An Entropy-based Method for Color Image Registration
Shu-Kai S. Fan
1
and Yu-Chiang Chuang
2
1
Department of Industrial Engineering and Management, National Taipei University of Technology,
1, Sec. 3, Chung-Hsiao E. Rd. Taipei 106, Taiwan, Taiwan
2
Department of Industrial Engineering and Management, Yuan Ze University, 135,
Yuan-Tung Rd., Chung-Li City, Taoyuan County 320, Taiwan, Taiwan
Keywords: Image Registration, Entropy, RGB Color Model.
Abstract: In this paper, an entropy-based objective function is developed according to the histogram of the color
intensity difference data. The proposed registration method is to orientate the sensed image toward the
reference image by minimizing the entropy of the color intensity differences by iteratively updating the
parameters of the similarity transformation. For performance evaluation, the proposed method is compared
to two noted registration methods in terms of a suite of test images. The experimental study is conducted to
verify the effectiveness of the proposed method. Through the experimental results, the proposed method is
shown to be very effective in image registration and outperforms the other two methods in terms of the test
image sets.
1 INTRODUCTION
In the research field of image registration, the cross-
correlation method has been widely recognized as a
standard intensity-based method. Cross-correlation is
used for measuring the similarity between the
reference and sensed images over the overlapped
region. Henceforth, the matching region
aforementioned is referred to as the overlapped
region between the reference and sensed images in
this study. There have been proposed several variant
forms of cross correlation, which additionally took
edge information into account for alleviating the
influence arising from image monotony. The
extended cross-correlation, named as the increment
sign correlation, based on the average evaluation of
incremental tendency of brightness in adjacent pixels
was proposed by Kaneko et al. (2002). This
registration method can be used for image scanning,
search and registration over a large scene. Another
well-known intensity-based method, termed the
normalized mutual information (NMI), is constructed
based upon information theory, and it is to measure
the statistical dependency between two random
variables. The NMI method is proposed by
Studholme et al. (1999), as defined by:
() ()
(, ) .
(, )
H
AHB
NMI A B
HAB

where ( ) (log( ( )))
X
H
AE pA is the entropy of
random variable
A and ()pA is the probability
distribution of random variable
A. The MI-based
methods, concerning with the histogram of the
overlapped region between the reference and sensed
images without involving the spatial information of
the relative pixels, may lead to local or even
“premature” optimum solutions to the transformation
model if intensity data in multimodal images are not
spatially invariant. In this light, several modifications
by adding extra information including gradient, edge
and region information have been proposed in the
literature. Herein, an entropy-based method is
proposed, which only makes use of spatial
information on the reference and sensed images
without applying additional spatial features. In
particular, color information is taken into account in
the proposed objective function. The remaining of
this paper is organized as follows. Section 2 provides
the details of the proposed image registration
function and the optimization method. In Section 3,
the experimental registration results obtained by
using the CC method, the NMI method and the
proposed method are compared by means of various
417
Fan S. and Chuang Y..
An Entropy-based Method for Color Image Registration.
DOI: 10.5220/0004210504170421
In Proceedings of the International Conference on Computer Vision Theory and Applications (VISAPP-2013), pages 417-421
ISBN: 978-989-8565-47-1
Copyright
c
2013 SCITEPRESS (Science and Technology Publications, Lda.)
test image sets. Lastly, the conclusion is drawn in
Section 4 and some directions for future research are
given.
2 THE PROPOSED IMAGE
REGISTRATION METHOD
The framework of the proposed image registration
method is pictorially shown in Fig. 1. To begin, two
images under registration are treated as the reference
image and the sensed image where applicable. In the
proposed image registration method, the parameter
set applied to the sensed image would be kept
updated according to the optimization method until a
pre-specified stopping criterion is met. The proposed
objective function (i.e., similarity measure),
constructed based on the color intensity differences
of corresponding pixels between the reference and
sensed images, is used as a yardstick for evaluating
the quality of the parameter set. The transformed
sensed image will be superimposed onto the
reference image according to the obtained parameter
set of the transformation function. The proposed
objective function and the optimization method will
be introduced as follows.
Figure 1: The procedure of the proposed method.
As two images are correctly orientated, it is
reasonable to allege that the pixels around the
corresponding positions (or local neighborhood)
from the images under registration should exhibit
similar intensity patterns in red, green and blue. On
this account, the summation of the absolute
differences of RGB values in the overlapped regions,
intuitively, ought to be minimized. Nonetheless, the
corresponding objects or features are, sometimes, not
represented in the same color representation due to
different modalities on different applications. It may
not be appropriate to directly use the summation of
absolute values of the differences of RGB intensity
values as the similarity measure.
In reality, there always exists color variation to a
certain degree between the sensed and reference
images. The color intensity differences between the
“transformed” sensed image and the reference image
are not possibly all close to zero as expected. Thus, it
is not a practically feasible choice to search for the
best parameter set of the transformation function by
directly minimizing the summation of the intensity
differences of RGB values. The overlapped region of
the two correctly aligned images should contain the
same objects and/or features, but in many practical
situations, the intensity values of RGB over
corresponding pixels may not be homogeneous. In
other words, the corresponding objects or features
obtained from different conditions, sensors or
viewpoints will possibly have different distributions
of the color intensity over the relative pixels.
Idealistically, the differences of the corresponding
pixels in each color are expected as close to a plane
surface as possible but not possible to be perfectly
zero. On this account, we propose to calculate the
entropy of the histogram of the intensity differences
of RGB values over the overlapped region between
the transformed sensed image and the reference
image. The overlapped region of two correctly
aligned images shall have minimum entropy in that
the color intensity difference distribution is
asymptotically convergent from an entropy point of
view. Namely, the reduced uncertainty is quantified
in lower entropy. Herein, the Shannon entropy
(Shannon, 1948) is employed as a measure of
registration for a probability distribution
P , and it is
defined by
-log.
pP
pp

For color images, the similarity measure is proposed
and illustrated as follows. The color intensity
differences on corresponding pixels in the overlapped
region between the reference image and the sensed
image are defined as follows:
(, ) (, ) (, ),
(, ) (, ) (, ),
(, ) (, ) (, ),
(
,
)
,
rRrSr
gRgSg
bRbSb
dxy I xy I xy
dxy I xy I xy
dxy I xy I xy
xy
overla
pp
ed re
g
ion




where ,
y indicate the pixel position, r, g, b
represent three different colors, and
(, )
R
I
xy and
(, )
S
I
xy are the intensity values of the given position
VISAPP2013-InternationalConferenceonComputerVisionTheoryandApplications
418
in the reference image and the sensed image,
respectively. The frequency histogram
(, , )hi jk of
the absolute difference
(, ), (, ), (, )
rgb
dxydxydxy in
the overlapped region counts according to:
(, , ) (, , ) 1,
( , ), ( , ), ( , ),
rgb
hi jk hi jk
i d xy j d xy k d xy



where i, j, k are the intensity values of three different
colors. The histogram is then converted into
probability
(, , )pi jk via dividing it by the
summation of the designed histogram,
(, , )hi jk . The
distribution range of the proposed difference is
different from the one for gray level images. The bin
number needs to be specified instead of the number
of bits for intensity representation in gray level image
registration because the frequency histogram is
extended to 3 dimensions. The entropy of the
intensity difference for color images (denoted by
EDC) between image A and image B is now defined
by:
000
( , ) ( , , ) log[ ( , , )],
jmax
kmax imax
kji
EDC A B p i j k p i j k




where A and B denote the reference and sensed
images, imax, jmax, kmax, are the maximum
numbers of the intensity values for three different
colors, and
(, , )pi jk is the probability of the
intensity difference for color images. The
optimization method will be used to anchor a
possibly lowest value of the objective function
(, )EDC A B for obtaining the best registration result.
If two images are correctly aligned without any
different intensity contrast, the objective function
(, )EDC A B is theoretically zero.
In this paper, it is also assumed that the scene is
far from the camera, so the perspective deformation
between images can be neglected. Under such
circumstances, the similarity transformation function
is employed to transform the sensed image while
aligned to the reference image. The function is
defined as follows:
[cos sin] ,
[sin cos] ,
X
Sx y h
YSx y k




where (, )
x
y and (, )
X
Y are the original location
and the transformed location;
S, θ,

, hk are the
scaling, rotational, and translational parameters for
the sensed image, respectively. The optimization task
attempts to locate the optimal parameter set
T
(, , , )Shk
p for the transformation function that
minimizes the objective function
(, )EDC A B
, i.e.,
ˆ
() ,
ˆ
arg min ( , ).
B Transform B
EDC A B

p
p

To optimize the proposed objective function, the
Powell’s method [9] will be used to solve the
objective function
(, )EDC A B
. To initialize the
search step, the scaling parameter is set to
1.0 , and
the remaining ones are all set to zero. In the next
section, the registration performance of the proposed
method will be assessed in terms of several test
image sets.
3 EXPERIMENTAL STUDY
In this section, an experimental study that evaluates
the proposed image registration method with the
other existing methods, the normalized mutual
information (NMI) method and the cross correlation
(CC) method, will be conducted in terms of different
test image sets. To perform fair comparisons among
different registration methods, the Powell’s method
with the same initial parameter setting and the
similarity transformation are applied to all these three
methods as the optimization tool. The test image sets
are shown in Fig. 2; from left to right are the
reference image and the sensed image, respectively.
The size of test images is of the size
256 256
pixels. For the NMI method, the histogram of the
intensity differences of the corresponding pixels
between the reference image and sensed image is
created with 256 bins due to the 8-bit representation.
To achieve better execution efficiency, the numbers
of bins are set to
32 32 32
for the histogram of
the color intensity differences of the proposed image
registration method.
Four test image sets shown in Fig. 2 are used for
evaluating three image registration methods. To
optimize these three objective functions by using the
Powell’s method, the search range of each parameter
for one-dimensional search is restricted within
[ 0.5, 0.5]
cc
SS
for the scaling parameter,
[45, 45]
cc


for the rotational parameter,
[( /4), ( /4)]
cc
h width h width
,
[( /4),
c
k height
,
(/4)]
c
k height
where width and height are
obtained from the test image size, for the
translational parameter, and a multiple of
1.5 to
the combined direction for pattern search. Note that
AnEntropy-basedMethodforColorImageRegistration
419
A1 A2
B1 B2
C1 C2
D1 D2
Figure 2: Four test image sets used in the experiment.
T
(, , , )
ccccc
Shk
p
is the “incumbent” parameter
setting in each iteration. The stopping criterion used
for halting the Powell’s method is satisfied if the
improvement of the current objective value over the
previous one is less than
4
10
. Once the obtained
parameter set transforms the sensed image outside of
the reference image, meaning no overlapped region
located, the optimization step in the Powell’s method
will be immediately stopped. The first test image set
is obtained from the regular digital camera, and there
exist small translational, rotational and scaling
differences between test images. Therefore, it is
anticipated that all these three methods would align
these two images successfully. Now consider the
registration result of the first image set shown in Fig.
3, which are taken from Dan-Shui MRT station, New
Taipei City. The CC method, the NMI and the
proposed methods produce satisfactory registration
results. In the second test image set, there are many
edge points and some regular patterns in images, and
also there exists a large horizontal translation
between images. The complexity in structure and the
intensity contrast pose a great challenge to image
registration. The resulting images obtained from the
CC method show that the right pillar in the sensed
image is mistakenly aligned to the left one in the
reference image due to the similar pattern between
two pillars. The NMI method yields the non-
overlapped result, meaning that the sensed image is
transformed outside of the reference image. The
proposed EDC method correctly aligns this test
image set through the different color information of
the pillars. The third test image set is the night scene
image set. Apparently, the CC method and the
proposed methods both generate accurate registration
results, and these two combined registration results
are very close to each other. Unfortunately, the NMI
method presents an incorrect result which aligns the
sensed image to the upper right side of the reference
image. For the last test image set, these two images
are very difficult to locate the correct parameter set
because of the limit of the transformation model. The
similarity transformation model can not compensate
for the difference of deformation from different
viewpoints. Therefore, the CC method and the
proposed EDC method can, at best, gain the
approximate parameter set. The combined resulting
image of the NMI method indicates that the sensed
image is transformed outside of the reference image.
Figure 3: Registration results of test image sets returned
by using the CC method, the NMI method.
VISAPP2013-InternationalConferenceonComputerVisionTheoryandApplications
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On the other hand, the proposed EDC method obtains
more correctly registered region on the bottom right
side of the reference image than the CC method. The
proposed method is coded by Borland C++ Builder
6.0. It takes, in general, less than 2 minutes for the
whole image registration process with one test image
pair in the experiment under Intel Core 2 Duo-
2.80GHz platform with 4 GB DDR SDRAM on the
Win7 system.
4 CONCLUSIONS
In this article, a new image registration method with
color information is presented. The new method is
developed based on the entropy of the color intensity
differences of corresponding pixels on the
overlapped region. The proposal attempts to reduce
the effects arising from different image-taking
conditions or sensors while registration. Toward this
end, the color information is taken into account in the
proposed objective function. To help search the
possibly best parameters in the similarity
transformation function, a well-known function
minimization algorithm, called the Powell’s method,
is borrowed from the field of numerical optimization
to solve the proposed objective function. A suite of 4
test image sets, with varying degrees of difficulty and
complexity, serve as the test bed for performance
evaluation. The experimental results show that the
proposed objective function presents more robust
convergence properties than the CC method and the
NMI method. Building upon this research, there are
still a number of interesting topics worth further
study in this area. For instance, non-rigid image
registration can be a very fruitful application area,
and other relevant image processing applications
should take place to further validate the effectiveness
of the proposed method.
REFERENCES
Kaneko, S., Murase, I., and Igarashi, S., 2002. “Robust
Image Registration by Increment Sign Correlation,”
Pattern Recognition, Vol. 35, Pp. 2223–2234.
Shannon, C., 1948. “a Mathematical Theory of
Communication,” Bell Syst. Tech. J. Vol. 27 Pp. 379-
423 and Pp. 623-656, 1948 Reprinted with Correction.
Studholme, C., Hill, D. L. G., and Hawkes, D. J., 1999.
“an Overlap Invariant Entropy Measure of 3D
Medical Image Alignment,” Pattern Recognition, Vol.
32, 1, Pp. 71-86.
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