Rongchang Zhaoand Yide Ma

1.School of Information Science and Engineering,Central South University,Changsha 410083,China;

2.School of Information Science&Engineering,Lanzhou University,Lanzhou 730000,China

Novel region-based image compression method based on spiking cortical model

Rongchang Zhao1,*and Yide Ma2

1.School of Information Science and Engineering,Central South University,Changsha 410083,China;

2.School of Information Science&Engineering,Lanzhou University,Lanzhou 730000,China

To get the high compression ratio as well as the high-quality reconstructed image,an effective image compression scheme named irregular segmentation region coding based on spiking cortical model(ISRCS)is presented.This scheme is region-based and mainly focuses on two issues.Firstly,an appropriate segmentation algorithm is developed to partition an image into some irregular regions and tidy contours,where the crucial regions corresponding to objects are retained and a lot of tiny parts are eliminated.The irregular regions and contours are coded using different methods respectively in the next step.The other issue is the coding method of contours where an effcient and novel chain code is employed.This scheme tries to fnd a compromise between the quality of reconstructed images and the compression ratio.Some principles and experiments are conducted and the results show its higher performance compared with other compression technologies,in terms of higher quality of reconstructed images,higher compression ratio and less time consuming.

data compaction and compression,image processing and computer vision,region-based image coding,neural network.

1.Introduction

Data compression is to fnd an approach to the representation of the information energy making use of the least codes.Image sparse representation is a critical point in image processing.There are many research efforts in image compression in the past decades and many classical methods are widely used.

The image compression method based on block,such as JPEG[1],H.261[2],H.264 and MPEG[3,4],is widely used because of its low computation complexity and especially it does not need any shape information of objects in the original images.It is at its best on photographs with smooth variations of tone and color,and poor at representing discontinuities or impulse in the image.So there are some inherent shortages,such as mosaic effect and objectionable block distortion that greatly affects the subjective quality of reconstructed images.

The second-generation image compression techniques [5,6]based on the human visual system(HVS)can achieve high compression ratio through identifying and making use of the features in the image while still maintaining the image quality.Among these techniques,the segmented image coding(SIC)[7]is thought to be a promising one.It is a region-oriented coding,which attempts to separate an image into some irregular regions with slowly varying image intensity by image edges,then applies appropriate coding techniques to each region and contour respectively.The discontinuous parts of an image are represented alone.

A region-oriented compression technique usually requires three main steps[8]:preprocessing,segmentation, coding of contours and texture components.The purpose of preprocessing is eliminating some tiny regions that slightly affect the coding quality,and enhancing the image and removing noise produced in the sampling process.This paper mainly focuses on the segmentation method,components coding and the performance of the proposed scheme. The relevant knowledge of image denoising and enhancing has been presented in[9,10].Segmentation assembles similar pixels into corresponding regions and separates those regions with dissimilar pixels.The compression techniques depend on this kind of segmentation method which has been explored for decades,and it is the segmentation method that determines the coding manner of SIC[8].

The frst key problem to be resolved in this paper is the segmentation method.The actual performance of regionbased representation depends highly on the segmentation algorithm.For coding purposes,Christopoulos[13]proposed that the segmentation algorithm should satisfy four properties:the number of regions must be controllable, the produced regions must be smooth enough,few smallregions should be produced and the contours should be smooth.There are many image segmentation or edge detection algorithms[12].The classical methods based on edge detection aim to fnd the boundary to separate different regions,such as Canny,Sobel,Prewitt and Laplace. The classical region-based approach of image segmentation is the threshold method,which could ensure the segmented regions closed but it is rough for the petty texture and the value of the threshold is hard to choose.Another approach based on regions starts with a unit,and then splits and merges with some criteria until the desired result is obtained[11,13].This approach could obtain preferable segmented images but the process of splitting and merging is diffcult to control.Subsequently,a variety of hybrid methods appear,for example watershed method[14,15], graph cut[16–19],geometric active contour model[20], and something like that.These methods could not only make the contours smooth,but also segment the main objects from a scene,but they could not distinguish the more pixels without a similar value.The proposed irregular region segmentation algorithm could fnd regions and natural edges of regions effectively by means of the series of output pulse images of the model and the connected component labeling method.The results will show that the new segmentation method can get a satisfed effect with less time-consuming when used in image compression.

Another critical problem to be resolved is the representation of regions and contour pixels.The basic approach is approximation of a weighted sum of basis functions and the coeffcients in that sum are quantized and coded [21–23]for regions while effcient chain codes are used for contour pixels.If the basis functions in a given region are orthogonal generally,the coeffcients of basis functions could be obtained easily and independently.But the initial basis is not orthogonal commonly,so the orthogonalization process is needed.So the adoption of basis functions needs to focus on in this paper.Two existing basis functions,the cosine function and the binary polynomial,are adopted to represent the pixel intensity of segmented irregular regions.For contours coding,the most used method is chain code.The conventional chain coding techniques show high effciency,but only exploit the limited coherence.The directional grid chain coding[24]exploites contour coherence with the Markov chain using a rectangular cell.In [25],the relative angle difference between the chain code and its previous element is coded by the Huffman code based on the probabilities of the Freeman codes.Motivated by this method,considering the computational complexity of the proposed scheme,a simple and effcient method is developed and used in the proposed scheme.

The spiking cortical model(SCM)[26,27],based on the Eckhorn’s neuron model[28],derives from the phenomena of synchronous pulse bursts in mammal’s visual cortex.SCM is a feedback network formed by the linking of a large amount of neurons,according to the elicitation of biological visual cortex pattern.The model assembles the similar neighboring neurons into the same region based on the linking between neurons,the multiplicative modulated inputs and the dynamic thresholds.The model could slight the minor difference between pixel values and fnd the tidy contours if used in image segmentation.The property of a synchronous pulse burst makes SCM ft for image smoothing,image segmentation,edge detection,image enhancement and feature extraction[26,27,37,38].

In this paper,a new kind of image coding method, named as irregular segmented region coding based on SCM(ISRCS),will be described specially in next section,and the principle of irregular segmented region coding based on the segmentation method is mainly investigated in detail.An effective region segmentation method which is suitable for irregular region segmentation is developed.SCM will be more suitable for the segmentation of irregular regions and the natural edge of objects in the original image.The coding scheme much better matches HVS[5]and will be not only able to achieve a higher compression ratio but also obtain reconstructed images with better quality.

The basic principle of the segmentation method based on SCM will be introduced in Section 2 and the mathematical analysis of representation of regions will be discussed in Section 3.Section 4 introduces an effective chain code,Section 5 deseribes the ISRCS coding and decoding framework and Section 6 is the experimental results and discusses.Section 7 concludes this paper.

2.Region segmentation based on SCM

This section will present the irregular region segmentation method based on the spiking cortical model.The aim of segmentation is to divide the image into non-overlapping regions with similar contribution and every region corresponds to a different object.The spiking cortical model derives from the phenomena of synchronous pulse bursts which could make simultaneous excitation of similar and adjacent stimulations.This mechanism gives a guarantee of effective collection of pixel with similar intensity and adjacent position.Afterward,a labeling method is adapted to label the connected components in the output of the model and complete the segmentation.So the segmentation algorithm will contain the following steps:generation of the output binary image and connected components labeling(CCL).

2.1Generation of binary image based on SCM

For simplicity,the revised form of SCM is given directlyas(1)–(5).

where subscript(i,j)is the identifcation number of a neuron,Iijis the external stimulation of a neuron,Fij[n]is the feedback input,Lij[n]is the linking input,Uij[n]is the internal activity,and Eij[n]is the dynamic threshold and it decreases exponentially.W is the synaptic weight matrices,f and g are decay consistent constants(0＜f＜1,0＜g＜1),V is the threshold amplitude constant,n is the iteration time,Yij[n]is the binary pulse output,Eij[n−1]is the previous dynamic threshold,and DIFFij[n]is the difference between the neuron(i,j)and its 8-neighborhood.Each part communicates with neighboring neurons through the synaptic weight W respectively.Then the neuron combines the feedback input with the linking input as the internal activity,and the sequential pulse sequence will be generated(Yij[n]=1)by SCM when the internal activity Uij[n]is greater than the dynamic threshold Eij[n].The linking input L derives from two parts:one is the coupled information and the other is the difference with its 8-neighborhood.The pulses produced by neighbors participate in the stimulus of this neuron through the multiplication with W.The difference enhances the impact of the rapid change on the image pixel value.

A two dimensional image with a size of M×N can be thought as a neural network with M×N neurons,and the intensity of pixels can be thought as its stimulus.As an approach,the SCM can be used in a segmentation algorithm because of the two following factors.

In those equations,if W =0 and without regard to DIFF,(3)turns into U[n]=F+fU[n−1],that means this network works with connectionless status.All the neurons with same input will pulse at the same time,and for the neuron,the more powerful stimulus,the easier impulse production.Because the impulse of the neuron only depends on its stimulus,the output pulse images can show the magnitude relationship of the stimulus but the space relation cannot be found.That means the network can capture pixels with the similar value.

If the stimulus is with the same value,in(3),U is only controlled by the impulse and the difference from the neighbors.The pulses also motivate its communications with the neighboring neurons.In(2)and(3)it should be noted that the inter-neuron communication only occurs when the output of the neuron is high.

A pulsed neuron may result in the synchronous impulse of its neighbors with approximate intensity.The model could catch not only the spatial information but also the information of the similar pixel value.The output pulse image contains features of the stimulus such as edge,texture and regional information and it is the source of the segmented image.

In the method,the pixel in an image corresponds to the neuron,and the value of Iijis formed by the intensity of corresponding image pixel.Then as the input,the image is submitted to the revised SCM which is ready for capturing the similar and adjacent simulations.Due to the difference DIFF,coupling L between the neuron stimulation and its neighbors,pixels with similar intensity are grouped together as a connected component.Therefore,the output matrix Y of the model is labeled using the number“0”and“1”to distinguish different regions and background of the image.

2.2Fast connected component labeling

In an output matrix,the element numbered as“1”means it belongs to the regions while the element numbered as“0”refers to those belonging to the background.Usually the contour is closed,but in a series of output pulse images, the pixels(whose value is 1)may be disconnected despite those pixels have the similar value.In this case,those disconnected pixels may not correspond to the same region in the original image.To search the pixels contained in the same region corresponding to the object,CCL is used. CCL is to assign a number to each connected region to distinguish different regions.The number is the only one in the image and the maximum one is the number of regions in the output image in general.

In this paper we adopt a sequential connected components label method.Suppose the previous labeling number is N0,all the pixels in a connected component can be labeled with the only and same number after the following two steps.

Step 1The output pulse image as Y is scanned from left to right,from top to bottom.If Y(i,j)=1,assign a value as V.The frst value in this step is N0+1 and the other V is chosen as:

Step 1.1If all the neighbors of Y(i,j)are zero,(i,j) is set as the background and it is not a pixel of the region.

Step 1.2If there is only one non-zero element in the neighborhood of(i,j),it is set using the only element.

Step 1.3If all the labels of the neighbors are the same, (i,j)is set as the same label.

Step 1.4If all the labels of the neighbors are not thesame,(i,j)is set as any label.Here,the neighbors with different labels must be resolved by means of a new type of data structure named as equivalence table in next step.

The equivalence table refers to the relationship of all the labels.The pixels,whose labels are contained in a same equivalence table,are assigned into the same region.For example,Eqlabel[4]={4,7,14,17,23},it means all the pixels labeled as 4,7,14,17,23 are from the same region.

Step 2The conficting label must be labeled again with the help of the equivalence table.The algorithm resorts each equivalence table by size and replaces the conficting label by the following relation.

Searchlabel[Eqlabel[i][j]]=Min(Eqlabel[i]),

Imlabel[i][j]=Searchlabel[Imlabel[i][j]].

Fig.1 Mapping between equivalence table and search table

3.Representation of irregular regions

The image encoding method,from a variety of mathematical essence,is to fnd a way to minimize the distortion of the image data of the sparse representation.Fortunately, the sparse representation model indicates that the image can be viewed as a linear combination of multiple basis functions,and only a few basis functions with large nonzero coeffcients.However,the common image compression methods based on block coding using the cosine function,wavelet functions are not suitable to represent the irregular image regions because they cannot be partitioned into rectangles with an integer number.In this section,a hybrid method based on both polynomial approximation and block coding is used in representation of irregular regions.

3.1Polynomial approximation

Let f(x,y)denote the intensity of the pixel corresponding to coordinate(x,y),f′(x,y)is the approximating function of f(x,y),and it can be represented by weighted sums of N basis functions{ϕ1,ϕ2,...,ϕN} which are parameterized by their corresponding coeffcients{c1,c2,...,cN},

The error function can be defned as

If N → ∞,it means{ϕi(x,y)}is a set of complete orthogonal basis functions,E is zero,else,to minimize E by c,for∀i,let∂E/∂ci=0,and the value of cicould be calculated as(8)by means of the orthogonal characteristic.

3.2Orthogonalization of basis functions

As proved in[29],in an N-dimensional subspace,a set of orthogonal basis functions always can be gotten from a set of linearly independent initial bases using the orthogonalization scheme of Gram-Schmidt(GS).To learn more about GS orthogonalization,please see[29].

Although the computation is greatly simplifed when orthogonal functions are used,the GS orthogonalization process is time-consuming.Furthermore,GS is space expensive because the previous basis functions must be stored in memory even though the function is used only once for computing of a single coeffcient.Another orthogonalization approach named Weakly Separable(WS)approach is introduced.The basis functions are regarded as two separable parts and every part could be computed independently and quickly.Here a few basic theories are listed,and more detailed explanation will be found in[30–32].

3.3Hybrid representation

To represent the irregular regions effectively and accurately,a class of discrete cosine transform(DCT)based approaches,called as shape-adaptive DCT(SA-DCT),isproposed by flling the irregular region with 0-valued pixels and handling the regions as rectangles.For example, SA-DCT flls the outer region with 0-valued pixels and creates a minimal rectangle which could envelop the irregular region,so the rectangle region can be represented by DCT coeffcients.The accuracy of this approach is unaffected because the flled pixels are zero,but the calculation is increasing.In addition,another approach is proposed that reduces the number of 0-valued pixels and transforms the irregular a region into regular region with few 0-valued pixels.

In this section,a hybrid representation method is proposed.With this approach,an irregular region is approximated by a series of rectangle blocks with a size of 8×8, then the part in the blocks is represented using block coding for a fast and effective approach and the part out of the blocks is coded by polynomial approximation owing to the ability of block coding.So the representation of irregular regions can be described in the schematic drawings with two parts as shown in Fig.2.

Fig.2 Flow diagram of the proposed hybrid region representation

4.Coding for contours

Chain coding is a common approach for representing the contours of images.The frst work on representing the curves using chain codes is done by Freeman[33]and the code is also called as Freeman Code.The chain code records the direction information of curves by a number sequence based on 4-neighbor or 8-neighbor.For the 8-neighbor,the sequence is{0,1,2,3,4,5,6,7},denoting an angle according to different movement directions along a curve from the starting point to the next.

The coding theory aims to eliminate some redundancy. There are a mass of structural information in Freeman codes,for example the next Freeman code element is very often the same as its predecessor[24].The statistical probability result of various angle differences between two elements in contour codes is shown in Table 1.It can be seen that,about 99%of the angle difference of Freeman codes is 0 or 45,and the Freeman codes of a contour are changing with a small direction or the adjacent code element is very often not changing when compared with the predecessor.The frst difference and the concept of entropy could be used to reduce a lot of information that is used to represent the unchanged code.In this method which is used to code the contours of irregular regions,it tries to reduce the redundancy by the frst difference of Freeman codes and Huffman coding.The Huffman code is based on the concept of entropy.Codes for more probable characters are shorter than the ones for less probable characters and each code can be uniquely decoded.After the frst difference and Huffman coding,the codes represent the information of contours of the region.The average bits per code are calculated as

where Piis the probability of the the ith code and Aiis the number of bits representing the code.

Table 1 Statistic of contours from the Berkeley segmentation Dataset-BSDS300[39]

5.ISRCS coding and decoding framework

In ISRCS,the contours can be coded with chain coding while the regions can be expressed approximately with a hybrid method.Pixels in a region of image f(x,y)can be expressed with an approximate function f′(x,y)which can be built through a set of arbitrary linearly independent basis functions{ϕ0,ϕ1,...,ϕN}and discrete cosine functions using the method of SA-DCT.

The framework of the ISRCS algorithm is shown in Fig.3.Firstly an input image is segmented into a lot of regions and its contours and then the regions and the contours are coded using different methods respectively.The contours are compressed with the help of Freeman chain while the regions are coded by the method of SA-DCT which is a hybrid method based on DCT and polynomial approximation.Finally region codes combining with the contour codes which depict the position of the corresponding region,act as the image codes.And at the receiver the image is reconstructed through the function f′(x,y)built by the coeffcients of each region and contour codes.

Fig.3 Framework of irregular segmented region coding

6.Experiments and analysis

In this section,a lot of experimentations are implemented to demonstrate the performance of ISRCS.In the frst part, the results obtained with the algorithm described in Section 5 are compared with other image coding methods:algorithm based on 2D-DCT,JPEG2000 based on wavelet and algorithm proposed in[40].The results demonstrate the strong points of ISRCS on the compression ratio and the quality of the reconstructed image.Results and analysis of region representation based on SA-DCT described in Section 3 will be presented in the second part of this section.Finally,the experiments about the coding scheme are presented.

6.1Comparison with other schemes

In this subsection,a lot of images are tested for comparison with other region-based image compression methods.Here Algorithm 1 denotes the image coding method based on ISRCS,Algorithm 2,the classical one which is used in JPEG,MPEG1 and MPEG2,is based on 2DDCT,Algorithm 3 is JPEG2000(the algorithm is realized by JPEG2000 developer toolkit[34])and Algorithm 4 is proposed in[40].The performance of the image coding algorithm will be shown with the reconstructed image and two quantitative parameters:the peak signal to noise ratio (PSNR)and the compression ratio(CR).

As shown in Fig.4,this section selects a few test images such as“Lena”,“House”and“Milkdrop”with 128×128, 8 bits to show the performance of different compression methods.Fig.4(a)is the original image,Fig.4(b)is reconstructed images based on Algorithm1,Fig.4(c)–(f)are zoomed from the reconstructed image based on Algorithms 1–4,respectively.At the same time the PSNR and CR of the images are shown in Table 2.

Table 2 PSNR(DB)and CR of the algorithms

The compared results represent that with the approximate CR,the PSNR of Algorithm 1 is higher than Algorithm 2.The blocks zoomed to 400%shown in Fig.4(d) present serious block distortion that is known as mosaic effect that destroys the natural edges and contours of objects in the original image,while Fig.4(c)–(f)contain no such.Fig.4(c)is broken by the block distortion and Fig. 4(d)is blurred although it is not block distortion.Compared with the proposed algorithm,reconstructed images based on JPEG 2000 and the method in[40]not reserve block distortion yet but JPEG 2000 is blurry for it loses part of high frequency components and method in[40]is weaker for the presentation of region contours.It means the performance of Algorithm 1 could get a profound performance because it can better retain the edges and details of image,and the ISRCS performs better in image compression.

6.2Characteristic of SA-DCT

Fig.4 Reconstructed image

Fig.5 Novel SA-DCT to representation of pixels in segmented region

For the representation of pixels in the region,a novel SADCT described in Section 5,where an irregular region is approximated by a series of rectangle blocks with a size of 8×8,then the pixels in the blocks are represented based on block coding and the pixels out of the blocks are coded by polynomial approximation.Fig.5 shows the processing of an example,where Fig.5(a)is a segmented image and a piece of region.Fig.5(b)and(c)are two existing SA-DCT methods,Fig.5(d)is the new SA-DCT method described in this paper.Fig.5(e)is the bivariate polynomial basis function where N=6,and Fig.5(f)is a sample of polynomial coeffcients.Fig.5(g)is the constructed region for the initial one presented in Fig.5(a).Here for image Fig. 5(g),PSNR=31.013when bits per pixels(bpp)is 1.01823.

The results of experiments of the representation of regions show that the coeffcients redundancy is smaller and

the representation of regions is effective,when the pixels in the blocks are represented based on block coding and the pixels out of the blocks are coded by polynomial approximation.Its problem is complicated calculation which will be resolved by fast algorithms and high-speed devices.

6.3Experiments about ISRCS

The results of the segmented algorithm described in Section 2 are shown.Fig.6(a)is the original image andFig.6(b)is the output pulse image after eight iterations. Fig.6(c)shows the segmented image using the proposed algorithm.Figs.6(d),(e)and(f)show the segmented image based on the watershed algorithm,the recursive shortest spanning tree(RSST)technique[35]and the algorithm described in[13].

Fig.6 Segmented images from different algorithms

The proposed segmented algorithm extracts contours based on the output pulse image of SCM after different iterations.Fig.6(b)is an example of the output image of SCM after eight iterations,Fig.6(c)is the proposed algorithm based on the output pulse image and the region connection method(89 regions,3 012 contour pixels).Fig. 6(d)is the image segmented with the watershed algorithm (196 regions,2 659 contour pixels).Fig.6(e)is the RSST algorithm(70 regions,8 031 contour pixels).Fig.6(f)is the algorithm of[13](300 regions,6 783 contour pixels). It could be observed that the output image series shows different precisions of the texture.The suited output must be chosen because the expected segmented image should not only catch and segment regions with homogeneous pixels,but also control the number of the smaller regions and contour pixels.The proposed algorithm eliminates the smaller regions and some inconsequential contours based on the region connected method.It could be observed that the shape of the regions is clear.The proposed algorithm catches most regions with fewer contour pixels compared with the two methods shown in Fig.6.

Most experiments show that quite a few of bits are spent for coding the contour pixels.Thus the number of contour pixels is very important in irregular segmented region coding because it determines the compression radio of the algorithm.In most applications,the segmented method is expected as controllable,the number of the contour pixels is smaller and the number of regions is controllable. The CR of ISRCS is controllable with parameter values of SCM by controlling the number of regions and contours. ISRCS is compared with the other algorithms and the results are shown in Fig.7.The global threshold is calculated based on the Otsu method.It could be observed that the values of the number of contour pixels per region in general accord with the value in method of[27]and the value is steady along with the increase of regions.The value in the other method is choppy and the ratio between the codeword length of contours and that of regions is small sometimes.With certain parameters of SCM,ISRCS can get a balanced ratio between the number of regions and that of contours.It not only obtains a higher compression radio, but also holds the clear contour outline and outputs the higher quality reconstructed image.

Fig.7 Relation between number of regions and number of contour pixels on the Berkeley Segmentation Dataset-BSDS300.

The relation between the compression radio and the number of regions is depicted in Fig.8 for test images from the Berkeley segmentation dataset.It can be observed that the CR changes slowly with the increasing of the number of regions.The effect of the region number upon the CR is not so seriously as the other algorithms because ISRCS alleviates the contradiction between the number of regions and the number of contours.Furthermore,the CR of ISRCS is better than the algorithm proposed in[13]when the number of regions is bigger than 300.So if more detailed texture is needed,the ISRCS can be chosen to get a good compression ratio.

As shown in Table 3,some experiments explore the relationship between the CR and image resolution,which are based on the platform of Pentium IV/CPU 2.4 GHz/ 1024 MB RAM,Microsoft Visual C++6.0.The test images are Lena,Milkdrop and House of 128×128, 256×256,512×512 and 768×768,and of 8 bits,respectively[36].

Fig.8 Relation between compression radio and number of regions on the Berkeley Segmentation Dataset-BSDS300.

It can be noticed that with the increase of original image resolution,the CR is increasing evidently with almost nondecreasing PSNR but more time-consuming obviously.It means that ISRCS maybe better suit for the compression of higher resolution images than the lower one.However, the algorithm is time consuming when resolution is higher, which could be resolved with the optimization of the ISRCS algorithm and special fast processing devices such as digital signal processor(DSP).

Although the proposed method is outstanding for the most of the test images,it is ordinary for the low resolution images with complex scenes.Based on the results in Fig.4,Tables 2 and 3,it is real that for the complex image“Lena”the method could get a smaller CR compared to other test images.It is due to that more region codes and contour codes are used because the complex image is segmented into more pieces of regions and more varied contours are produced to represent these regions.If a perfect segmentation method is developed,this scheme will get a fascinate result.

Table 3 Coding characteristics of different resolutions based on ISRCS

7.Conclusion

An effcient irregular segmented image coding method based on the spiking cortical model is represented and named as ISRCS in this paper.In the framework of ISRCS,the mission is divided as two parts:segmentation and coding of homogenous regions.The segmented method divides an input image into contours and regions. This paper proposes a segmented method based on the output pulse image of SCM and the region connection method.This method gives clear regions and smooth contours because the segmented image not only holds most contours of the objects,but also obtains some clear texture which is mapped to a same object or has the homogenous pixels.It is suitable for image coding because of the representation of the region by orthogonal basis functions.In addition,this method could control the number of the regions and contours by the parameters of SCM,which could be a choice for the compression radio.

Furthermore,the representation of contour pixels and regions is studied.The ISRCS adopts an effective chain code which could reduce the bit rate when coding the contour pixel.The weakly separable basis function and GS basis functions are studied for region representation.The ISRCS could not only obtain the details but also get higher compression ratios.Much interest has been given to the segmented image coding,but,to the best of our knowledge, little attention has been given to irregular segmented region coding based on SCM recently.This work is just an attempt in the image coding using SCM and most works would be studied in the future.

Acknowledgment

We would like to express our sincere thanks to David Taubman for JPEG2000 developer toolkit named Kakadu Software.We are also very grateful to Maojun Su,Chunliang Qi,Beidou Zhang,Wenrui Yu,who kindly helped us to complete some experiment and this paper.

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Biographies

Rongchang Zhao was born in 1982.He received his Ph.D.degree in radio physics from Lanzhou University in 2011,and held a postdoctor fellowship with School of Information Science and Engineering,Central South University.He is now working in Central South University.His current research interests include image processing,pattern recognition and conputer vision.

E-mail:byrons.zhao@gmail.com

Yide Ma was born in 1963.He received his Ph.D.degree from the Department of Life Science, Lanzhou University,Gansu,China,in 2001.He is currently a professor in the School of Information Science and Engineering,Lanzhou University.He has published more than 50 papers in major journals and international conferences and several textbooks. His current research interests include artifcial neural networks,digital image processing,pattern recognition,digital signal processing,and computer vision.

E-mail:ydma@lzu.edu.cn

10.1109/JSEE.2015.00021

Manuscript received December 27,2013.

*Corresponding author.

This work was supported by the National Science Foundation of China (60872109)and the Program for New Century Excellent Talents in University(NCET-06-0900).