This article was downloaded by: [UNIVERSITY OF ADELAIDE LIBRARIES]On: 10 December 2014, At: 08:54Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: MortimerHouse, 37-41 Mortimer Street, London W1T 3JH, UK

Intelligent Automation & Soft ComputingPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/tasj20

Image Super-Resolution Fusion Based onHyperacutiy Mechanism and Half Quadratic MarkovRandom FieldAiye Shi a , Chenrong Huang b , Mengxi Xu b & Fengchen Huang aa College of Computer and Information Engineering , Hohai Universityb Department of Computer Engineering , Nanjing Institute of Technology , Nanjing ,China E-mail:Published online: 01 Mar 2013.

To cite this article: Aiye Shi , Chenrong Huang , Mengxi Xu & Fengchen Huang (2011) Image Super-Resolution FusionBased on Hyperacutiy Mechanism and Half Quadratic Markov Random Field, Intelligent Automation & Soft Computing,17:8, 1167-1178, DOI: 10.1080/10798587.2011.10643219

To link to this article: http://dx.doi.org/10.1080/10798587.2011.10643219

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”)contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensorsmake no representations or warranties whatsoever as to the accuracy, completeness, or suitabilityfor any purpose of the Content. Any opinions and views expressed in this publication are the opinionsand views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy ofthe Content should not be relied upon and should be independently verified with primary sources ofinformation. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands,costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly orindirectly in connection with, in relation to or arising out of the use of the Content.

This article may be used for research, teaching, and private study purposes. Any substantial orsystematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution inany form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Intelligent Automation and Soft Computing, Vol. 17, No. 8, pp. 1167-1178, 2011 Copyright © 2011, TSI® Press

Printed in the USA. All rights reserved

1167

IMAGE SUPER-RESOLUTION FUSION BASED ON HYPERACUTIY MECHANISM AND HALF QUADRATIC MARKOV RANDOM FIELD

AIYE SHI

1, CHENRONG HUANG2, MENGXI XU

2, FENGCHEN HUANG1

1College of Computer and Information Engineering Hohai University

2Department of Computer Engineering

Nanjing Institute of Technology Nanjing, China

Email: ayshi.hhu@gmail.com, ayshi@hhu.edu.cn

ABSTRACT—In the image super-resolution reconstruction (SRR) process, the uncertainty factors such as the accuracy level of registration and the constraint method to solution will affect the reconstructed result. In this paper, we propose an SRR method using the combined hyperacuity mechanism with half quadratic Markov random field (MRF) in the frame of maximum a posteriori (MAP). A steepest-descent optimization algorithm is used to find the high resolution image. In the process of optimization, the initial estimate of high resolution image is firstly obtained by fusing the whole low resolution images inspired by the visual hyperacuity mechanism of flying insects. Then, the registration parameters and high resolution image are implemented jointly in order to reduce the uncertainty of image registration. Moreover, the adaptive regularization method is used to reduce the effect of randomness by man-made adjustment. The experimental results demonstrate our proposed method effective. Key Words: MRF, MAP estimation, Super-resolution Reconstruction, Visual Hyperacuity

1. INTRODUCTION

Resolution enhancement of image is helpful for the extraction and analysis. However, the resolution of image can be degraded because of the limit of density and size of imaging system and the effect of lighting, the movement and uncertainty in signal collection and processing. An effective method to improve the resolution of image is to fuse multiple low resolution images with complementary information, and this technique called super-resolution resolution (SRR). Over the past 20 years, the SRR has been an active research topic in image processing, which is widely used in remote sensing, military scout, video surveillance, medical diagnostics and industrial product detection [1-3].

The image SRR methods can be divided into two categories: frequency domain methods and spatial domain methods. The main idea of SRR methods in frequency domain is by removing alias in frequency to improve the resolution of images. The basic procedure of these methods include: assessment of registration, Fourier transform, image reconstruction and the inverse Fourier transform, and finally the high resolution image can be obtained. The frequency-domain-based SRR method has been firstly proposed by Tsai and Huang in 1984[4]. After that many researchers extended it and improved it [1, 5, 6]. The advantage of this method is its simplicity of theory basis and low computational cost. Because this method can impose in translation motion, and there is

Dow

nloa

ded

by [

UN

IVE

RSI

TY

OF

AD

EL

AID

E L

IBR

AR

IES]

at 0

8:54

10

Dec

embe

r 20

14

1168 Intelligent Automation and Soft Computing

limited capacity of involving prior knowledge, therefore the performance of frequency domain SRR methods is not good when compared with the spatial domain SRR methods.

For spatial-domain SRR, we can obtain the steady solve by adding a constraint condition in the reconstruction. These methods mainly include non-uniform method, iterative back-projection method, POCS method, regularization method, filter method and learned-based method [7-13]. In the regularization method, the representative method is based on statistical reconstruction method, which has a good convergence and the result of reconstruction is only. Therefore, it has wide application.

The chosen priori model in the routine statistical reconstruction method includes GMRF and HMRF models. Hardie et al proposed a joint motion estimation and image SRR method, in which the GMRF model was used [9]. Schultz et al proposed a SRR method for video images using MAP method, in which HMRF is applied. After that, they proposed a observation model based on motion compensation subsampled matrix [10]. Yu He et al proposed a soft MAP blind SRR method [11]. Belekos et al proposed a SRR method for video images using spatially adaptive multichannel GMRF model [12].

Because GMRF model is quadratic function, thus the reconstructed image has over smoothed edge. HMRF model has advantage over GMRF in the preservation of edge; however, the threshold T is not easily determined and chosen by the experience based on the specific object.

Furthermore, in the ordinary SRR method, the initial high resolution estimation is obtained by the bilinear interpolation or high level interpolation of the reference low resolution image. Without using the whole low resolution images, the initial high resolution estimate using this method is not sufficient and the uncertainty information is existed in the reconstructed image. For the above analysis, in this paper, we choose the half quadratic function MRF model (HQMRF). The main feature of this mode is that it can overcome the over smooth such as in the GMRF model and avoid the problem of choosing the threshold such as in the HMRF model. Moreover, the initial high resolution image during the iterative processing is obtained by the hyperacuity mechanism of flying insect and this method can overcome the shortcoming of information deficiency of the routine interpolation of the reference low resolution image.

2. THE PROPOSED IMAGE SRR METHOD

The scheme of proposed method is depicted in Figure 1, which is divided into three modules: image registration module, hyperacuity module and MAP+HQMRF module. Firstly, each low resolution image is registered to the reference low resolution image, and the initial high resolution image is obtained by the principle of hyperacutiy. Then the results of the former model are the input of the MAP+HQMRF model. Finally, the final high resolution estimation is obtained by iterative optimization algorithm.

Figure 1. Scheme of the proposed SRR method

Image registration

Hyper- acutiy

MAP+ HQMRF

High resolution image

Image registration

Low resolution image

Dow

nloa

ded

by [

UN

IVE

RSI

TY

OF

AD

EL

AID

E L

IBR

AR

IES]

at 0

8:54

10

Dec

embe

r 20

14

Image Super-Resolution Fusion Based on Hyperacuity Mechanism and Half Quadratic Markov Random Field 1169

It is important that the accuracy of image registration for image SRR (it is noted that accurate registration is not necessary for image SRR, but this SRR method has large computational cost [13]). The image registration method has feature-based registration method and pixel-based registration method. Although feature-based image registration has widely been used, the complexity and reliability of matching of feature points have not good been solved. Moreover, when the size of reference image and input image are small, the feature-based image registration failed to accomplish because of few feature points. In this work, we adopt the pixel-based image registration method of Keren [14]. This is because this registration method is based on gradient according to from rough to fine strategy, thus it has low computational cost and high accuracy registration. In addition, we carry out jointly registration and SRR in order to reduce the uncertainty in the registration and improve the accuracy of the reconstructed high resolution image.

2.1 Initial High Resolution Estimation Based on Hyperacutiy In the implementation of the proposed method, it is the key problem that how to obtain the

initial high resolution image estimate when to find the final high resolution image using the optimization algorithm. In this work, inspired by the hyperacuity of flying insects, we adopt the hyperacuity mechanism to obtain the initial high resolution estimate. Insects have the ability to extract high resolution information from a coarse matrix of photoreceptors so that they are capable of detecting movements of a fraction of their photoreceptor diameter. This ability was termed as hyperacuity. Hyperacuity is defined as “a project into a cartridge shares a common visual axis and thus views an overlapped sample of the same point in space” [15].

Heiligenberg proposed a simple mechanism to explain hyperacutiy [16]. Suppose there are 2 1M photoreceptors, denoting ,k M M , and the response of thk photoreceptor is a

Gaussian function which is centred at k . Suppose the external stimulation for thk photoreceptor

is denoted as v , then the output of thk photoreceptor for the stimulation 0v is 0b v k , and the

b x is defined as

2 2/21

2x wb x e

w (1)

In this paper, low resolution observed images are supposed virtual compound eye images of insects. The SRR is thought as integration or mosaic of insect’s visual information. Based on the hyperacuity mechanism of insect, the initial high resolution estimation 0x can be obtained by the

equation (1) using the registered images, which is something like the normalized convolution technique [17, 18].

The initial high resolution image obtained by the hyperacuity mechanism of insect has the following advantages:

1) The whole low resolution images are used to reduce the uncertainty otherwise using the interpolation of the reference low resolution image.

2) The final high resolution image is obtained by the iterative optimized method. The initial high resolution estimation has not relation to the final high resolution image in theory, however, the initial high resolution image estimation by the hyperacuity can avoid falling into the local optimized value in the iterative process, and the final high resolution image can approach to the real high resolution image.

Dow

nloa

ded

by [

UN

IVE

RSI

TY

OF

AD

EL

AID

E L

IBR

AR

IES]

at 0

8:54

10

Dec

embe

r 20

14

1170 Intelligent Automation and Soft Computing

2.2 Joint MAP Estimation Based on HQMRF Model

2.2.1 Observation Model In this research, the expression for the thk low resolution image is given by

k k k ky = DHT r x + η 1, 2,...,k K (2)

where ky is an 1 2 1M M lexicographically ordered vector of the thk low resolution image,

and x is an 1 2 1N N lexicographically ordered vector that represents the original high resolution

image of the object/scene. kT is an 1 2 1 2N N N N warping matrix for thk low resolution image

that represents the geometric transformation of the image due to affine transform model camera motion or relative camera position. The 1 2 1 2N N N N matrix H is the blur or the point spread

function matrix, the 1 2 1 2M M N N matrix D denotes the down-sampling operator, kr is the

registration parameter of the kth low resolution image corresponding to the reference low resolution image, kη denotes a lexicographically ordered 1 2 1M M noise field in the thk low resolution

image. K represents the number of low resolution images. Equation (11) can be expressed as follows:

y Wx η (3)

where

1 2, , ,TT T T

k y y y y

1 2

T

k k 1 1 1 2 2 2 k kW D H T r ,D H T r , , D H T r

1 2, , ,TT T T

k η η η η

The above SRR problem is ill posed problem. It can be obtained by the following MAP method:

ˆˆ, arg max Pr ,

arg max Pr , Pr Pr

x,r

x,r

x r x r y

y x r x r (4)

Suppose that the noise is independent and identically distributed (i.i.d) white noise, with zero mean and variance 2 and the signal noise ratio is high and the number of registration parameters is

small. The effect of Pr r is not considered in the SRR. We have

2

21

ˆˆ , arg max ,

arg min log Pr , log Pr

argmin22

Kk k

ck c C

E

V

x,r

k

x,r

x r x r

y x r x

y W r xx

(5)

Dow

nloa

ded

by [

UN

IVE

RSI

TY

OF

AD

EL

AID

E L

IBR

AR

IES]

at 0

8:54

10

Dec

embe

r 20

14

Image Super-Resolution Fusion Based on Hyperacuity Mechanism and Half Quadratic Markov Random Field 1171

where ,E x r is cost function, cV x is some function of a local group points c called cliques,

and C denotes the set of all cliques throughout the image. In the processing of minimizing the cost function, the registration parameter estimation r and

high resolution image estimation x are obtained by the alternatively minimization, such as:

1 1 1ˆ ˆˆ ˆarg max , , arg max ,q q q qE E r x

r x r x x r (6)

where q represents the times of iterative reconstruction. Because ,E x r is not readily differentiable with respect to r for general motion model, the

update of r is performed by the method of [14] with the current estimate ˆ qx in this work.

2.2.2 HQMRF Model In equation (5), the choice of the clique potential cV x is crucial, as it embeds important prior

information about the image to be reconstructed. The prior model can be chosen as

c cc C c C

V x g d x

(7)

where cd x is a local spatial activity measure of the image and has a small value in smooth regions

and a large value at edges. In order to preserve the edge of the reconstructed image, we choose the HQMRF model, whose

potential function is:

22 1 2g n n (8)

where n is the difference between neighboring pixel values. For small value of n, the g n

approaches to the quadratic form, and for large value of n, the g n is linear. HQMRF function is

strictly convex and continuous derivable function, which is satisfied with the seven regularized condition by the definition of edge-preserving by Pierre Charbonnier [19]. Given the registration parameters, the optimization of cost function ,E x r can be using the gradient descent algorithm.

Using above potential function and assuming a first-order MRF neighbourhood, we have

, ,1 , , 1i jd x x i j x i j , , ,2 , , 1i jd x x i j x i j

, ,3 , 1,i jd x x i j x i j , , ,4 , 1,i jd x x i j x i j (9)

Given the current estimation ˆ qkr , then the gradient of ,E x r is given by

21

q qTK k k k kq q

k

g G

kW r W r x yx y (10)

where is a smoothing parameter� the gradient value of qG at location ,i j is given by

Dow

nloa

ded

by [

UN

IVE

RSI

TY

OF

AD

EL

AID

E L

IBR

AR

IES]

at 0

8:54

10

Dec

embe

r 20

14

1172 Intelligent Automation and Soft Computing

2

2

2

2

, 2 , 1, 1 , 1,

2 , 1, 1 , 1,

2 , , 1 1 , , 1

2 , , 1 1 , , 1

qG i j x i j x i j x i j x i j

x i j x i j x i j x i j

x i j x i j x i j x i j

x i j x i j x i j x i j

(11)

In equation (10), how to select the regularization parameter is a key problem. The regularization parameters control the measure of smoothness in the final solution of (5). If the value of is too large, the reconstructed image will be smoothed over. On the other hand, if the value of is too small, the noise will not be filtered out, thus leaving the approximate solution far from converging with the true solution. Hence, there needs to be a proper balance of smoothness and preservation of information when regularization is implemented.

Based on the above analysis, it is desirable to impose small on edges and large to smooth regions for the high resolution image estimation, so that both the edge preservation and noise suppression can be achieved simultaneously. In this paper, we adopt the following adaptive regularization parameters by the Hu he’s conclusion [20]:

2

21 1 2

2

K Kk k k

kk k

k cc C

y V

y W r x

x

(12)

3. IMPLEMENTATION OF THE PROPOSED METHOD

The proposed SRR method has the following steps: Step1: Set iteration number 0q and obtain the initial registration parameters 0r using the

Keren’s method. Step2: Obtain the initial high resolution image by the hyperacuity using 0r and equation (1).

Step3: For 1,2, ,k K , compute the registration parameters qkr according to equation (6).

Step4: Compute the gradient qg x y according to equations (10) and (11).

Step5: Given the step size q , compute 1 ˆˆ ˆ ˆ ,q q q q q qk k g x x x r .

Step6: If 1ˆ ˆ ˆq q qk k k x x x , where is predetermined value, or the set number of

iteration is reached, stop. Step7: Let q=q+1, go to Step 3.

4. EXPERIMENTAL RESULTS AND ANALYSIS

In this work, we firstly use the remotely sensed image to test the performance of our SRR method. The IKONOS multispectral data, Nanjing district, which was acquired in 2002-03-26, is used in this experiment. We choose the blue band (spectral range is 0.45μm -0.52μm) as the original high resolution image, whose size is 256 256 , as shown in Figure 3 (a). In addition, for the sake of the processing, the original high resolution image is rescaled to 8-bit gray images.

Dow

nloa

ded

by [

UN

IVE

RSI

TY

OF

AD

EL

AID

E L

IBR

AR

IES]

at 0

8:54

10

Dec

embe

r 20

14

Image Super-Resolution Fusion Based on Hyperacuity Mechanism and Half Quadratic Markov Random Field 1173

Figure 2. Original high resolution image and low resolution reference image. LEFT: low resolution reference image. RIGHT: original high resolution image

The simulated low resolution images are produced by blurring with a point spread function (PSF), globally shifting, sub-sampling and adding with AWGN noise. The PSF was generated from a Gaussian blur with variance 1.7. The down/up horizontal and vertical sampling ratio are 1 2 4L L . Global shift belongs to the set generated from the Cartesian product of

0,1,2,3 0,1,2,3 . The reference image is shown in Figure 2 (right)

In the experiment, the registration parameters between simulated low remote-sensed images were computed by the Keren’s registration algorithm. In the implementation, in order to speed the registration process and improve the accuracy of the registration, three level of Gaussian pyramid are constructed. Besides, the registration process is finished by the coarse to fine pyramid.

The bilinear interpolation of the referenced image is shown in Figure 2 (c). Bilinear interpolation, GMRF SRR method, HMRF SRR method, POCS method and Hardie’s method are compared with the proposed method, respectively. First order MRF model given in equation (9) is used in GMRF, HMRF and the proposed method. Gradient descent optimization algorithm is also used in GMRF, HMRF method. In the optimization processing of GMRF and HMRF, the choosing of step and regularization parameter are determined by the trial and error to provide the best result. It is not the best choose to use the trial and error method, but this can reduce the computation cost. The simulation results are shown in Figure 3 (a)-(f).

In the GMRF-based MAP super-resolution reconstruction, the selected parameters are as follows: 20q , 2 5 , 1 , 0.05 , and 55 10 . The convergence can be achieved at the

twelfth iteration and the reconstructed image is shown in Figure 3 (b). In the HMRF-based MAP super-resolution reconstruction, the selected parameters are as

follows: 20q , 2 5 , 1.1 , 0.05 , 0.8T , and 55 10 . The convergence can be

arrived at the twelfth iteration and the reconstructed image is shown in Figure 3 (c). For the POCS-based SRR method, we make use of the SRR software [21]. The result of this

method can be seen in Figure 3 (d). In the Hardie’s experiment, the selected parameters are as follows: 20q , the step size

being chosen adaptively, 0.091 and 55 10 . The convergence can be arrived at the twelfth iteration and the reconstructed image is shown in Figure 3 (e).

In the proposed super-resolution reconstruction, the selected parameters are as follows: 20q , 2 5 , 1 , being determined by the equation (12) and 55 10 . In the

hyperacutiy algorithm, w is chosen to be 0.316. The convergence can be achieved at the fourteenth iteration. And the reconstructed image is shown in Figure 3 (f).

Dow

nloa

ded

by [

UN

IVE

RSI

TY

OF

AD

EL

AID

E L

IBR

AR

IES]

at 0

8:54

10

Dec

embe

r 20

14

1174 Intelligent Automation and Soft Computing

(a) (b) (c)

(d) (e) (f)

Figure 3. Results of different SRR methods. (a) Result of bilinear interpolation of the reference image. (b) Result of GMRF method. (c) Result of HMRF method. (d) Result of POCS method. (e) Result of Hardie’s method. (f) Result of the proposed method.

From the Figure 3, it is obvious that the result of the proposed method is better than the other methods considering the aspect of the building and road. We also observe that the result of GMRF, HMRF, and our method are less noisy. However, the reconstructed image using the proposed method is the best one.

PSNR and RMSE Comparisons of all SRR are shown in Table I, respectively. From Table I, we can see that the PSNR value is the largest and the RMSE value of the proposed is the smallest compared with other SRR methods. This shows that our proposed method is effective.

Table I. PSNR and RMSE comparison for different SRR methods

PROJECT PSNR RMSE BILINEAR

INTERPOLATION 24.8780 14.5426

GMRF+MAP 29.9654 8.0960 HBRF+MAP 30.2091 7.8720

POCS 29.7083 8.3392 HARDIE 27.6413 10.5797

PROPOSED 31.3551 6.8990 IDEAL ∞ 0

Dow

nloa

ded

by [

UN

IVE

RSI

TY

OF

AD

EL

AID

E L

IBR

AR

IES]

at 0

8:54

10

Dec

embe

r 20

14

Image Super-Resolution Fusion Based on Hyperacuity Mechanism and Half Quadratic Markov Random Field 1175

In the second experiment, we use the real low resolution image sequences to test each SRR methods. The former 20 frames of the DISK image sequences are chosen in the experiments, which has only global translation, and the resolution factor is 4 [22]. In order to the fairness, the Keren’s registration method is applied to each SRR method. The result of each SRR method is shown in Figure 4.

In the GMRF-based MAP super-resolution reconstruction, the selected parameters are as follows: 20q , 2 5 , 2 , 0.05 , and 55 10 . In the HMRF-based MAP

super-resolution reconstruction, the selected parameters are as follows: 20q , 2 5 , 1.4 ,

0.05 , 0.5T , and 55 10 . For the POCS-based SRR method, we also make use of the SRR software [21]. In the experiment of Hardie’s method, the selected parameters are as follows:

20q , the step size being chosen adaptively, 0.07 and 510 . In the proposed

super-resolution reconstruction, the selected parameters are as follows: 20q , 2 5 , 1.3 ,

being determined by the equation (12) and 510 . In the hyperacutiy algorithm, w is chosen 0.361.

Because no ideal high resolution image can be used, the PSNR and RMSE cannot be computed for real low resolution video. But from the Figure 4, we can see that the result of bilinear interpolation is the worst compared with other SRR methods because only the reference image is used. POCS-based method has the better quality than that of bilinear interpolation method and the worst quality than those of other methods. From the Figure 4, we can also see that the proposed SRR method has the better quality than those of other SRR methods and the words of the reconstructed applying with the proposed method has better definition. This shows that the proposed method is effective for real low resolution image sequences perceptually.

5. CONCLUSION

In this work, we try to introduce the hyperacuity principle of the insect into the image SRR. By the combined the MAP and HQMRF model, the registration and high resolution image can be obtained jointly, which can reduce the uncertainty in the SRR and improve the quality of the reconstructed image. For the experiments of the simulated low resolution images and real video sequences, the proposed method is effective from the objective analysis and subjective evaluation. It is necessary to point out that the computation cost is large when the initial high resolution estimation is obtained using the principle of the hyperacuity. Therefore, it is important to find the balance between the complexity and the quality of the reconstructed image. This work can be done in future work.

ACKNOWLEDGEMENT

This paper was supported by National Natural Science Foundation (NSF) of China (No.60774092, 60872096) and the Fundamental Research Funds for the Central Universities (No.2009B20614).

REFERENCES

1. S. C. Park, M. K. Park, M. G. Kang. Super-resolution image reconstruction: a technical overview [J]. IEEE signal processing magazine, 20(3):21-36, 2003.

2. S. Farsiu, D. Robinson, M. Elad, et.al. Advances and challenges in super-resolution[J]. International Journal of Imaging Systems and Technology, 14(2):47-57, 2004.

3. P. Milanfar. Super-resolution imaging. CRC Press, 2011.

Dow

nloa

ded

by [

UN

IVE

RSI

TY

OF

AD

EL

AID

E L

IBR

AR

IES]

at 0

8:54

10

Dec

embe

r 20

14

1176 Intelligent Automation and Soft Computing

(a) (b) (c)

(d) (e) (f) Figure 4 Results of different SRR methods. (a) Result of bilinear interpolation of the reference image. (b) Result of GMRF method. (c) Result of HMRF method. (d) Result of POCS method. (e) Result of Hardie’s method. (f) Result of the proposed method.

4. T. S. Huang, R. Y. Tsai. Multi-frame image restoration and registration[J]. Advances in computer vision and Image Processing, 1(317-339), 1984.

5. P. W. Hao, G. H. Xu. Spatial resolution improvement of digital image in frequency domain [J]. Science in China (Series E), 28(003):235-244, 1999.

6. P. Vandewalle, S.E. Susstrunk, and M. Vetterli. A frequency domain approach to registration of aliased images with application to superresolution. EURASIP Journal on Applied Signal Processing, 2006:1-4, 2006.

7. S. Farsiu, M.D. Robinson, M. Elad, et.al. Fast and robust multiframe superresolution[J]. IEEE Transactions on Image Processing, 13(10):1327-1344, 2004.

8. M. H. Cheng, H. Y. Chen and J. J. Leou. Video super-resolution reconstruction using a mobile search strategy and adaptive patch size [J]. Signal Processing, 91, 1284-1297, 2011.

9. R.C. Hardie, K.J. Barnard, E. E. Armstrong. Joint MAP registration and high-resolution image estimation using a sequence of undersampled images[J]. IEEE Transactions on Image Processing, 6(12):1621-1633, 1997.

10. R. R. Schultz, R. L. Stevenson. Extraction of high-resolution frames from video sequences. IEEE Transaction on Image Processing, 5(6): 996-1011.

11. Y. He, K. H. Yap, C. Li, and L. P. Chau. A soft MAP framework for blind super-resolution image reconstruction [J]. Image and Vision Computing, 27(4):364-373, 2009.

12. S. P. Belekos, N. P. Galatsanos, A. K. Katsaggelos. Maximum a posterriori video super-resolution using a new multichannel image priori [J]. IEEE Transactions on Image Processing, 46(5):872-880, 2010.

Dow

nloa

ded

by [

UN

IVE

RSI

TY

OF

AD

EL

AID

E L

IBR

AR

IES]

at 0

8:54

10

Dec

embe

r 20

14

Image Super-Resolution Fusion Based on Hyperacuity Mechanism and Half Quadratic Markov Random Field 1177

13. M. Ebrahimi, E. R. Vrscay. Multi-frame superresolution with no explicit motion estimation[C]. Proceeding of International Conference on Image Processing, Computer Vision and Pattern Recognition, Las Vegas, USA, 2008.

14. Keren D, Peleg S, Brada R. Image sequence enhancement using sub-pixel displacements[C]. 742-746, 1988.

15. D.T. Riley, W.M. Harmann, S.F. Barrett, et al. Musca domestica inspired machine vision sensor with hyperacuity[J]. Bioinspiration & Biomimetics, 026003, 1-13, 2008.

16. Heiligenberg W. Central processing of sensory information in electric fish [J]. Journal of Comparative Physiology A: Neuroethology, Sensory, Neural, and Behavioral Physiology, 161(4):621-631, 1987.

17. Pham Tq. Robust fusion of irregularly sampled data using adaptive normalized convolution [J]. EURASIP Journal on Applied Signal Processing, 1-12, 2006.

18. A. Katartzis and M. Petrou, “Robust Bayesian estimation and normalization convolution for super-resolution image reconstruction”, IEEE Conference on Computer Vision and Pattern Recognition, pp.1-7, 2007.

19. Charbonnier P, Blanc-Feraud L, Aubert G, et.al. Deterministic edge-preserving regularization in computed imaging [J]. IEEE Transactions on Image Processing, 6(2):298-311, 1997.

20. He H, Kondi Lp. Resolution enhancement of video sequences with simultaneous estimation of the regularization parameter[J]. Journal of Electronic Imaging, 13(3):586, 2004.

21. http://lcav.epfl.ch/software/superresolution 22. http://users.soe.ucsc.edu/~milanfar/software/sr-datasets.html

ABOUT THE AUTHORS

A. Shi is an associate professor at the College of Computer and Information Engineering, Hohai University, China. He received his PhD in hydroinformatics from Hohai University in 2009. His current research interests include image fusion and image superresolution reconstruction.

C. Huang is a professor at the Department of Computer Engineering, Nanjing Institute of Technology, China. She received the PhD degree in Computer Application from Nanjing University of Science and Technology, Nanjing, China in 2005. Her area of research is centered on the image segment and image fusion.

Dow

nloa

ded

by [

UN

IVE

RSI

TY

OF

AD

EL

AID

E L

IBR

AR

IES]

at 0

8:54

10

Dec

embe

r 20

14

1178 Intelligent Automation and Soft Computing

M. Xu is a lecturer in School of Computer Engineering, Nanjing Institute of Technology, P.R. China. She received her MSc in Water Science and Engineering Department of UNSCO-IHE in the Netherlands in 2007. Her current research interests include remote sensing information processing, image processing and analysis, and hydroinfomatics.

F. Huang is an associate professor at the College of Computer and Information, Hohai University, China. His current interest includes telemeter and remote control, signal processing and intelligent system.

Dow

nloa

ded

by [

UN

IVE

RSI

TY

OF

AD

EL

AID

E L

IBR

AR

IES]

at 0

8:54

10

Dec

embe

r 20

14