True color image segmentation by an optimized multilevel activation function

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A novel neuro-fuzzy-genetic approach is presented in this article to segment a true color image into different color levels. A MUSIG activation function induces multiscaling capabilities in a parallel self organizing neural network (PSONN)
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   Abstract   - A novel neuro-fuzzy-genetic approach is presented in this article to segment a true color image into different color levels. A MUSIG activation function induces multiscaling capabilities in a parallel self organizing neural network (PSONN) architecture. The function however resorts to equal and fixed class responses, assuming the homogeneity of image information content. In the proposed approach, genetic algorithm has been used to generate optimized class responses of the MUSIG activation function. Subsequently, the color images are segmented by applying the resultant optimized multilevel sigmoidal (OptiMUSIG) activation function. Comparative results of segmentation of two real life true color images indicate better segmentation efficiency of the OptiMUSIG activation function over the standard MUSIG activation function.  Keywords  - Color image segmentation, parallel SONN, MUSIG, segmentation evaluation metrics I. INTRODUCTION Image segmentation and classification is a challenging task in the image processing fraternity owing to the variety and complexity associated therein. The  problems of image segmentation become more uncertain and severe when it comes to color image segmentation. A complicated computational effort is required to process the color images due to the variety and enormity of the color intensity gamut along with the processing overhead involved. A score of works on color image segmentation can be found in the literature [1] [2]. Belongie et al.  [2]  proposed a stochastic model based technique for color image segmentation. A robust color image segmentation approach has been devised by Krishnana et al.  [3] using morphological watershed methods. In this approach, the HSV color space has been employed to define the color contrast gradient, which is multiplied with multiscale morphological gradient of the intensity image to overcome the problem of over segmentation. An active contour based method named graph partitioning active contour (GPAC) has been introduced for color image segmentation by Sumengen et al.  [4]. This algorithm works on the basis of the similarity or dissimilarity of the  pixels. An unsupervised multiscale color image segmentation algorithm has been designed by employing mean shift analysis (MS) [5].  Neural network architectures have also been employed to consider the task of color image processing, given their inherent features of parallelism and graceful degradation. Color image segmentation problems are widely solved by the self organizing map (SOM) [6] due to their ability of retrieving the dominant color content of images. An ensemble of multiple SOM networks [6] are applied for color image segmentation based on color and spatial features of image pixels. The binary objects from a noisy binary color image can be extracted quite efficiently  by a single multilayer self organizing neural network (MLSONN) [7] by means of self supervision. In this network, backpropagation algorithm has been used to adjust the network weights with a view to arriving at a convergent stable solution. However, the multilevel objects cannot be extracted from an image by this network as it uses the bilevel sigmoidal activation function. A  parallel version of the MLSONN (PSONN) architecture [8] consisting of three independent MLSONNs (for component level processing) apart from a source layer and a sink layer, has been proposed to extract pure color images from a noisy background. The architecture uses the generalized bilevel sigmoidal activation function with fixed and uniform thresholding. Bhattacharyya et al.  [8] introduced a multilevel sigmoidal (MUSIG) activation function for mapping the multilevel input information into multiple scales of gray. True color images can be segmented into different levels of colors using the PSONN architecture guided by the MUSIG activation function. However, the MUSIG activation function assumes uniformity and homogeneity in the image data to  be processed. Genetic algorithms (GAs) [9] are derivative-free stochastic search techniques based on some evolutionary  phenomena. GAs are suitable for obtaining approximate solutions for multi-variable optimization problems. Basically, the parallel searching techniques are performed to search the best solution over a number of possible solutions. GAs are applied in different arena of the technology, such as, image processing, portfolio management, data mining, etc. In this article, genetic algorithm is applied to generate the optimized class boundaries of a MUSIG activation function to be used for segmentation of true color images into different classes. The proposed optimized multilevel sigmoidal activation (OptiMUSIG) function is generated  by these dynamically generated class boundaries with variable thresholds. Two real life true color images have  been used to demonstrate the application of the proposed approach. The standard correlation coefficient (  ρ  ) [8] and the empirical measure, Q  due to Borsotti [10] have been applied to evaluate the segmentation efficiency of the  proposed approach. True Color Image Segmentation by an Optimized Multilevel Activation Function Sourav De 1 , Siddhartha Bhattacharyya 1 , Susanta Chakraborty 2 1 Department of CSE & IT, University Institute of Technology, The University of Burdwan, Burdwan-713104, West Bengal, India 2 Department of CST, Bengal Engineering & Science University, Shibpur-711103, West Bengal, India (sourav.de@gmail.com, dr.siddhartha.bhattacharyya@gmail.com, susanta_chak@yahoo.co.in) 978-1-4244-5967-4/10/$26.00 ©2010 IEEE   II. FUZZY SET THEORETIC CONCEPTS A fuzzy set [11] is a collection of objects, denoted generically by  x , with certain degree of membership. A membership function,  µ A (  x i ), i  = 1, 2, 3,..., n  characterizes a fuzzy set  A  = {  x 1 ,  x 2 ,  x 3 , ......,  x n }.  µ A (  x i ) lies in [0,1]. The subnormal linear index of fuzziness (  s l  ν  ) [10] for a subnormal fuzzy subset with support  s  A S   ∈  [  L , U  ],  L   ∈  [0, 1], U    ∈  [0, 1] and  L   ≤   U  , is given by ( ) ( )  ( ) ( ) { } 1 2min,  s nl A i A ii  x L U xn ν µ µ  = ⎡ ⎤ = − − ⎣ ⎦ ∑  (1) III. GENETIC ALGORITHM Genetic algorithm (GA) [9], population-based optimization technique, is loosely based on natural selection and evolutionary process. The population passes through successive generations in the sense that at each generation the better solutions are allowed to survive and reproduce, while the unfit ones are forced to wipe out. Each individual solution, also called a chromosome , represents a potential solution to the problem being solved. The degree of correctness of a particular solution or the quality of solution in solving the problem is known as  fitness . An initial population is created from a random selection of solutions. Different probability distributions, such as uniform distribution or a random selection from a  population may be used for selection, so that the best individual has the greatest probability to be chosen. Crossover   is usually applied to the selected pairs of chromosomes with a probability equal to a given crossover rate . In the mutation  operation, a single bit in the chromosome is selected randomly based on the mutation rate  to modify an individual. As the generation  proceeds, the average fitness is expected to improve, and the best individual throughout the generation is selected as solution. IV. PARALLEL SELF-ORGANIZING NEURAL  NETWORK (PSONN) ARCHITECTURE The parallel self-organizing neural network (PSONN) architecture [8] is a parallel version of the multilayer self organizing neural network (MLSONN) [7]. Three independent single three layer self organizing neural network (TLSONN) architectures, comprising an input layer, one hidden layer and an output layer are incorporated in the PSONN. In addition a source and a sink layer are also present for component level  processing. The source layer in the PSONN architecture is fed with the primary color components, which are then  processed in the constituent TLSONNs and the sink layer generates true color output images. The three parallel TLSONN architectures operate in a self supervised mode on multiple shades of color component information. The linear indices of fuzziness of the subnormal color component information, obtained at the respective output layers are applied to determine the system errors. The interconnection weights are adjusted using the standard  backpropagation algorithm. This method of self supervision is continued until the system errors at the output layers of the three independent TLSONNs fall  below some tolerable limits. The corresponding output layers of the three independent TLSONNs produce the segmented color component outputs. These segmented component outputs are finally fused at the sink layer of the PSONN network architecture to produce the final segmented true color image. Interested readers may refer to [8] for details regarding the dynamics and operation of the PSONN architecture. V. OPTIMIZED MULTILEVEL SIGMOIDAL (OPTIMUSIG) ACTIVATION FUNCTION The characteristic multilevel sigmoidal activation function utilized by PSONN [8] is presented in this section. The multilevel sigmoidal (MUSIG) activation function [8] is the extended version of the bipolar form of the sigmoidal activation function, which has the ability to generate multilevel outputs corresponding to the multiple scales of gray. It is given by [8]  1[(1)]1 1(;,)  K  MUSIG x cl   f x cl e  β   β β  λ β θ  β  β  ξ ξ  −− − − −= =+ ∑  (2) where ξ   β   represents the multilevel class responses. It is given by 1  N  C cl cl   β  β β  ξ  − =−  (3) where,  β   represents the gray scale object index (1 ≤    β   <  K  ) and  K   is the number of gray scale objects or classes. The ξ   β   parameter represents the number of transition levels/lobes in the MUSIG function pertaining to the number of target classes. The gray scale contributions of the  β  th  and (  β    −  1) th  classes are denoted by the cl   β   and cl   β  -1 , respectively. The maximum fuzzy membership of the gray intensity contribution of pixel neighborhood geometry is represented by C   N  . The threshold parameter ( θ  ) in the MUSIG activation function is fixed and uniform. But this activation function assumes homogeneity in the input data due to the inherent fixed threshold. Hence, the transfer characteristics of the activation function given in Equation 2 are independent of the nature and distribution of the data operated upon. But, real life images generally exhibit a fair amount of heterogeneity and the class levels would differ from one image to another. An optimized form of the MUSIG activation function, using optimized class boundaries derived from the image context can be represented as var  1[(1)]1 1 opt opt opt opt   K OptiMUSIG x cl   f e  β  λ β θ  β  β  ξ  −− − − −= =+ ∑  (4)   where, opt  cl   β  are the optimized gray scale contributions corresponding to optimized class boundaries. opt   β  ξ   are the respective optimized multilevel class responses. θ  var   is a variable threshold. It depends on the optimized class  boundaries and is represented as 1 var  2 optopt opt  clcl cl   β β  β  θ  − −= +  (5) Hence, the threshold depends on the nature context of data to be processed. VI. EVALUATION CRITERIA FOR SEGMENTATION Different evaluation measures for segmentation have  been proposed in the literature [10]. These include the standard correlation coefficient (  ρ  ) [8], different evaluation function  F [10],  F’   [10] and Q  [10], etc. The standard correlation coefficient (  ρ  ) is used to measure the degree of similarity between the segmented and the srcinal images. A higher value of  ρ   implies better quality of segmentation. However, correlation coefficient has some limitations as it is computationally intensive. It is very much sensible to image skewing, fading, etc. that inevitably occur in imaging systems. Another quantitative evaluation function (  EF  ), Q  is  proposed by Borsotti et al.  [10]. It is denoted as 221 ()1()[()]1000.1log  N kk k  Mkk  eNS QMN SSS  = = ++ ∑  ( 6 )  where,  N   is the number of arbitrarily shaped regions of the image  M  . If the number of pixels in region k   is represented as  RE  k   , then S  k  =|  RE  k  | is the area of region k  . Here,  N   ( S  k  ) stands for the number of regions having an area S  k  . 2 k  e is the squared color error of region k  . It is given as 22(,,) ˆ(()()) r   jvvk vrgbpR eCpCRE  ∈ ∈ = − ∑ ∑ . Here,  ( ) vk  CRE   is the average value of feature v  (red, green or  blue) of a pixel  p  in region k   and is represented as  ()()/ k  vkvk  pRE  CRECpS  ∈ = ∑  where C  v   (  p ) denotes the value of component v  for pixel  p . A lower value of Q  implies better quality of segmentation. VII. PROPOSED METHODOLOGY The proposed approach of color image segmentation  by an OptiMUSIG activation function with PSONN architecture has been carried out by the following phases.  A. Designing of OptiMUSIG activation The most important part of the color image segmentation approach is to generate the optimized class  boundaries ( opt  cl   β  ) in the proposed OptiMUSIG activation function. The GA-based optimization  procedure is applied to generate these optimized class  boundaries. The number of classes (  K  ) and the pixel intensity levels are fed as inputs to the GA-based optimization procedure characterized by a single point crossover operation. The reproducing chromosomes are selected by a proportionate fitness selection scheme. The segmentation efficiency measures (  ρ   and Q ) are used as the fitness function for this phase. The derived optimized class levels ( opt  cl   β  ) are applied to determine the corresponding opt   β  ξ   parameters using 3. The derived opt   β  ξ   parameters are used to obtain the different transition levels of the OptiMUSIG activation function.  B. Segmentation of the component color images by the OptiMUSIG activation function with the independent SONNs The individual TLSONNs guided by the designed OptiMUSIG activation function are applied to segment each color component in this phase. The neurons of the different layers of the SONN architecture generate different individual color level responses to the input signal. The processed input signal propagates to the succeeding network layers. The system errors for each SONNs are evaluated at the corresponding output layers  based on the subnormal linear indices of fuzziness (given  by 1) of the outputs obtained. The interconnection weights  between the layers are adjusted by these errors. The resultant color component images at the respective output layers are produced in the independent TLSONNs by this self supervised procedure. The final segmented outputs are derived by fusing these color component segmented outputs. VIII. RESULTS Results of segmentation true color images of dimensions 256 × 256 with OptiMUSIG activation function are reported for  K   = 8 classes with λ  =4. Table I shows the optimized class boundaries of the target classes for each color component. The heuristic class boundaries used by MUSIG activation function are shown in Table II. The true color segmented images obtained by the OptiMUSIG activation function with the optimized class responses pertaining to Table I, are shown in Fig. 1. Fig. 2 shows the true color segmented images with the fixed class responses of Table II. It is observed from Tables (I & II) that better segmentation is attained with the OptiMUSIG activation function as compared to that obtained with the conventional MUSIG activation function.   IX. DISCUSSIONS AND CONCLUSION A new approach for true color image segmentation using a PSONN architecture guided by OptiMUSIG activation function is presented in this article. The optimized class boundaries of the input true color images are used to design the OptiMUSIG activation function. Better segmentation is achieved by the proposed activation as compared to the heuristically designed MUSIG activation function. However, methods remain to  be investigated to find out the optimum number of target classes. The authors are currently engaged in this direction. REFERENCES [1] H. C. Chen, W. J. Chien and S. J. Wang, “Contrast-based color image segmentation,”  IEEE Signal Processing   Letters , vol. 11, no. 7, pp. 641-44, 2004. [2] S. Belongie, C. Carson, H. Greenspan and J. Malik, “Color  and texture based image segmentation using EM and its application to content-based image retrieval,” in  Proc. of   International Conf. on Computer Vision , pp. 675-682, 1998. [3]  N. Krishnan and K. Krishnaveni, “A Multiscale Morphological Watershed Segmentation using Color  Composite Gradient and Marker Extraction,”  International   Journal of Imaging Science and Engineering   (IJISE), vol. 2, no. 2, pp. 195-200, 2008. [4] B. Sumengen, B. S. Manjunath, “Graph Partitioning Active Contours (GPAC) for Image Segmentation,”  IEEE Trans. on Pattern Analysis and Machine Intelligence , vol. 28, no. 4, pp. 509-521, 2006. [5] Q. Luo and T. M. Khoshgoftaar, “Unsupervised multiscale color image segmentation based on MDL principle,”  IEEE  Trans. on Image Processing  , vol. 15, no. 9, pp. 2755- 2761, 2006. [6] Y. Jiang and Z. H. Zhou, “SOM Ensemble-Based Image Segmentation,”  Neural Processing Letters , vol. 20, no. 3,  pp. 171-178, 2004. [7] A. Ghosh, N. R. Pal and S. K. Pal, “Self-Organization for Object Extraction Using a Multilayer Neural Network and Fuzziness Measures,”  IEEE Trans. on Fuzzy Sys. , vol. 1, no. 1, pp. 54-68, 1993. [8] S. Bhattacharyya, P. Dutta, U. Maulik and P. K. Nandi, “Multilevel activation functions for true color image segmentation using a self supervised parallel self  organizing neural network (PSONN) architecture: A comparative study,”  International Journal on Computer  Sciences , vol. 2, no. 1, pp. 09-21, 2007, ISSN 1306-4428. [9] D. E. Goldberg, Genetic Algorithm in Search Optimization and Machine Learning  , New York: Addison-Wesley, 1989. [10] H. Zhang, J. Fritts and S. Goldman, “An entropy-based objective evaluation method for image segmentation,” in   Proc. of SPIE Storage and Retrieval Methods and   Applications for Multimedia , 2004. [11] T. J. Ross and T. Ross,  Fuzzy Logic with Engineering   Applications , McGraw Hill College Div., 1995.  T ABLE I O PTIMIZED C LASS B OUNDARIES FOR T EST I MAGES WITH T WO M EASURES Measure Class Levels  ρ  Lena = 0.943 R={43, 96, 100, 191, 223, 237, 238, 255}; G={0, 73, 146, 157, 176, 217, 224, 255}; B={32, 70, 95, 118, 134, 154, 180, 238}  ρ  Baboon = 0.961 R={0, 34, 37, 62, 199, 211, 247, 255}; G={0, 60, 77, 103, 141, 191, 199, 255}; B={0, 44, 72, 106, 139, 188, 232, 255} Q Lena = 0.148 R={43, 141, 166, 167, 202, 208, 220, 255}; G={0, 36, 48, 64, 136, 147, 182, 255}; B={32, 49, 79, 93, 109, 139, 206, 238} Q  baboon = 0.602 R={0, 47, 73, 96, 116, 129, 177, 255}; G={0, 71, 96, 113, 134, 161, 189, 255}; B={32, 54, 122, 124, 148, 162, 195, 255} T ABLE II F IXED C LASS B OUNDARIES FOR T EST I MAGES WITH O BTAINED  ρ  Lena  = 0.9231,  ρ  Baboon  = 0.8976, Q Lena = 1.000, Q Baboon =1.000   Image Color Levels Lena R={43, 50, 75, 90, 120, 140, 200, 255}; G={0, 50, 100, 130, 160, 180, 190, 255}; B={32, 75, 85, 95, 135, 195, 205, 238} Baboon R={0, 30, 44, 52, 110, 135, 160, 255}; G={0, 20, 30, 104, 112, 137, 201, 255}; B={0, 30, 40 148, 206, 210, 217, 255} Fig.1 8-class segmented test images with optimized class  boundaries (a)(b) with  ρ   and (c)(d) with Q  fitness functions Fi28-classsementedtestimaeswithheuristicclassboundaries
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