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Cellular Automata based Edge Detection. Cellular Automata Definition. A discrete mathematical system characterized by local interaction and an inherently parallel form of evolution
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Cellular Automata Definition A discrete mathematical system characterized by local interaction and an inherently parallel form of evolution Each cell in cellular automata is discrete in time and the variable depends upon the its own state and neighbor at some particular time. In mathematical formalism, a cellular automata is defined as the quadruple CA = (L,S,N,f) here, L regular lattice S a discrete state set N neighborhood of size n f function that specifies transition rule
Basic Rule of Cellular Automata Start with the simple system that possesses a finite state The system will consist of a lattice structure with a network at small neighborhoods There will be a rule of interaction, defined at the local levels, which will be applied at the same time throughout the cellular space. The system will be allowed to evolve. Here, The challenge is to see how the evolving state can be used as the main engine of the computing device.
Edges in an image An edge is a boundary or a contour at which a significant change occurs in some of the physical aspects of the image.Edges are the points in a digital image at which luminous intensity, color or texture changes sharply. These includes discontinuities in depth discontinuities in surface orientation changes in material properties variations in scene illumination
Cellular Automata Model in edge detection Given an image as initial configuration state it is required that the cellular automaton reaches a final configuration where the only active cells correspond to the borders of the image. The model for border detection of a digital image is based on a bi-dimensional cellular automaton A = (S,N,f) with S = color associated with the edge pixel N is the von Neumann and Moore Neighborhood
Cont……….. And the local function is f: s5 -> s (von Neumann) f(s1, s2, s, s3, s4) = 0 if |s – si| < thres i = 1 to 4 f(s1, s2, s, s3, s4) = s if |s – si| >= thres i = 1 to 4 And the local function is f: s9 -> s (Moore) f(s1, s2, s, s3, s4, s5, s6, s7, s8) = 0 if |s – si| < thres i = 1 to 8 f(s1, s2, s, s3, s4, s5, s6, s7, s8) = s if |s – si| >= thres i = 1 to 8
Image processing for surface detection a box of pixel wxw were slide in the binary image so as to found the global threshold global threshold was the average number of pixel having value 1or higher inside the sliding box from the entire box in the image This global threshold was used to find the image matrix. In the matrix 1 represent box with number of non-zero pixel greater than the global threshold.
Cont… we found out that there was some relationship between the 1’s and 0’s boxes with their neighbor we applied some neighborhood technique to remove some error with the image.
Conclusion Experimental method Focus more on medical skin image where discontinuity on the surface orientation is looked Local function is experimental. Edges can be detected with more accuracy with change in size of the window. But need more experimentation and modification Modification may be use of local threshold than global one.
References • [1] Popovici A., Popovici D., “Cellular Automata in Image Processing”, http://www.nd.edu/~mtns/papers/17761_4.pdf • [2] Ganguly N., Sikdar B.K. , Deutsch A., Canright G., Chaudhuri P.P. , “ A survey on Cellular Automata”, http://www.cs.unibo.it/bison/publications/CAsurvey.pdf • [3] Bhattacharjee S. , Raghavendra U., Chowdhury D.R, Chaudhuri P.P, “ An Efficient Encoding Algorithm for Image Compression Hardware based on Cellular Automata”, http://ieeexplore.ieee.org/iel3/4225/12263/00565829.pdf?tp=&arnumber=565829&isnumber=12263 • [4] Dogaru R., Glesner M., Tetzlaff R., “Cellular Automata Codebook applied to compact Image Compression”, http://www.ann.ugal.ro/eeai/archives/2006/Lucrare-02-Dogaru.pdf • [5] Lafe O., “Data Compression and Encryption Using Cellular Automata Transforms”, http://www.quikcat.com/pdfs/cat_white_paper.pdf • [6] http://phylogeny.ist.unomaha.edu/mediawiki/index.php/Steph for images.
