Uniform Cellular Automata Linear Rules for Edge Detection

In this paper we discuss the application of two-dimensional linear cellular automata rules to the problems of edge detection in monochromatic images. We proposed an efficient and simple method of edge detection based on uniform cellular automata transition matrix representation. We investigate of cellular automata linear rules for edge detection by using matrix representation, in some cases they are strong and some other rules are not in fact useful for practical edge detection. All rules give computationally effective result since the computation mechanism consist only matrix multiplication. Finally, we present some results of the proposed linear rules for edge detection and compare with some classical results.

[1]  Dong-Ho Lee,et al.  Construction of Group Rules for VLSI Application , 2007, SCSS.

[2]  Laura Caponetti,et al.  A genetic approach to edge detection , 1994, Proceedings of 1st International Conference on Image Processing.

[3]  D. Vu,et al.  Edge detection using neural networks , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[4]  Kim L. Boyer,et al.  Optimal infinite impulse response zero crossing based edge detectors , 1991, CVGIP Image Underst..

[5]  Pabitra Pal Choudhury,et al.  Characterisation of a particular hybrid transformation of two-dimensional cellular automata , 1999 .

[6]  Jean-Marc Chassery,et al.  Edge detection by estimation and minimization of errors , 1997, Pattern Recognit. Lett..

[7]  Peter de Souza,et al.  Edge detection using sliding statistical tests , 1983, Comput. Vis. Graph. Image Process..

[8]  Raymond H. Chan,et al.  Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization , 2005, IEEE Transactions on Image Processing.

[9]  Paul L. Rosin.  Training cellular automata for image processing , 2005, IEEE Transactions on Image Processing.

[10]  T. Pavlidis,et al.  Residual Analysis for Feature Detection , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  Jun Shen,et al.  An optimal linear operator for step edge detection , 1992, CVGIP Graph. Model. Image Process..

[12]  Jerry D. Gibson,et al.  Handbook of Image and Video Processing , 2000 .

[13]  Paul L. Rosin.  Training Cellular Automata for Image Processing , 2006, IEEE Trans. Image Process..

[14]  Pabitra Pal Choudhury,et al.  Theory and Applications of Two-dimensional, Null-boundary, Nine-Neighborhood, Cellular Automata Linear rules , 2008, ArXiv.

[15]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[16]  Wen-June Wang,et al.  A novel edge detection method based on the maximizing objective function , 2007, Pattern Recognit..

[17]  David Sher,et al.  Chi2 Test for Feature Detection , 1993, Pattern Recognit..

[18]  Suchendra M. Bhandarkar,et al.  An edge detection technique using genetic algorithm-based optimization , 1994, Pattern Recognit..

[19]  Robert M. Haralick,et al.  Digital Step Edges from Zero Crossing of Second Directional Derivatives , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[20]  Thomas O. Binford,et al.  On Detecting Edges , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[21]  Suchendra M. Bhandarkar,et al.  An edge detection technique using local smoothing and statistical hypothesis testing , 1996, Pattern Recognit. Lett..

[22]  Thomas J. Hebert,et al.  Optimized edge detection using a priori models , 1994, Proceedings of 1st International Conference on Image Processing.

[23]  S. Wolfram,et al.  Two-dimensional cellular automata , 1985 .

[24]  Sim Heng Ong,et al.  Edge detection using a neural network , 1994, Pattern Recognit..

[25]  Paul L. Rosin.  Image processing using 3-state cellular automata , 2010, Comput. Vis. Image Underst..

[26]  Humberto Bustince,et al.  Generating fuzzy edge images from gradient magnitudes , 2011, Comput. Vis. Image Underst..

[27]  Irwin Edward Sobel,et al.  Camera Models and Machine Perception , 1970 .

[28]  Pabitra Pal Choudhury,et al.  Matrix algebraic formulae concerning some exceptional rules of two-dimensional cellular automata , 2004, Inf. Sci..

[29]  Mário António da Silva Neves Ramalho,et al.  Edge detection using neural network arbitration , 1995 .

[30]  Brian G. Schunck,et al.  A Two-Stage Algorithm for Discontinuity-Preserving Surface Reconstruction , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[31]  Wim Hordijk,et al.  Cellular automata for image noise filtering , 2009, 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC).

[32]  John von Neumann,et al.  Theory Of Self Reproducing Automata , 1967 .

[33]  C. A. Murthy,et al.  Thresholding in edge detection: a statistical approach , 2004, IEEE Transactions on Image Processing.

[34]  Selman Uguz,et al.  Reversibility Algorithms for 3-State Hexagonal Cellular Automata with periodic Boundaries , 2013, Int. J. Bifurc. Chaos.

[35]  S. Wolfram.  Statistical mechanics of cellular automata , 1983 .

[36]  Robert M. Nishikawa,et al.  An evaluation criterion for edge detection techniques in noisy images , 2001, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205).

[37]  Gang Chen,et al.  Edge detection by regularized cubic B-spline fitting , 1995, IEEE Trans. Syst. Man Cybern..