An Entropy-based Method for Color Image Registration

Shu-Kai S. Fan

and Yu-Chiang Chuang

Department of Industrial Engineering and Management, National Taipei University of Technology,

1, Sec. 3, Chung-Hsiao E. Rd. Taipei 106, Taiwan, Taiwan

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:

() ()

(, ) .

(, )

AHB

NMI A B

HAB











where ( ) (log( ( )))

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

 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.









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

overla

ed re

ion









where ,

y indicate the pixel position, r, g, b

represent three different colors, and

(, )

xy and

(, )

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] ,

Sx y h

YSx y k







  





where (, )

y and (, )

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

(, , , )Shk



p for the transformation function that

minimizes the objective function

(, )EDC A B



, i.e.,

() ,

arg min ( , ).

B Transform B

EDC A B













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]

SS

for the scaling parameter,

[45, 45]





for the rotational parameter,

[( /4), ( /4)]

h width h width

[( /4),

k height

(/4)]

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.

(, , , )

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



. 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

420

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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