Title: Edge detection using fractal imaging

Authors: Matthew Demers

Addresses: Department of Mathematics and Statistics, University of Guelph, 50 Stone Road E, Guelph, ON, N1G 2W1 Canada

Abstract: Many direct approaches to edge detection appear in the literature. Typical approaches approximate gradients or second-order derivatives in images with the goal of finding curves along which there is a sharp transition in intensity. In fractal image compression, one seeks to approximate a target image by the fixed point of a contractive operator called a local iterated function system with grey-level maps (LIFSM). These map parent blocks in an image to smaller child blocks; grey-level maps adjust the shading of shrunken blocks. The fixed point of this operator approximates the target image. We outline an edge detection technique by introducing changes to LIFSM, allowing for overlapping child blocks and multiple parent blocks. The edge detector takes into account two different criteria: clustering of parent blocks, and values of grey-level map parameters. We show that this approach to edge detection can give results comparable to established edge detection techniques.

Keywords: fractal imaging; edge detection; applied analysis; self-similarity; optimisation; fractal image compression; local iterated function; grey level maps; LIFSM.

DOI: 10.1504/IJMMNO.2012.049602

International Journal of Mathematical Modelling and Numerical Optimisation, 2012 Vol.3 No.4, pp.266 - 280

Published online: 30 Aug 2014 *

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