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