Fusion of Visible and Infrared Images Based on Spiking Cortical Model in Nonsubsampled Contourlet Transform Domain

Transcription

1 The 014 7th International Congress on Image and Signal Processing Fusion of Visible and Infrared Images Based on Spiking Cortical Model in Nonsubsampled Contourlet Transform Domain Xinyu Liu Being Electro-Mechanical Engineering Institute Being, China Tianzhu Xiang School of Geodesy and Geomatics Wuhan University Wuhan, China Abstract A novel fusion algorithm for spatially registered infrared and visible images fusion based on the spiking cortical model (SCM) in nonsubsampled contourlet transform (NSCT) domain is proposed in this paper. NSCT can effectively surmount the defect of the absence of shift-invariance in contourlet transform to avoid pseudo-gibbs phenomena. Source images are decomposed by NSCT to acquire the coefficients of lowpass subbands and highpass subbands. In the proposed fusion method, the energy of Laplacian that computed by the lowpass subband, which stands for the edge features of the lowpass subband, is employed and inputted to motivate SCM. For the highpass subbands, a modified spatial frequency that calculated through the highpass subband is introduced and applied as the gradient features of the highpass subbands to motivate SCM. Experiments demonstrate the proposed algorithm can make great progress in image fusion, and achieve better effect than conventional methods in both objective evaluation and visual appearance. Keywords- Image fusion; NSCT; SCM; EOL; Spatial frequency; Infrared image. I. INTRODUCTION As is known, image fusion is the combination of redundant information and complementary information from varied imaging sensors in order to create a composite which is more comprehensive and accurate, and which possesses a better description about the scene than any of the single original image [1]. And the fused image is created to enrich image content and to make it more conveniently for the users to detect and recognize targets, and also to improve its situational awareness. Up to now, image fusion, as a significant computer vision and image processing technology, has been widely applied in the target recognition, remote sensing, computer vision, medical imaging, robotics and military applications. The visible and infrared (IR) image fusion is one of the most useful cases, especially in military, remote sensing, security and surveillance fields. Visible images have high spatial resolution and good image quality, while they cannot detect the hidden objects; and infrared images are capable of showing the unseen objects of interest in some poor environment while the image quality is low []. However, the fused image can fully absorb the advantages of the visible and infrared images, and significantly improve the detection and recognizable localization of the target is in the IR image concerning its background that is in the visible image, and make it suitable for subsequent processing tasks. In recent decades, fusion methods experience a fast and enormous development. Among them, various kinds of pixellevel fusion algorithms have been proposed [3, 4]. Among them, the simple fusion method is to average two original images. But this method fails to take into accounts any measures of the information content of the original images. Recently, researchers have been aware that multi-scale decomposition is greatly beneficial for image analysis for the purpose of fusion, such as Laplacian pyramid transform, contrast pyramid transform, discrete wavelet transform (DWT) [5], complex wavelet transform [6] etc. As an excellent method of multi-scale transforms, wavelet transform becomes a widely used multi-scale decomposition (MSD) tool for image fusion because of its outstanding performance for piecewise smooth functions in one dimension and joint information representation at the spatial-spectral domain. But wavelet has its own limits. The two-dimensional (D) wavelets are gained by a tensor-product of one-dimension wavelets, and are expensive for representing steep image transitions such as edges because wavelets aren t able to represent the smoothness along contours. Moreover, wavelets have limited directions, and cannot effectively represent textures and fine details in images. To overcome the limits of wavelets, many new multi-scale transforms are put forward and introduced to image fusion (e.g., bandelet, curvelet, contourlet, etc.). Among them, contourlet transform (CT) [7], which is referred as a true D image representation method, was pioneered by Do and Vetterli in 005, which is accomplished by the combination of the Laplacian pyramid and the direction filter bank [8]. In contrast to the conventional wavelets, contourlet transform is not only multi-resolution and localized, but also multidirection and anisotropy. As a consequence, CT can effectively represent images containing contours and textures. However, due to the upsample and downsample operations, CT lacks of shiftinvariant, so it may bring about pseudo-gibbs phenomena. Therefore, Da Cunha etc. proposed nonsubsampled contourlet transform (NSCT) [9], which retains the excellent characteristics of contourlet transform such as multi-resolution and multi-direction, and what s more, possesses fully shiftinvariant. Consequently, the NSCT is referred as the most This work was jointly supported by the National Science Foundation of China (No ) /14/$ IEEE 747

2 optimal representation of D images. When NSCT is brought into image fusion, much more information can be extracted and infused into the fused image, and the effects of mis-registration on the fusion results can also be effectively weakened. Thus, NSCT is adopted as a MSD tool in this paper. Another core point of MSD-based fusion algorithms is the employed fusion rules, which is vital to image fusion. The common fusion rules can be briefly concluded as pixel- and region-based fusion rules. According to human visual system (HVS), our eyes are insensitive to a single pixel, and image clarity is reflected by pixels in regions. Therefore, the pixelbased fusion rules have some limits. While region-based fusion rules exploit the neighborhood features such as variance, energy, gradient, which reflect the importance of image information, to guide the coefficients selection. In recent years, PCNN [10] and the modified PCNNs such as ICM, SCM [11], which have characteristics of the global coupling and pulse synchronization of neurons so as to make full use of local image information, have a wide application in image processing and are beneficial for the fusion. Researchers have put forward many image fusion methods based on transform domain and PCNN which achieve good performance. However, in most of these methods, single pixel value in MSD domain is often utilized as the input of the neuron directly. Indeed, HVS is sensitive to edges, directional features, etc. rather than individual pixel. So only using single pixel is not enough. It is much reasonable to use some image features to motivate PCNN. In this paper, a novel infrared and visible image fusion method based on SCM which is derived from PCNN and has light computation compared with PCNN is proposed in NSCT domain. The selection rules of the lowpass subbands and the highpass directional subbands are stated in detail, respectively. Experiment results show the proposed method has better effectiveness, and can preserve not only the spectral information of visible image, but the thermal target information of infrared image. The remaining of the paper is organized as follows. Section II briefly reviews the theory of NSCT. Section III describes the model of SCM, a new modified PCNN. Section IV illustrates the proposed fusion scheme in detail using SCM in NSCT domain. And experimental results and analysis are presented in Section V. The conclusions are given in Section VI. II. NONSUBSAMPLED CONTOURLET TRANSFORM To escape frequency aliasing of the CT, enhanced directional selectivity and gain shift-invariance, Da Cunha etc. proposed NSCT achieved by nonsubsampled pyramid decomposition and nonsubsampled filter banks. NSCT removes downsample and upsample during the process of decomposition and reconstruction of image; and instead it is constructed upon nonsubsampled pyramid (NSP) and nonsubsampled directional filter bank (NSDFB). First, the NSP divides the original image into a low-frequency subband and a high-frequency subband. And then the NSDFB splits the highfrequency subband into series of directional subbands. This process is then iterated on the low-frequency subband repeatedly, as displayed in Fig.1. Figure.1.The two stage decomposition framework of NSCT III. SPIKING CORTICAL MODEL Pulse coupled neural network (PCNN) is known as third generation artificial neural networks proposed by Eckhorn in 1990 [1]. In recent years, a series of PCNN-based fusion algorithms have been proposed [13]. But the performance of these methods is limited due to its computational complexity. Traditional PCNN models for image fusion require complex calculations and a huge number of iterations to calculate the values of parameters, and the parameters which depend the quality of image fusion could only be adjusted manually [14]. So kinds of modified PCNN models have been presented, which are more suitable in image processing. Spiking cortical model, namely SCM, pioneered by Zhan et al. [11], is one of the modified PCNN. SCM has fewer parameters than PCNN, and can decrease the computational complexity, describe human visual perception better, and achieve better effect in image processing fields, such as image segmentation [15], image fusion [14, 16], etc. Like traditional PCNN models, the relation between network neurons and image pixels is a one-to-one correspondence. SCM is made up of three parts: the receptive field, modulation field and pulse generator. The SCM model is displayed in Fig.. In Fig., the input signals are divided into two channels. Feeding input is the primary input and linking input is the secondary input of lateral connections with neighboring neurons. The input stimulus S, generally gained by the normalized gray level, is accepted by the feeding input, and the internal activity U unites the feeding input and the linking input. The U is then compared with the dynamic threshold E and E decreases with iteration gradually. And U gathers signals until it exceeds E and then fires the output. Simultaneously the threshold E enlarges greatly. And then the Figure.. The SCM neuron model 748

3 neuron output Y, either the binary value 0 or 1, will be fed back to linking input with a delay of an iteration iteratively. Each neuron will output two states, i.e. firing and nonfiring. In this paper, we take the SCM model which is derived from Zhan et al. s model. The SCM mathematic expression described as follows: U[ n] = fu[ n 1] + S (1 + WpqYpq[ n 1]) (1) pq E [ n] = ge [ n 1] + hy [ n 1] () 1, 1 if > 0.5 Y [ n] = (1 + exp( γ ( U [ n] E [ n]))) 0, else In these formulas, except for the variables mentioned above, others explain as follows: (i, j) is image pixels or neurons position, and n denotes iteration times. W pq is synaptic weight matrix that is used for the linking field and which depends on the distance between neurons. f and g are decay coefficients of U and E, respectively, h is magnitude coefficient of dynamic threshold E, is the parameter of sigmoid function. Sigmoid function has the property of nonlinearity which is used to produce the pulse. Sigmoid curve is similar to the S shape, and its slope increases as increases. Generally speaking, it is difficult to set the iteration number n in traditional PCNN or SCM image processing field. In most researches, the iteration number n is decided by experiments or experience. In Zhan et al. s paper, the iteration number n of SCM is set as 37 times. It s known to all, if n is too large, it will be time-consuming, and if n is too small, the optimal image processing effect could not be obtained because of the losing of the synchronous impulse characteristic of SCM. And those methods whose iteration number n is set as a fixed constant are not applicable to any occasions. To set the iteration number n properly, here we exploit the time matrix [17-19] T, whose size is the same to the external input S and output Y, to adaptively assign the iteration times n. T is defined as: n, if Y [ n] = 1 for the first time T [ n] = T [ n 1], otherwise where T denotes each neuron's first firing time. The time matrix maps the spatial information onto the time information. Time matrix has three possibilities: (1) T is zero if the neuron has never fired; () T is n if the neuron fires at the time of n for the initial time; (3) T remains invariant if the neuron has fired. And the iteration will carry on unless all neurons have fired, that is to say, each element of T is nonzero. Moreover, those image pixels which have the similar intensity values in the source image often enjoy the same or similar firing time. Thus by using time matrix, SCM model can retain space information, but also describe time information of each neuron, including image gray distribution, which will benefit further processing much more. (3) (4) IV. PROPOSED FUSION METHOD The proposed fusion method will be discussed at great length in this section. NSCT is firstly adopted as the multiscale decomposition tool to provide a multi-scale multidirectional image representation, which has an unparalleled advantage over wavelet and can eliminate the pseudo-gibbs phenomena that occur around singularities in contourlet. And then we use SCM which motivated by energy of Laplacian (EOL) in lowpass subband and a modified spatial frequency (MSF) in highpass subband to make an informed decision on the choice of low- and high-pass subband coefficients in NSCT domain. A. Fusion Rules The low-frequency parts include the main outlines information of the sub-images, and the high-frequency components stand for fine details, including the edges, directional features, etc. So the fusion rules are the core of the whole fusion algorithm. So in this paper, we take different rules for lowpass subband and highpass subband. In general, in these SCM-based methods, the single pixel s value in MSD domain is employed as the external stimulus to motivate the neuron. While in reality, HVS is often sensitive to edges, directional features, etc. rather than the single pixel. So only using single pixel is not enough. It will be more reasonable to exploit features to motivate SCM. In this paper, we utilize EOL [0] which represents the edge feature and MSF [1] which denotes gradient energy to motivate SCM in NSCT domain for the first time. The detailed fusion rules can be described as follow. (1) Lowpass subband fusion rule The traditional methods such as average or weighted average obtain poor visual effect and will lose some spectral information. In this paper, we use one of image feature, the energy of Laplacian of image, which can reflect the edge features of the lowpass subbands, to motivate the SCM neurons. The complete mathematic expression of EOL is display in the following equations. EOL + = ( f f ) (5) ii jj i j where f + f = f( i 1, j 1) 4 f( i 1, j) f( i 1, j+ 1) ii jj 4 f( i, j 1) + 0 f( i, j) 4 f( i, j+ 1) f( i+ 1, j 1) 4 f( i+ 1, j) f( i+ 1, j+ 1) where f (, i j ) indicates the NSCT coefficient at (i, j), and fii, f jj denote the energy of Laplacian in i and j direction, respectively. () Highpass subband fusion rule Conventional fusion rules are based on maximum rule, or regional features such as variance, energy and gradient. But they are poor in preserving image details. So we introduce a modified spatial frequency applied as the gradient features of highpass subbands to motivate SCM and generate pulse of (6) 749

4 neurons. Spatial frequency (SF) takes the gradient energy to measures the whole activity of subbands coefficients in the window in rows and columns by using slipping window. In this article, the spatial frequency is improved and extended. The modified spatial frequency (MSF) adds the frequency changes in two diagonal directions besides the computation of variations in vertical and horizontal directions. And so the image information can be reflected more comprehensively. If there is a M N image I, I(i,j) is the pixel gray value located at (i,j), the MSF is defined as: MSF = RF + CF + MDF + SDF (7) where RF, CF, MDF and SDF express the row frequency, the column frequency, the main angular frequency and the auxiliary diagonal frequency, respectively: 1 RF = I i j I i j [ (, ) (, 1)] (8) MN i= 1 j= 1 CF = I i j I i j [ (, ) ( 1, )] (9) MN i= j= 1 MDF = 1 1 I i j I i j [ (, ) ( 1, 1)] (10) MN i= j= SDF = 1 1 I i j I i j + [ (, ) ( 1, 1)] (11) MN i= j= (3) The fused coefficients select As description above, the smaller firing time means the bigger gray value in the time matrix. And so the time matrix can also be used to determine the fusion coefficients. We can select the coefficients of sub-image whose firing time in time matrix is smaller. So we employ single pixel firing time as a determination to choose the coefficients of source sub-images as formula (1). I I, if : T (N) T (N) lk, lk, lk, lk, ir, ir, v, = F, lk, lk, lk, I if T T v, ir, v,, : (N) (N) (1) lk, lk, lk, where I V,, I ir, and IF, denote the NSCT coefficients of l-th layer k-th direction sub-images of visible image, IR image and lk, lk, fused image at (i,j), respectively, T (N) and T (N) denote the ir, V, firing time, N denotes the total iteration times. After fusing all the sub-images through the method above, we can acquire the fused sub-images finally. To guarantee the consistency of all subbands coefficients, we take the consistency checking and adjustment [1] to subbands to optimize the fused coefficients under the majority principle. That is to say, we can handle each pixel like this: if there are at least 6 pixels from infrared image in the 3 3 neighborhood of a pixel, the pixel should be adjusted as the corresponding pixel in infrared image, otherwise, the original coefficients remain unchanged. B. Fusion step The flow chart of our proposed fusion algorithm is shown in Fig.3. Before fusion, all source images must be spatially registered. The detailed fusion process is composed by four steps listed as follows: (1) Perform the NSCT on the spatially registered original infrared and visible images, respectively, and get one lowpass subband image and a group of highpass directional subband images. () Fuse subband coefficients via SCM-based fusion rule: a. The coefficients of the sub-images from infrared and visible images are all normalized between 0 and 1. And calculate EOL as described in formula (5) ~ (6) on lowpass and MSF as described in formula (7) ~ (11) on highpass. Take them as the input of feeding channel to stimulate SCM, respectively. b. Initialize U[0] = Y[0] = T [0] = 0, E [0] = 1, in the meantime, every neuron does not fire. This setting mode is to make neurons activated as quickly as possible, so as to avoid unnecessary void iterations. c. Compute U[ n ], E[ n ], Y[ n ], T[ n] according to formula (1)~(4). d. Complete the step (c) iteratively unless every neurons has been activated, namely each element in T is nonzero. Then, the fused coefficients can be selected via time matrix according to formula (1), and take consistency test. (3) Take the inverse NSCT to reconstruct the fused image. V. EXPERIMENTAL RESULTS AND DISCUSSION To demonstrate the effectiveness of our proposed fusion method, some experiments have been conducted. In this section, we test the algorithm proposed in this paper through two typical groups of visible and infrared visible images. A. Experimental introduction In this paper, the NSCT multi-scale decomposition filter bank and DFB are 9/7 and pkva, respectively, the MSD layers are 5, and directions in every layer are set to be [0,1,3,4,4] from coarser to finer scale, respectively. And the parameters of SCM set via experiments are as follows: f, g Figure.3. The flow chart of the proposed fusion algorithm 750

5 h and γ are assigned to be 0., 0.9, 0, and 1, respectively; weight matrix of linking field is: W=[0.707,1,0.707;1,0,1;0.707,1,0.707]. To demonstrate the advantages of the algorithm proposed in this paper, the proposed algorithm is evaluated and compared with other seven fusion methods: the average method, the Laplacian pyramid (LP) method, the DWT method, the SWT method, the DTCWT method, the Contourlet method, the NSCT method. The later six methods take the absolute maximum choosing rule for high-frequency coefficients and averaging combination rule for low-frequency coefficients. And all multi-scale transform take 3 layers decomposition except NSCT, other parameters are as follows: DWT and SWT take db, CT take [,3,4], 9/7, pkva. NSCT take the same parameters as same as that in the proposed method. For the purpose of better evaluating the effect of the fused images, besides visual observation, we also adopt the objective evaluation method to compare results of all kinds of fusion methods objectively. The paper takes five objective metrics: information entropy (IE) [], mutual information (MI) [3], root mean square cross-entropy (RCE) [], standard deviation (SD) [14], Q [4]. Information entropy quantifies the richness of information in the fused images. If the information entropy is larger, this shows that the fused image owns the more abundant information amount. And mutual information calculates how much information can be transferred to the final fused image from source images. With the value of mutual information increasing, the fused image can obtain more and more information from the source images. The RCE is calculated to describe the degree of the difference between source images and the final fused image. The smaller the RCE is, the more information the fused image extracts from the source images. The standard deviation shows the statistical distribution of fused image and describes the contrast of the fusion image. The larger SD denotes that the distribution of gray level in image is more dispersed, and that the image contrast is bigger, and that the visualization of the information is better. The last metric Q measures the amount of edge information etc. transferred from the original images to the final fused images via a Sobel edge detector. If the Q is bigger, the much more edge information will be preserved in the fused result, and the better performance of fusion will be achieved. B. Performance evaluation The ultimate fused results based on eight methods in this paper are shown in Fig. 4 and 5. From the experiments above, we can easily find that the fusion result based on the proposed method synthesizes much more significant information and brings about less distortion than the fusion results based on other seven methods. In Fig.4, Fig.4 (a) and (b) are visible image and infrared image with respect to the same scene and come from UN Camp images. And fusion results of methods adopted in this paper which are the average method, LP-based, DWT-based, SWT-based, DT-CWT-based, CT-based, NSCT-based and our proposed method are display in Fig.4 (c) ~ (j). (a) Visible image (c) Average method (e) DWT-based (g) DTCWT-based (i) NSCT-based (b) Infrared image (d) LP-based (f) SWT-based (h) CT-based (j) The proposed method Figure.4. The fusion results of UN Camp images; (a) Source visible image; (b) Source infrared image; (c)~(j) Fusion results of the average method, LP-based, DWT-based, SWT-based, DT-CWT-based, CT-based, NSCT-based and the proposed method. From the fusion results display above, the average method has low contrast and loses many details such as the light dots along the road, veins details on the bush. And the DWT-based fusion image and CT-based fusion image exhibit some Gibbs phenomena, especially around people, while SWT-based, DTCWT-based, NSCT-based exhibit better visual quality than them because the later are shift-invariant. So we can conclude that the shift variance caused by the subsampling operator, has a greatly influence on the performance of image fusion. Because of the subsample process, some important information will be lost, and the error that happens during the process of image reconstruction will be expanded. For visual effects, the NSCT-based and our proposed method has better performance, 751

6 they can highlight the objects of interest and preserve the detailed information of the background, especially the proposed method. In the Fig.4 (j), the fused result by our method, contains the more clearly observable people who comes from the infrared image 4(b), and has higher contrast, and preserves the background information better, such as the trees, fences in visible image 4(a). Furthermore, fewer artifacts are injected into the fused image in the fusion process, and the fusion image appears more natural. Table 1 shows evaluation results of eight methods in Fig. 4. The IE of our proposed method reaches maximum, meaning our fused image contains the largest information amount. The MI achieves the good result and only smaller than average method and NSCT-based method, while average method obtains poor visual effect discussed above. So it illustrates that NSCT-based results extracts much more information from the original images. Meanwhile, the RCE of our method obtains minimum, which indicates that our fused image has smaller difference with the source images and comparatively better fusion result. And the SD of our method is maximum, which represents that our fusion result has the best contrast. In addition, Q also has the maximum in our proposed method, which denotes that the method in our paper extracts more edge information from source images and preserves them well. The second simulation displays in Fig.5. Fig.5 (a) and Fig.5 (b) are visible image and infrared image which come from OCTEC images. And Fig.5(c)~(j) are the results of eight fusion methods. From the visual effect, the fused results in Fig.5(c)~(i) preserve little visible source information and center more on the description of the infrared original image, so the seven fusion results are more vague than the one by our method. And the result of the method proposed in this paper not only extracts more target information from infrared image, such as people and fire point, but also obtains more clearly background information, such as the roof of the houses. What s more, the method in the paper fuses more details from source image especially the clouds. Compared with the other seven methods, our method takes full advantages of the two original images, has a better contrast and owns much better visual performance. The objective evaluation results on Fig.5 are listed in Table II. From Table II, the proposed fusion algorithm has better image quality than the fused image of the other methods. Except for MI, the values of IE, SD of our proposed method are biggest and the RCE is smallest. And Q is only smaller than the result by NSCT. So our proposed method can extract the main information and details from original images and infuse them into the final fused image effectively. Moreover, our method also obtains more reasonable global contrast and is much excellent for representing the detailed information such as contours and edges. This result s trend is similar to the first one. From the discussion above, we can see the fused result of our proposed method is strongly correlative with the original images, and it can preserve more image details well, such as edges. And this indicates that our proposed method does well in image fusion for visible and infrared images and outperforms other traditional methods both on visual effect and (a) Visible image (c) Average method (e) DWT-based (g) DTCWT-based (b) Infrared image (d) LP-based (f) SWT-based (h) CT-based (i) NSCT-based (j) The proposed method Figure.5.The fusion results of OCTEC images; (a) Source visible image; (b) Source infrared image; (c)~(j) Fusion results of the average method, LPbased, DWT-based, SWT-based, DT-CWT-based, CT-based, NSCT-based and the proposed method. objective evaluation. So we can conclude that our proposed algorithm in this paper can achieve favorable fusion result for infrared and visible images. VI. CONCLUSION In this paper, a novel fusion algorithm of infrared and visible images based on SCM is proposed in NSCT domain. The excellent characteristics of flexible multi-scale and multidirection of NSCT is combined with the characteristics of global coupling and pulse synchronization of SCM. In addition, we employ image features to motivate SCM, instead of only using the coefficients in conventional PCNN or SCM models 75

7 TABLE I. EVALUATION RESULTS OF EIGHT METHODS FOR UN CAMP methods IE RCE MI SD Q Average LP DWT SWT DTCWT CT NSCT Proposed TABLE II. EVALUATION RESULTS OF EIGHT METHODS FOR OCTEC methods IE RCE MI SD Q Average LP DWT SWT DTCWT CT NSCT Proposed in image processing. The energy of Laplacian, which is used to stand for edge feature in low-pass subbands in NSCT domain, is applied to stimulate SCM. For high-pass subbands, the modified spatial frequency is adopted to stimulate SCM in NSCT domain. Lots of experiments have been made and the results powerfully show that the proposed algorithm outperforms the other fusion algorithms in both visual quality and quantitative evaluation. ACKNOWLEDGMENT We would like to thank the anonymous reviewers for their careful work and invaluable suggestions. This work was jointly supported by the National Natural Science Foundation of China (Grant No ). We are also grateful for TNO Human Factors Research Institute in the Netherlands for providing the experiment images. REFERENCES [1] Mahajan S, Singh A. A comparative analysis of different image fusion techniques. Image, 014, (1): [] Liu Huan-Xi, Zhu Tian-Hong, Zhao Jia-Jia. Infrared and visible image fusion based on region of interest detection and nonsubsampled contourlet transform.journal of Shanghai Jiaotong University (Science). 013, 18(5): [3] Smith M I, Heather J P. A review of image fusion technology in 005. Defense and Security. International Society for Optics and Photonics, 005: [4] Yang Bo, Jing Zhong-Liang, Zhao Hai-Tao. Review of pixel-level image fusion. Journal of Shanghai Jiaotong University (Science). 010, 15(1): 6-1. [5] Pajares Gonzalo, Manuel De La Cruz Jesús. A wavelet-based image fusion tutorial. Pattern Recognition. 004, 37(9): [6] Selesnick I. W., Baraniuk R. G., Kingsbury N. C. The dual-tree complex wavelet transform. IEEE Signal Processing Magazine. 005, (6): [7] Do M. N., Vetterli M. The contourlet transform: an efficient directional multiresolution image representation. IEEE Transactions on Image Processing. 005, 14(1): [8] Bamberger, R. H., Smith, M. J. T. A filter bank for the directional decomposition of images: theory and design. IEEE Transactions on Signal Processing. 199, 40(4): [9] Da Cunha A. L., Zhou J., Do M. N. The nonsubsampled contourlet transform: theory, design, and applications.image Processing, IEEE Transactions on. 006, 15(10): [10] Wang Zhaobin, Ma Yide, Cheng Feiyan, Yang Lizhen. Review of pulse-coupled neural networks. Image and Vision Computing. 010, 8(1): [11] Kun Zhan, Hongjuan Zhang, Yide Ma. New Spiking Cortical Model for Invariant Texture Retrieval and Image Processing. Neural Networks, IEEE Transactions on. 009, 0(1): [1] Eckhorn R., Reitboeck H. J., Arndt Mt, Dicke P. Feature linking via synchronization among distributed assemblies: Simulations of results from cat visual cortex. Neural Computation. 1990, (3): [13] Monica Subashini M., Sahoo Sarat Kumar. Pulse coupled neural networks and its applications. Expert Systems with Applications. 014, 41(8): [14] Wang Nianyi, Ma Yide, Zhan Kun. Spiking cortical model for multifocus image fusion. Neurocomputing. 014, 130: [15] Yuli Chen, Sung-Kee Park, Yide Ma, Ala R. A New Automatic Parameter Setting Method of a Simplified PCNN for Image Segmentation. Neural Networks, IEEE Transactions on. 011, (6): [16] Wang Nianyi, Ma Yide, Zhan Kun, Yuan Min. Multimodal Medical Image Fusion Framework Based on Simplified PCNN in Nonsubsampled Contourlet Transform Domain. Journal of Multimedia. 013, 8(3) : [17] Ma Yide, Lin Dongmei, Zhang Beidou, Liu Qing, Gu J. A Novel Algorithm of Image Gaussian Noise Filtering based on PCNN Time Matrix. IEEE International Conference on Signal Processing and Communications( ICSPC), 007: [18] Ma Yide, Lin Dongmei, Zhang Beidou, Xia Chunshui. A Novel Algorithm of Image Enhancement Based on Pulse Coupled Neural Network Time Matrix and Rough Set. IEEE Fourth International Conference on Fuzzy Systems and Knowledge Discovery(FSKD), 007, 3: [19] Liu Qing, Ma Yide. A new algorithm for noise reducing of image based on pcnn time matrix. Journal of Electronics & Information Technology. 008(08): [0] Zhenfeng S., Jun L., Qimin C. Fusion of infrared and visible images based on focus measure operators in the curvelet domain. Appl Opt. 01, 51(1): [1] Zhang Lai-gang, Wei Zhong-hui, He Xin, Zhang Yan, Liang Guo-long. A new image fusion algorithm based on wavelet transform. LOS ALAMITOS: IEEE, 010: 3, V1-V59. [] Liu Jingyu, Wang Qiang, Shen Yi. Comparisons of several pixel-level image fusion schemes for infrared and visible light images. IEEE Instrumentation and Measurement Technology Conference(IMTC), 005, 3: [3] Qu Guihong, Zhang Dali, Yan Pingfan. Information measure for performance of image fusion. Electronics Letters. 00, 38(7): 313. [4] Xydeas C. S., Petrovic V. Objective image fusion performance measure. Electronics Letters. 000, 36(4):