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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
• 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 latticeS a discrete state setN 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
Medical Image of a skin
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
Cellular image (von Neumann)
Cellular Image Moore
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.
Matrix representing the image
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.
Final Result
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.
Other experimental Results
Original Image
Cellular Image (von Neumann)
Cellular Image (Moore)
Result
Original Image
Cellular Image (von Neumann)
Cellular Image (Moore)
Result