to decompose a given observation
matrix X into a product of two matrices, A and S.
However, ICA achieves this by using
the probabilistic independence property of the source
signals. In ICA, the original signals are estimated as
the mixtures of the observed signals, and the mutual
independence of the estimated signals is maximized
by tuning the mixing coefficients. Hence, ICA may
be able to separate reflection components. The
number of different observed signals must be greater
than or equal to the number of the original signals in
ICA. The major disadvantage of this technique is
iterative and sometimes converges difficultly.
B. SPECULAR-TO-DIFFUSE MECHANISM
Robby T. Tan, Ko Nishino et... al.[2]
introduced specular-to diffuse Mechanism. To
separate the reflection components of uniformly
colored surfaces from a single input image. To
accomplish this, use the method on chromaticity,
particularly on the distribution of specular and
diffuse points in maximum chromaticity-intensity
space. Briefly, the method is as follows: Given a
single colored image taken under a uniformly
colored illumination, first identify the diffuse pixel
candidates based on color ratio and noise analysis,
particularly camera noise.
Color ratio,
=
(5)
u is the scalar value.
Chromaticity,
σ(x) =
(1)
( )
Let d and s be row vectors representing diffuse and
specular reflection images; the matrix S is composed
of these vectors:
d
S=
(2)
s
From (2) the mixing matrix A can be written as
1 f(ψ )
1 f(ψ )
A=
(3)
⋯
1 f(ψ )
Thus,
X = AS
(4)
( )
( )
σ(x) =
( )
Maximum chromaticity,
( )
̅( )
( )
( )
(6)
(7)
is a color vector. is a maximum chromaticity.
Normalize both input image and diffuse pixel
candidates simply by dividing their pixels values
with known illumination chromaticity. Color
constancy algorithms can be employed to estimate
the illumination chromaticity. From the normalized
diffuse candidates, estimate the diffuse maximum
chromaticity by using histogram analysis. Having
obtained the normalized image and the normalized
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International Journal of Emerging Technologies and Engineering (IJETE)
Volume 1 Issue 1 January 2014, ISSN 2348 – 8050
diffuse maximum chromaticity, the separation can
be done straightforwardly using a specular-to-diffuse
mechanism, a new mechanism which is introduced.
Fig. 2 shows the flow diagram of specular-to-diffuse
mechanism. Given an input image of uniformly
colored surfaces, at first group the pixels of the
image based on their color ratio (u) values. Then, for
every group of u, identify the diffuse point
candidate, which implies identifying the diffuse
pixel candidates. Using estimated illumination
chromaticity, normalize all diffuse pixels candidates
as well as the input image. Based on the normalized
diffuse pixel candidates, using histogram analysis.
Calculate a unique value of normalized diffuse
maximum chromaticity. By knowing the normalized
diffuse chromaticity, separate the normalized input
image by using the specular-to-diffuse mechanism,
producing normalized diffuse and specular
components. Finally, to obtain the actual
components, multiply both normalized components
by the estimated illumination chromaticity. The
method can be implemented to handle multicolored
surfaces by using color-ratio or hue-based color
segmentation; both color ratio and hue value will be
independent from specularity if the specular
reflection component is pure white.
Fig.2. Flow diagram of specular-to-diffuse
mechanism
Finally, renormalize the reflection components to
obtain the actual reflection components. Fig. 3(a)
shows the estimation of actual diffuse maximum
chromaticity for Victor KY-F70. Although some
points that, due to ambient light in shadow regions,
produce uncharacterized distribution, the diffuse
chromaticity was still correctly obtained. The
separation result using this camera is shown in
Figs. 3(c) and 3(d). In this method this mechanism is
accurate in separating the reflection components
when given only the diffuse chromaticity of the
normalized image but inaccurate illumination
chromaticity estimation, which implies inaccurate
grouping and inaccurate separation using specular to
diffuse mechanism.
Fig. 3. (a) Diffuse maximum chromaticity estimation
for an image taken by Victor KY-F70. (b) Input
image. (c) Diffuse reflection component. (d)
Specular reflection component.
C.
INTENSITY
LOGARITHMIC
DIFFERENTIATION
Robby T. Tan et... al [3]. used a novel
method to separate diffuse and specular reflection
components, The main insight of the method are in
the chromaticity-based iteration with regard to the
logarithmic differentiation of the specular-free
image. The specular-free image is described as:
İ(X) = ṁ (X) Λ̇(X)
(8)
̇
̇
̇
̇
where I={Ir,Ig,Ib} is the image intensity of the
specular-free image, Λ̇={Λṙ,Λġ,Λḃ}is the diffuse
chromaticity, and ṁ
is the diffuse weighting
factor.
Fig. 4. (a) Normalized input image. (b) Specular-free
image by setting Λ = 0.5 The specular components
are perfectly removed, but the surface color is
different.
Fig. 4a shows a real image of a
multicolored scene. By setting Λ = 0.5 for all
pixels, we can obtain an image that is geometrically
identical to the diffuse component of the input image
(Fig. 4b). The difference between both is solely in
their surface colors. This technique can successfully
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International Journal of Emerging Technologies and Engineering (IJETE)
Volume 1 Issue 1 January 2014, ISSN 2348 – 8050

remove highlights mainly because the saturation
values of all pixels are made constant regarding the
maximum chromaticity, while retaining their hue. It
is well-known that, if the specular component’s
color is pure white, then diffuse and specular pixels
that have the same surface color will have identical
values of hue. Considering a diffuse pixel which is
not located at color discontinuities in Fig. 4a, it is
described
as: I (X ) = m (X ) Λ .The
spatial
parameter (x1) is removed from Λ since the pixel is
not located at color discontinuities. Apply
logarithmic and then differentiation operation on this
pixel, the equation becomes:
( ) + log Λ
log ( ) = log
(9)
These two processes are done iteratively
until there is no specularity in the
normalized image.
 All processes require only two adjacent
pixels to accomplish their task and this local
operation is indispensable in dealing with
highly textured surfaces.
This ability plays an important role as a termination
condition in the iterative framework, which removes
specular components step by step until no specular
reflection exists in the image. All processes are done
locally, involving a maximum of only two
neighboring pixels. In this method the separation
problem in textured surfaces with a complex
multicolored scene can be resolved without requiring
explicit color segmentation .The drawback of this
has computational time and complexity is high.
Given a single colored image, is normalized by the
illumination color using known illumination
chromaticity, which produces an image that has a
pure white specular component. Using this image,
generate a specular-free image by simply shifting the
intensity and maximum chromaticity of the pixels
nonlinearly while retaining their hue. This image has
diffuse geometry exactly identical to the diffuse
geometry of the input image; the difference is only
in their surface colors. Thus, by using intensity
logarithmic differentiation on both the normalized
image and its specular-free image, then determine
whether the normalized image contains only diffuse
pixels.
D. USER ASSISTED SEPARATION:
In [4] Anat Levin and Yair Weiss et. al... introduced
a quantitative comparison of different likelihood
models and different filters sets. In this paper, a
technique that works on arbitrarily complex images
but the problem is simplified by allowing user
assistance. The user manually mark certain edges
(or areas) in the image as belonging to one of the
two layers. a hundred edges. Each marked edge
gives an additional constraint for the problem. least
squares problem reweighted by the previous step
solution. A prior derived from the statistics of
natural scenes, one can obtain on the statistics of
natural scenes it use a prior on images that is based
on the sparsity of derivative filters. This sparsity
prior is optimized using the iterative reweighted
least squares (IRLS) approach, which poses the
problem as a sequence of standard least squares
problems, each excellent separations using a
relatively small number of labeled gradients.
The input image I(x) is a linear combination of two
unknown images the image behind the glass, I1 and
the image reflected by the glass, I2. These two
images sum linearly as
log
( )=
log
( )
(10)
Fig. 5. Flow diagram of separation method
Fig. 5. illustrates the basic idea of separation
method.
 First, given a normalized image, a specularfree image is generated.
 After that, the diffuse verification verifies
once again whether the normalized image
has diffuse-only pixels.
( , )=
( , )+
( , )
(11)
Figs.6 shows the input images with labeled
gradients and our results. In this compare the
Laplacian prior and the sparse prior, versus the
number of labeled points. The Laplacian prior gives
good results although some ghosting effects can still
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International Journal of Emerging Technologies and Engineering (IJETE)
Volume 1 Issue 1 January 2014, ISSN 2348 – 8050
be seen (i.e., there are remainders of layer 2 in the
reconstructed layer 1). These ghosting effects are
fixed by the sparse prior. Good results can be
obtained with a Laplacian prior when more labeled
gradients are provided. In this method sparcity prior
is the supervised approach, which will translate to
finding a likelihood function that when combined
with user marks, will minimize the error of
decomposed images but the amount of user
interaction required to achieve good results is still
quite large.
Fig. 6. Comparing Laplacian prior with a sparse
prior. (left) When a few gradients are labeled, the
sparse prior gives noticeably better results. (right)
When more gradients are labeled, the Laplacian
prior results are similar to the sparse prior.
E.
CONSTRAINED
OPTIMIZATION
TECHNIQUE
It is difficult to directly measure the physical
quantities from images without prior knowledge [4].
Such physical quantities could be indirectly
estimated by incorporating them as unknown
variables into an optimization formulation for
reflection separation. However, this would make the
optimization formulation overcomplicated. To
address these issues a reflection model is introduced
which is based on a smooth alpha matte assumption.
a. Reflection Model And Assumptions
The input to our problem consists of multiple
polarized images captured from the same view point
but with different rotation angles of the polarizer.
For each input image, we model the effect of
reflection by the following equation for each of three
color channels:
Ii(x) = αi(x) R(x) + B(x)
(12)
where Ii, R and B are the input image, reflection
layer and background layer, respectively, x is pixel
coordinates, i is an image index and αi is a matte that
represents the amount of reflection remaining in
each of the polarized input images.
b. Gaussian Pyramid Construction
Each input image Ii(x) is downsampled to construct the Gaussian image pyramid.
At each scale, the mask image and reflection guide
map are built. This image is used as the base for the
preceding operations.
Assumptions:
1. The gradients of the reflection layer and those of
the background layer are mutually exclusive.
2. Spatial variation of αi within an image is smooth,
that is, ∇αi(x) = 0. This assumption comes from the
fact that we are targeting at planar (smooth) surface
reflection for which varies smoothly with the
variation of the angle of incidence and other physical
quantities.
c. Guide Map Computation And Mask Image
Computation
Reflection Guide Map can be computed
using a formula given below:
∇Ii(x) = R(x) ∇αi(x) + αi(x) ∇R(x) + ∇B(x)
(13)
Where ∇ = (∂/∂x, ∂/∂y)T is the gradient operator.
Spatial variation of αi within an image is smooth,
that is, ∇αi(x)=0.
Therefore this equation can be rewrite as
∇ (x)
(x)∇R(x)or∇B(x) if max ∇ (x) ≥ t
=
(x)∇R(x) + ∇B(x)
otherwise
where maxj∣∇Ij (x)∣ is the maximum magnitude of
the gradient among all ∇Ii(x) and t is the threshold
for image gradients in the first assumption. The
threshold is determined by selecting the top two
percentages of pixels which have the largest gradient
magnitudes among all pixels in the input images.
Note that according to this Equation, the
contribution of ∇B(x) to ∇Ii(x) is fixed for all input
images, while that of ∇R(x) varies depending on the
values of αi(x). Hence, if the variance of ∇Ii(x) over
the input images is large, it is likely that the gradient
∇Ii(x) is from the reflection layer. Similarly, if the
variance of ∇Ii(x) over the input images is small, it
is likely that the gradient ∇Ii(x) is from the
background layer. Therefore, the large gradient
pixels, that is, the pixels with maxj∣∇Ij (x)∣ ≥ t can
be classified into two layers, depending on their
gradient variances over the images. We construct a
mask image M(x) which identifies the pixels with
large gradients: M(x) = 1 if maxj∣∇Ij (x)∣ ≥ t, and
M(x) = 0 otherwise. The mask image consists of two
parts, MR(x) and MB(x), which indicates the large
gradient pixels from the reflection layer and the
background layer, respectively.
d. Optimization Formulation
Formulate reflection separation as an energy
minimization problem. Our energy function is
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International Journal of Emerging Technologies and Engineering (IJETE)
Volume 1 Issue 1 January 2014, ISSN 2348 – 8050
derived from Bayes’ rule for a maximum a posteriori
(MAP) estimate together with the soft constraints
from the reflection guide map:
max
, ,
Where
L(I |α , R, B)
=
=
+
+
‖ (x) − (
+ B(x))‖
L(α )
(L( I |α , R, B)) +
L(R)
L(B)
L(α )
(x)R(x)
‖α (x) − α (x)‖
+ γ ‖∇ (x)‖
L(R)
=
∉
‖∇R(x)
− ∇R (x)‖ +γ ‖∇R(x)‖
L(B)
=
Intensity diff, (c) sparsity prior, (d)ICA , (e) Input
images, (f) Ground truth (from left to right).
Table.1.Rmse Comparison Table
(15)
(16)
(17)
Results of various
methods
RMSE
of
background
layer
RMSE of
reflection
Layer
(a)MAP
6.11
9.48
(b)Intensity diff
12.21
19.67
(c) sparsity prior
12.02
13.43
(d) ICA
76.65
69.85
MAP method achieved the lowest RMSE compared
to three previous methods that is; it generated the
separation results closest to the ground truth layers
than the three others.
4. CONCLUSION
(18)
‖∇B(x)
− ∇B (x)‖ +γ ‖∇B(x)‖
L(I |α , R, B) is the data term. L(α ) , L(R) and L(B)
are the terms that reflect the soft constraints and
(x), R(x) and
regularization for Unknowns
B(x),respectively. λ , λ and λ are weights for
L(α ), L(R) and L(B). γ1,γ 2 are balancing between
the soft constrain and regularization for each
(x), R(x) and B(x).
3. RESULTS AND DISCUSSIONS
For each reconstructed layer, root mean square error
(RMSE) is calculated which quantifies the difference
between an estimated image and a ground truth
image. Following Table.1 summarizes the RMSEs
for the examples illustrated in Figs.8.In Fig.8.The
RMSEs with respect to the ground truth layers are
shown.
Fig. 8. Reflection separation results for a synthetic
example with spatially-varying mattes.(a)map, (b)
In this paper, a breif literature survey for reflection
separation is discussed and the RMSE performance
for
various
techniques
MAP,
Intensity
differentiation, sparsity prior, and ICA are having
background layer values of 6.11, 12.21, 12.02 and
(19) respectively, are analysed. The MAP estimate
76.65
provide better performance than other three
methods. In future to get improved RMSE value,
contrast of the image is enhanced. Using contrast
enhacement the hidden details of the image is
obtained so it can generate superior result for
reflection separation.
ACKNOWLEDGEMENT
I would like to express my gratitude to all,
those who gave me the possibility to complete this
paper. I owe a sincere prayer to the LORD
ALMIGHTY for his kind blessings and giving me
full support to do this work, without which this
would have not been possible.
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International Journal of Emerging Technologies and Engineering (IJETE)
Volume 1 Issue 1 January 2014, ISSN 2348 – 8050
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International Journal of Emerging Technologies and Engineering (IJETE)
Volume 1 Issue 1 January 2014, ISSN 2348 – 8050
Fig. 8. Reflection separation results for a synthetic
example with spatially-varying mattes.(a)map, (b)
Intensity diff, (c) sparsity prior, (d)ICA , (e) Input
images, (f) Ground truth (from left to right).
Fig. 6. Comparing Laplacian prior with a sparse
prior. (left) When a few gradients are labeled, the
sparse prior gives noticeably better results. (right)
When more gradients are labeled, the Laplacian
prior results are similar to the sparse prior.
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