A Simple, General Model for the Affine Self-similarity of Images

Authors:
Simon K. Alexander;Edward R. Vrscay;Satoshi Tsurumi
Affiliations:
Department of Mathematics, University of Houston, Houston, USA 77204;Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, Canada N2L 3G1;Department of Information and Computer Engineering, Gunma National College of Technology, Maebashi, Japan 371-8530
Venue:
ICIAR '08 Proceedings of the 5th international conference on Image Analysis and Recognition
Year:
2008

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Abstract

A series of extensive numerical experiments indicates that images, in general, possess a considerable degree of affine self-similarity, that is, blocks are well approximated by a number of other blocks --- at the same or different scales --- when affine greyscale transformations are employed. We introduce a simple model of affine image self-similarity which includes the method of fractal image coding (cross-scale, affine greyscale similarity) and the nonlocal means denoising method (same-scale, translational similarity) as special cases.