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Optik 124 (2013) 5447– 5453

Contents lists available at ScienceDirect

Optik

jou rn al homepage: www.elsev ier .de / i j leo

auchy Biogeography-Based Optimization based on lateral inhibition formage matching

iaohua Wanga, Haibin Duana,∗, Delin Luoa,b

State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, Beijing 100191, PR ChinaSchool of Information Science and Technology, Xiamen University, Xiamen 361005, PR China

r t i c l e i n f o

rticle history:eceived 28 October 2012ccepted 23 March 2013

eywords:

a b s t r a c t

In this paper, a hybrid method of Cauchy Biogeography-Based Optimization (CBBO) and Lateral Inhibition(LI) is proposed to complete the task of complicated image matching. Lateral inhibition mechanism isadopted for image pre-process to make the intensity gradient in the image contrastively strengthened.Biogeography-Based Optimization (BBO) is a bio-inspired algorithm for global optimization which isbased on the science of biogeography, searching for the global optimum mainly through two steps:

iogeography-Based Optimization (BBO)auchy mutation operatorateral inhibition (LI)mage matching

migration and mutation. To promote the optimization performance, an improved version of the BBOmethod using Cauchy mutation operator is proposed. Cauchy mutation operator enhances the explorationability of the algorithm and improves the diversity of population. The proposed LI-CBBO method for imagematching inherits both the advantages of CBBO and lateral inhibition mechanism. Series of comparativeexperiments using Particle Swarm Optimization (PSO), LI-PSO, BBO and LI-BBO have been conducted todemonstrate the feasibility and effectiveness of the proposed LI-CBBO.

. Introduction

Image matching is an area of great importance in the field ofmage processing as it is a fundamental task for many applicationsf computer vision such as image registration and image fusion1]. Many image matching algorithms have been developed [1–4]nd they can be classified as image statistics based algorithm ormage properties based algorithm [3]. The former algorithm ana-yzes the attributes of image that reflect the similarity between theemplate and the original image such as absolute difference, meanbsolute difference, square difference, and mean square difference.he later makes use of the image features such as border, uniqueoints, texture, entropy, and energy. The performance of imageroperties based algorithm depends on the quality and stability ofhe selected features, which vary in different situations. The imagetatistics based algorithm makes better performance and widelysed as it is independent from extensive feature extractions.

Image matching is a process of searching in the right sub-imagen the reference image according to the known template. Image

atching algorithm based on image properties has been commonly

sed to detect interesting objects in complex images under variousircumstances. In the matching process, similarity values betweenhe template and all possible positions in the source image have to

∗ Corresponding author. Tel.: +86 10 8231 7318.E-mail address: hbduan@buaa.edu.cn (H. Duan).

030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved.ttp://dx.doi.org/10.1016/j.ijleo.2013.03.124

© 2013 Elsevier GmbH. All rights reserved.

be computed. Therefore, the time cost can be tremendous [4]. Manyglobal optimization algorithms such as Genetic Algorithm (GA) [5],Ant Colony Optimization (ACO) [6], Artificial Bee Colony (ABC) [7],and Particle Swarm Optimization (PSO) [8] can be applied as thesearching strategy to reduce the time cost. In this paper, CauchyBiogeography-Based Optimization [9] (CBBO) is presented to solvethe image matching problem.

BBO is a new algorithm proposed by Simon [9], which emulatesthe geographical distribution and the migration of species in anecosystem. In BBO, every habitat represents a feasible solution. Inorder to find a solution with the best aspects, the concepts and mod-els of biogeography are applied. The Habitat Suitability Index (HSI)is introduced to measure the goodness of the habitat. BBO worksmainly based on two mechanisms: migration and mutation. Withthe migration mechanism, poor solutions can accept a lot of newfeatures, which may improve the quality of those solutions. Fur-thermore, solutions do not have the tendency to clump togetherin similar groups due to its new type of mutation operation inBBO. Elitism operation [10], which can retain the best solutionsin the population from one generation to the next, can also makethe BBO algorithm more efficient in both aspects of migration andmutation.

To avoid the potential weakness lying in the basic mutation

mechanism of the method, the Cauchy mutation operator is inte-grated into the standard biogeography based optimization (CBBO)to enhance its exploration ability and to improve the diversity ofpopulation.

5 ik 124 (2013) 5447– 5453

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its associated probability PS. The mutation rate m(s) is given in thefollowing function proportional to PS:

m(s) = mmax(1 − Ps

Pmax) (3)

448 X. Wang et al. / Opt

In this paper, Lateral Inhibition [11] (LI) is introduced into CBBO.he hybrid model is named as Biogeography-Based Optimizationased on Lateral Inhibition (LI-BBO). The lateral inhibition mech-nism is discovered and verified by Hartline [11] and his researcheam when they carried out an electrophysiology experiment onhe limulus’ vision. It has been used in the field of image edgextraction, image enhancement, etc. With the lateral inhibitionechanism, the characters of the original image and the position of

xtracted edge are more stable. Even if variable intensity of illumi-ation changes the gray of the image, the edges can still be extractedffectively with the lateral inhibition. The comparative results showhat the proposed method LI-CBBO, which combines the advan-ages of both CBBO and LI, manifests better performance comparedo other bio-inspired algorithms.

The remainder of this paper is organized as follows. Section introduces the principle of CBBO with Cauchy mutation opera-or and elitism. In addition, the correlation function used in thelgorithm is presented this section. Section 3 proposes the princi-le of the LI. In section 4, the detailed implementation proceduresf the proposed LI-CBBO algorithm for image matching are speci-ed, followed by section 5, a series of comparative experiments arebtained to verify the effectiveness of the proposed approach. Theoncluding remarks are contained in the final section.

. Cauchy Biogeography-Based Optimization

.1. Principles of the BBO algorithm

BBO is an optimization algorithm for multimodal optimizationroblems inspired by the geographical distribution and the migra-ion of species in an ecosystem. The problem can be of any arean life as long as a qualitative measure of the suitability of a givenolution can be obtained [12–17]. In this paper, the BBO techniques applied to the image matching problem.

The BBO algorithm is developed based on the mathematics mod-ls of biogeography, which explains how species emigrate andmmigrate within the habitats, how new species arise, and howpecies become extinct. BBO works mainly based on two mecha-isms called migration and mutation. In BBO, a set of habitats aresed to present the candidate solutions, and Suitability Index Vari-bles (SIVs) are introduced to describe each habitat’s feature. HSI ishe evaluation criteria to measure the quality of the solution, analo-ous to fitness in other population-based optimization algorithms.ith migration and mutation mechanisms, the solutions with high

SI tends to share their features with those with low HSI. Thus, poorolutions accept a lot of new features from good solutions. With aabitat H, a vector of SIVs following the migration and mutationteps, the algorithm can eventually reach the optimal solution.

.2. The migration strategy

BBO migration is a probabilistic operator that adjusts each solu-ion Hi by sharing features between solutions. In BBO, the migrationtrategy is similar to the evolutionary strategy in which manyarents can contribute to a single offspring [16]. Migration cane expressed as Hi(SIV) ← Hj(SIV)[17]. Each individual has its own

mmigration rate � and emigration rate �, which are related to theumber of species on the island. The immigration and emigrationates can be calculated as follows when there are S species in theabitat:

ES

�s = Smax

�s = I(1 − S

Smax)

(1)

Fig. 1. The relationship between the number of species and the migration rates.

where E is the maximum emigration rate, and I is the maximumimmigration rate, while Smax is the largest possible number ofspecies that the habitat can support. The immigration and emigra-tion curves are presented in Fig. 1.

The equilibrium species number S0 is reached when the emigra-tion rate � is equal to the immigration rate �. A linear migrationmodel is illustrated in Fig. 1, but it might be more complicated [18].Nevertheless, this simple model gives us a general description ofthe process of immigration and emigration.

Suppose that there are N habitats, Hi is one of them, whose immi-gration rate is �i, and Hj is another habitat whose emigration rateis �j. The migration process can be presented in Fig. 2.

The probability Ps, which represents the probability that thehabitat contains exactly species S, changes from time t to time t + �t.It is updated as follows:Ps(t + �t) = Ps(t)(1 − �s�t − �s�t) + Ps−1�s−1�t + Ps+1�s+1�t (2)

2.3. New mutation strategy with Cauchy operator

Mutation strategy can enhance the diversity of the population,which helps to decrease the chances of getting trapped in localoptima. On the other hand, elitism is applied to guarantee the sur-vival of the best individual(s) [10]. Solutions with very high HSI andvery low HSI have equally lower probability to mutate, while solu-tions with medium HSI have relatively higher probability to mutate.Mutation is a probabilistic operator that randomly modifies SIV of asolution based on its a priori probability of existence. Species countprobabilities PS is used to determine mutation rates. Suppose thata habitat with S species is selected to execute the mutation oper-ation, a chosen variable (SIV) is randomly modified according to

Fig. 2. The migration process of CBBO.

X. Wang et al. / Optik 124 (2013) 5447– 5453 5449

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Fig. 3. The mutation process of CBBO.

here mmax is a user-defined parameter, and Pmax is the maximumpecies count probability.

In order to enhance the exploration ability of BBO, a new muta-ion operator based on Cauchy operator is introduced instead of

odifying a selected dimension of the solution vector randomly.he probability density function of Cauchy distribution can beescribed as follows when the location parameter is 0, and the scalearameter is 1.

(x; 0, 1) = 1

�(

1 + x2) (4)

hen, the Cauchy mutation is expressed as follows:′i (j) = min(Hi) + (max(Hi) − min(Hi)) × � × f (Hi(j); 0, 1) (5)

here Hi(j) is the j-th dimension variable of individual Hi, and1(Hi(j)) indicates that a Cauchy distributed number is generated forach individual. With this method new individuals are generatedn range of min(Hi) to max(Hi).

Suppose that habitat Hi∈SIVR represents a feasible solution toome problem, Cauchy mutation process can be presented in Fig. 3.

. Lateral inhibition mechanism

The lateral inhibition mechanism was discovered and verifiedy Hartline when he carried out an electrophysiology experimentn the limulus’ vision [11] in 1932. Each microphthalmia of limulus’mmateum is regarded as a receptor, which is inhibited by its adja-ent receptors. The inhibited effect is mutual and spatially summed19]. The nearer the certain receptors are, the stronger the inhibitedffect will be.

In retinal image, the intensively excited receptors in illumi-atingly light area inhibit those in illuminatingly dark area moretrongly than the latter to the former [20]. Therefore, the contrastnd the distortion of sensory information are enhanced. Thus therinciple of lateral inhibition can be applied on image processing. Inhis section, lateral inhibition mechanism is adopted to pre-processoth the original and the template images to stress the spatial res-lution and increase the accuracy of the image matching.

The following lateral inhibition model is proposed by Hartlinend Ratliff with series of electrophysiological experiments [21]:

p = ep +n∑

j=1

kp,j(rj − r0p−j), p = 1, 2, .., n; j = 1, 2, ..., n; j /= p. (6)

In order to introduce this mechanism to image processing, Eq.6) is modified to a two-dimensional version as given in Eq. (7).

(m, n) = I0(m, n) +M∑ N∑

˛i,jI0(m + i, n + j) (7)

i=−Mj=−N

here �i,j is the lateral inhibition coefficient of the pixel (m + i, + j) to the central pixel (m,n). I0(m,n) is the original gray value

Fig. 4. The image matching method.

of pixel (m,n). R(x,y) is the gray value of pixel (m,n) obtained bylateral inhibition. M × N is the scale of the receptive field.

In vision nerve system, the relations among one nerve cell toits surrounding nerve cells are relatively stable and consistent, andthey are independent to the directions. Therefore, the weight val-ues should be made mutually symmetric according to the center.Suppose that the size of receptive field chosen in this paper is 5 × 5,the competing coefficient of the lateral inhibition network is asfollows:

R(m, n) = ˛0 × I0(m, n)

+˛1[

1∑j=−1

1∑i=−1

I0(m + i, n + j) − I0(m, n)]

+˛2[

2∑j=−2

2∑i=−2

I0(m + i, n + j) − I0(m, n) −1∑

j=−1

1∑i=−1

I0(m + i, n + j) − I0(m, n)]

(8)

Because the vision nerve cells are situated at the same inputplane and the competing coefficients are close to zero, the templateof lateral inhibition coefficient satisfies:

˛0 + 8˛1 + 16˛2 = 0 (9)

In this paper, we choose ˛0 = 1, ˛1 = −0.025, ˛2 = −0.075 to formthe following matrix as the modulus.

F =

⎡⎢⎢⎢⎢⎢⎢⎣

−0.025 −0.025 −0.025 −0.025 −0.025

−0.025 −0.075 −0.075 −0.075 −0.025

−0.025 −0.075 1 −0.075 −0.025

−0.025 −0.075 −0.075 −0.075 −0.025

−0.025 −0.025 −0.025 −0.025 −0.025

⎤⎥⎥⎥⎥⎥⎥⎦

(10)

After combining the modulus template F with Eq. (8), a new grayscale of the image can be obtained. The image’s edge is extractedby the following equation:

B(x, y) ={

255..........R(x, y) ≥ T

0.............R(x, y) < T(11)

Where T is a user-defined threshold value, and R(x,y) is the grayvalue of pixel (x,y) processed by lateral inhibition.

4. Hybrid CBBO and lateral inhibition

4.1. The fitness function of LI-CBBO

The fitness function is defined to calculate the HSI for each habi-tat in different situations of the problems. As analyzed before, graycross-correlation measurement basing image matching algorithmhas strong ability to suppress noise and the performance of simple

5450 X. Wang et al. / Optik 124 (2013) 5447– 5453

I-CBBO

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Fig. 5. Flow chart of L

alculation. However, it is time-consuming. Therefore, the imageatching method presented in Fig. 4 is chosen to calculate the

tness of CBBO and reduce computational load. This method isuitable for the lateral inhibition processed images.

Where (xo + i, yo + j) and (i,j)are the coordinates of the pixel inhe original image and the template respectively. M×N is the sizef the template. B(xo + i, yo + j) and Bt(i,j) are the gray value of theixel (xo + i, yo + j) and (i,j) respectively processed by equation (11).uppose that the size of the original image is P×Q, the range of theoordinate in the original image for matching is 0 ≤ x < P − M + 1,

≤ y < Q − N + 1. In BBO, the maximum value fitness stands for theest HSI, correspondingly the habitat is the best solution of the

mage matching problem.

.2. The procedure of LI-CBBO

LI-CBBO combines the efficiency of CBBO and the accuracy ofI. In this section, LI-CBBO is applied to the template matchingroblem. The main steps involved in this process are given below:

Step 1: Image pre-processing. Obtain the original image andhe template image, and convert them into grayscale format. Filtermages to remove the noise. Use the lateral inhibition mechanismo pre-process both the original and template images according toquations (8–11) and save the new matrixes of images.

Step 2: Initialize the CBBO parameters. Derive a method ofapping problem solutions to SIVs and habitats, which is prob-

em dependent. Initialize the maximum species count Smax and theaximum migration rates E and I, the maximum mutation ratemax, and an elitism parameter Keep. Initialize the step size used

or numerical integration of probabilities dt.

for image matching.

Step 3: Initialize habitats. Randomly initialize a set of habitatswith each habitat corresponding to a potential solution.

Step 4: Calculate � and �. For each habitat, map the HSI to thenumber of species S, the immigration rate �, and the emigrationrate � according to equation(1).

Step 5: Migrate. Probabilistically use immigration rate �i andemigration rate �i to modify each non-elite habitat. Re-computeeach HSI according to equation (1).

Step 6: Mutate. For each habitat, update the probability of itsspecies count according to Eq. (2). Mutate each non-elite habitatbased on its probability according to Eqs. (3) and (5), and re-compute each HSI according to section 4.1.

Step 7: If the stopping criterion is satisfied, stop the iterationsand output the solution, otherwise, go to Step 4 for the next iter-ation. This loop can be terminated after a predefined number ofiterations, or after an acceptable problem solution has been found.

The detailed flow chart of the proposed LI-CBBO approach forimage matching is shown in Fig. 5.

5. Comparative experimental results

In order to verify the feasibility and effectiveness of our pro-posed algorithm LI-CBBO for image matching, we conduct a setof comparative experiments in this section. The methods are pro-grammed using Matlab 2010 and implemented on a PC with 512 MBof RAM under Windows XP operating system. Based on the tests and

practical experience, the initial parameters of the LI-BBO methodare set as follows. The total population size is decided by the sizeof the images, the number of generations N = 100, the step sizeused for numerical integration of probabilities dt = 1, the maximum

X. Wang et al. / Optik 124 (2013) 5447– 5453 5451

Fig. 6. Matching results for Case 1 (a) Template image (115 × 62); (b) Templateimage processed by the lateral inhibition; (c)Original image (413 × 600); (d) Originali

mm

(s

toFLipo

Fig. 7. Matching results for Case 2 (a) Template image (71 × 82); (b) Template imageprocessed by the lateral inhibition; (c) Original image (333 × 500); (d) Original image

mage processed by the lateral inhibition; (e) Matching result by LI-CBBO.

igration rates I = 1, E = 1, the maximum mutation probabilitymax = 0.001, the number of elitisms keep = 3.

The results of the experiment with the template image115 × 62) shown in Fig. 6(a) and the original picture (413 × 600)hown in Fig. 6(c) are given.

Template and original images processed by the lateral inhibi-ion are shown in Fig. 6(b) and (d). It is obvious that the edgef the image is enhanced and the detail loss of image is avoided.rom the experiment results given in Fig. 6(e), it is clear that the

I-CBBO method can certainly find the location of the templaten the original image successfully and accurately. One more com-lex case is given in Fig. 7 to enhance the function of LI-CBBOptimization.

processed by the lateral inhibition; (e) Matching result by LI-CBBO.

From the experimental results shown in Fig. 6 and Fig. 7it is obvious that the spatial resolution of the images can bestressed and the edge information is enhanced as well. Theimage matching problem is solved effectively with the LI-CBBOalgorithm. The results confirm that our proposed method isstable for solving image matching problems in different situa-tions.

Further experiments are given in Fig. 8 and Fig. 9 to verify thestability and advantage of the LI-CBBO. For each case, the algo-

rithm runs for 10 times independently and the evolutionary curvesare obtained to test the stability of the proposed algorithm. Toprove that the performance of LI-CBBO is better than others, somecompetitive bio-inspired intelligent methods should be chosen.

5452 X. Wang et al. / Optik 124

Fig. 8. Comparative results for case 1. (a) Evolutionary curves of PSO; (b) Evolu-tionary curves of LI-PSO; (c) Evolutionary curves of BBO; (d) Evolutionary curves ofLI-BBO; (e) Evolutionary curves of LI-CBBO; (f) Evolutionary curves in comparison.

Fig. 9. Comparative results for case 2. (a) Evolutionary curves of PSO; (b) Evolu-tionary curves of LI-PSO; (c) Evolutionary curves of BBO; (d) Evolutionary curves ofLI-BBO; (e) Evolutionary curves of LI-CBBO; (f) Evolutionary curves in comparison.

(2013) 5447– 5453

Comparative experiments are conducted by using PSO, LI-PSO, BBO,LI-BBO, and LI-CBBO. Different algorithms are presented to matchthe same template image and original image. For comparison pur-poses, the fitness values of different methods are normalized. Thepopulation sizes and the numbers of iterations of all these algo-rithms are set to be the same.

In Fig. 8 and Fig. 9, the evolutionary curves of the PSO, LI-PSO, BBO, LI-BBO and LI-CBBO are all presented. Among them, theconverging rate of LI-CBBO is the fastest apparently. From the com-parative results, it is obvious that the LI-CBBO converges muchfaster than the other four methods. On the other hand, the BBO con-verges much faster than PSO. Furthermore, the converging rate andaccuracy of our proposed algorithm shows that the LI-BBO methodis more reliable than the other three algorithms and it can solvethe image matching problems effectively under different environ-ments.

6. Conclusions

This paper develops a hybrid algorithm LI-CBBO to characterizeimage features and measure the degree of similarity between orig-inal image and template efficiently and effectively. BBO is a newsimulated biological intelligent algorithm which is of some fea-tures that are unique to the biology-based optimization methods.Cauchy mutation strategy is applied to improve the performancein CBBO. Furthermore, LI-CBBO is much better than CBBO as it useslateral inhibition in the image pre-processing for edge extractionand takes advantages of the accuracy and stability of it. Comparativeexperimental results using the proposed method, basic PSO, LI-PSO,basic BBO, and LI-BBO algorithms are also given to demonstrate thatthe proposed LI-CBBO approach is practicable and effective. It mayfinally be concluded that LI-CBBO is a more effective and robustimage matching method.

Our future work will focus on applying this novel techniqueto more complicated patterns and real-world images in compli-cated noisy environments, and implement this hybrid approachwith embedded processors.

Acknowledgements

This work was partially supported by Natural Science Foun-dation of China (NSFC) under grant #61273054 and #60975072,National Key Basic Research Program of China under grant#2013CB035503, Program for New Century Excellent Talentsin University of China under grant #NCET-10-0021, Aeronau-tical Foundation of China under grant #20125568003 and#20115151019, Top-Notch Young Talents Program of China, andOpen Funding Project of State Key Laboratory of Virtual RealityTechnology and Systems Beihang University under grant #BUAA-VR-13KF-01.

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