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Image Super-Resolution Based on Honey-Bee Mating Optimization Algorithm

Saeideh Sarmadi, S.M. Reza Soroushmehr, Shadrokh Samavi Department of Electrical and Computer Engineering

Isfahan University of Technology Isfahan, Iran

Abstract— Super-resolution image reconstruction is a technique to reconstruct a high resolution image from a set of blurred and noisy low resolution images of a scene. Over recent years different methods have been introduced to increase the resolution of an image. Optimization algorithms based on swarm-intelligence have been developed and applied to various engineering fields for several decades. Process of honey bee mating has been considered as an optimization method based on insects behavior. In this paper, we propose a super-resolution method using honey bee mating optimization algorithm. The experimental results show better performance of the proposed algorithm as compared with some other super-resolution methods.

Keywords- Honey-bee mating optimization, registration, resolution, super-resolution.

I. INTRODUCTION In many image processing applications, producing a high

resolution image is required. The term resolution refers to the number of pixels in an image. An image with higher resolution has more pixels and represents more accurate and detailed information [1]. Resolution of an image depends on imaging device. Whatever resolution of an image taken by a sensor increases, the sensor price will increase too [2]. Thus, using a sensor with higher resolution is not a suitable solution. So, In such a case techniques to improve the resolution of images are more considerable.

The process of combining information of several observed low resolution images to obtain a higher resolution image is called super-resolution image formation. Super-resolution are being utilized in several applications like video surveillance, remote sensing, satellite imaging, medical imaging, video standard conversion and etc [3].

The first hypothesis of enhancing an image resolution is existence of multiple low resolution images captured from same scene. These low resolution images are down-sampled, shifted and in some cases are rotated version of the original scene. Super-resolution techniques use given information of different images (i.e. shift and rotation) for image recovery. Hence, super-resolution is possible only if there is relative movement between pixels from one image to another one. Motions between images may be controlled or uncontrolled motions. Therefore, the first stage in some super-resolution

methods is registration. Registration estimates motions among pixels from one image to the others and also it aligns observed low resolution images according to the estimated motion parameters. In this work, we assume that registration stage has already been done and we focus our attention to the second stage of super-resolution. In the second stage, multiple aligned low resolution images are fused into a higher resolution one.

During last decades, numerous super-resolution methods have been proposed [4-10]. Irani and Peleg in [5] introduced an Iterated Back Projection (IBP) method. The idea of the IBP is to start with an estimation of the high resolution image and iteratively refine it by considering a gradient image. Gradient image is the sum of the difference between each low resolution image and the estimated high resolution image. The super-resolution method proposed in [7] is a robust version of IBP and the only difference between them is in the computation of gradient, which is by the median of all errors.

Takeda in [6] proposed a generalization of kernel regression method for image denoising, upscaling, interpolation and fusion. Islam in [8] introduced a spatio-temporal kernel regression method for video super-resolution. Another approach for image super-resolution uses the iterated conditional modes (ICM) algorithm in Bayesian framework based on Markov random field [9].

Optimization algorithms based on swarm-intelligence have been developed and applied to various engineering fields for several decades. In such optimization, the search algorithm is inspired by the process of marriage in real honey-bee. [11]. In this paper, a new approach is presented to enhance the resolution of an image based on honey-bee mating optimization (HBMO) algorithm.

The rest of the paper is organized as follows: In the next section, we briefly describe super-resolution as an inverse problem. The proposed algorithm is explained in section III. Simulation results are presented in section IV and finally section V concludes this paper.

II. PROBLEM DESCRIPTION Super-resolution technique is the fusion of multiple

observed low resolution images into a higher resolution one. Image capturing process as depicted in Fig.1 consists of four following stages: (1) warping, (2) blurring, (3) down-sampling

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and (4) adding with noise. These stages canfollows:

Y DBWX n

Here, X and Y denote the original highand the obtained low resolution image respewarping. Image blurring which may occuprocess is modeled by convolving the imagfilter. In Equation (1) parameter B representsAlso, decimation operator is denoted by D noise signal.

Therefore, super-resolution is an inverse denoising, de-blurring and up-sampling to rresolution image. The goal of a super-resolutrecover the high resolution image, X , froresolution images, Y which is in fact the inprocess. super-resolution techniques consist ofirst step, it estimates relative motion betwresolution images. Then in the second stimages according to the motion parameprevious step and produces a high resolsuccess of super-resolution techniques strongaccuracy of motion estimation. In the next sthat the motion parameters are known. Henreconstruct the high resolution image parameters.

III. PROPOSED ALGORITH

In this section we briefly describe HMBafter that details of the proposed super-resbased on HMBO are explained.

A. HBMO Modelling HBMO algorithm steps are represented

algorithm starts with a set of individuals geThis set composes the initial solutions namethe corresponding fitness of each solutiSolutions are ordered according to their fitnbest one is set as queen. Queen starts matingspeed and energy. After each transition, qenergy decrease according to the following eq

1 1

In these equations, and are quenergy in transition. Also, and are din [0, 1]. In this stage, by using a probability

Xt

WarpW

HR imageFigure. 1. Model of image degradation

n be formulated as

(1)

h resolution image ctively. W denotes

ur during imaging ge with a low-pass s blurring operator. and N denotes the

problem including reconstruct a high tion technique is to om a set of low nverse of imaging of two steps. In the

ween observed low tep, it fuses these eters obtained in lution image. So, gly depends on the section we suppose nce, our goal is to

based on these

HM BO algorithm and solution algorithm

d in Fig. 2. This enerated randomly. ed “drones”. Then ion is calculated. ness value and the g flight with initial queen's speed and quations:

(2)

(3)

ueen's speed and decreasing factors y function defined

in Equation (4), a set of solutiosolutions to form mating pool. , ∆In Equation (4), P Q, D is solution D by Queen Q and between fitness value of queedrone passes the probability fspermatheca. Mating flight is spermatheca will be full or qNext, by applying intermediabest solutions and the selectedare generated (broods). Using produced from parent1 and pa1where Ratio is a scalar in the ra

To improve the new generaand different heuristic functiteration, fitness of heuristic fufunction with larger fitness valimprovement. Then, the best sfound and compared with queethan queen, it is replaced with q

B. Super-Resolution AlgorithmThe pseudo code of propo

based on HBMO algorithm irequired parameters are definqueen's speed and energy, resworker bees. Workers are consiare used to improve broods. Irepresents the capacity of queemaximum number of broods thmating flight is repeated b time

Figure. 2. Honey bee mating

B

pingW

BluringD

Decimation +NoiseYt

LR imagons are selected from the initial

/ (4)

the probability of selecting a ∆ f is the absolute difference en and selected solution. If the function, it is added to queen's continuing until the capacity of

queen's energy reaches to zero. ate crossover operator between d solutions, new set of solutions

following formula, children are arent2: 2 1 (5)

ange [0,1].

ated solutions, mutation operator tions are employed. In each

unctions is updated and heuristic lue gets more chance in solution solution among new solutions is en. If the best solution is better queen.

m osed super-resolution algorithm is illustrated in Fig. 3. Firstly, ned and initialized. S and E are spectively. W is the number of idered as heuristic functions that In this code spermatheca_size n's spermatheca which indicates

hat will be born. In the best case, es.

g optimization algorithm [11]

ge

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Algorithm: Super-resolution image reconstruction Inputs: : Speed of Queen : Energy of Queen : Speed reduction factor : Energy reduction factor : Number of workers : Number of broods Max_iter : Maximum number of iteration Spermatheca_size : Size of spermatheca Begin 1: Generate D drones randomly as initial solutions 2: Calculate drones’ fitness 3: Select best drone and set it as (Queen) 4: While (iteration Max_iteration) 5: While ( E > 0 ) % mating flight 6: Select a drone at random (Di) 7: ∆ | | , prob = ∆ 8: Generate r randomly. 9: IF ( prob r && Ns Spermatheca_size) 10: Add to Spermatheca and set it as Si 11: 1 ; 12: End If 13: S = × S; 14: E = × E; 15 End while 16: For brood = 1 to

17: Apply intermediate crossover 18:

19: Mutate bi

20: Select a heuristic function from list W according to its probability

21: Employ selected worker to improve the bi

22: update the worker’s fitness based on the amount of drone’s improvement

23: End For 24: If

25: Swap bi and Q 26: Generate New drones randomly 27: End while End Output : Q (Queen)

Figure. 3. Proposed super-resolution algorithm

In the main body of algorithm (line (1)), drones are generated randomly as an initial solution. Each drone represents a high resolution image. Their finesses are calculated and the initial solutions are sorted according to their fitness. Then the best one is selected as queen (line (3)). Queen starts mating flight with maximum speed and energy. Each time, if the probabilistic condition (according to Equation (4)) (line (7)) is satisfied and the queen's spermatheca is not full (line (9)), drone (solution) is selected and its sperm is stored in queen's spermatheca (list of selected solutions) to produce child (new solution). denotes the number of selected drones which increases by one (line (11)). Queen's speed and energy decrease by and factors, respectively (lines (13, 14)). While queen has enough energy and spermatheca is not full, mating continues.

In the second half of the pseudo-code, by applying intermediate crossover, broods (new solutions) are produced (line (18)). To improve these broods ( ) mutation operator and

different heuristic functions are employed (lines (19-21)). Heuristic functions are chosen according to their probability. In each iteration, based on the amount of brood's improvement, fitness values of heuristic functions are updated. Proportion to the fitness value, heuristic functions get chance to improve broods (lines (22)). This loop repeats times that equals with the number broods. Then, by calculating fitness of broods, the best brood is found and compares with queen. If it is better than queen, the queen is replaced with it (lines (24,25)). The main loop of program is repeated _ times. consequently, the output of algorithm is the queen which is the best high resolution image in this process.

IV. SIMULATION RESULTS In order to compare the result of reconstructed high

resolution image with the original one, a set of low resolution images is generated from a single 512×512 high resolution image by applying random translations and rotations to the original image. The images are convolved with a 3×3 kernel to simulate the blur due to the image acquisition, and then they are down-sampled by a factor of in each dimension. Thus, low resolution images are obtained according to imaging model presented in Fig.1.

The first low resolution image that has no translation and rotation is used as a reference image in image registration procedure. Fig. 4(a) and 4(b) show the original high resolution and the reference low resolution image respectively.

As mentioned before, we assume that registration stage has already been done. For registration procedure, we use Keren method [10]. Threrfore, estimated motion parameters are available. In our experiments four low resolution images with down-sampling factor of 2 are used. We compare our result with interpolation, iterated back projection (IBP), robust super-resolution (RS) and genetic algorithm (GA) by implementing them on several well-known images. Peak signal-noise ratio (PSNR) is chosen for assessment parameter. The result of interpolation, IBP, RS, GA and the proposed HBMO algorithm for two images are presented in Fig. 4 and Fig. 5. Duo to the lack of space, results of only two images are presented and all of images (high resolution and low resolution) are shown at the same size.

Table Ι shows PSNR comparison of the proposed algorithm for two test images. The results show the improved performance of HBMO algorithm in compare with other super-resolution methods. Also, Simplicity in implementation of HBMO algorithm is another advantage of this algorithm.

TABLE Ι: Comparison of PSNR (dB) of super-resolution methods

Method Image Pepper Barbara

Interpolation 26.3305 23.6570

IBP 25.1511 21.1115

RS 28.7299 23.4968

GA 28.7194 24.1443

HBMO 28.8831 24.1558

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(a) (b)

(c) (d)

(e) (f)

(g) Figure. 4. Super-resolution results for image 'Pepper' (a) Original image, (b) Reference low resolution, (c) Interpolation, (d) IBP, (e) RS, (f) GA and (g) HBMO.

V. CONCLUSION In practice, images captured by a small low cost digital

camera are often blurred and degraded due to limits of the imaging equipments. Therefore, super-resolution techniques are used to produce a high resolution image from a set of low resolution images. In this paper, we presented a novel technique for super-resolution image reconstruction based on honey-bee mating optimization algorithm. Simulation results showed that the proposed algorithm provides better performance in comparison with some other methods in visual quality as well as PSNR.

(a) (b)

(c) (d)

(e) (f)

(g) Figure. 5. Super-resolution results for image 'Barbara'.(a) Original image, (b) Reference low resolution, (c) Interpolation, (d) IBP, (e) RS, (f) GA and (g) HBMO.

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[2] S. Chaudhuri, Super-resolution imaging, Norwell, MA: Kluwer, 2001, p. 2.

[3] P. Milanfar, Super-Resolution Imaging, CRC Press, 2010, p. 22-23. [4] G. Caner, A. M. Tekalp and W. Heinzelman, “Super resolution recovery

for multi-camera surveillance imaging,” in Proc. IEEE International Conference on Multimedia and Expo (ICME '03), vol. 1, pp. I-109-I-112, 2003.

[5] M. Irani and S. Peleg, “Improving resolution by image registration,” CVGIP: Graph. Models Image Processing, vol. 53, pp. 231-239, 1991.

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[6] H. Takeda, S. Farsiu, and P. Milanfar, “Kernel regression for image processing and reconstruction,” IEEE Trans. on Image Processing, vol. 16, pp. 349-366, Feb. 2007.

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