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Bifurcation Properties of Image Gaussian Scale-Space Model

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Abstract:

In this paper we investigate local bifurcations of Gaussian scale-space model by virtue of singularity theory. Through introducing a special equivalence, we present five normal forms of the two dimensional Gaussian scale-space model. Based on those representatives, we further explore the evolution behavior of critical points of the model. Specifically, the creation and annihilation phenomena of extreme points and saddle points are demonstrated. The result shows that the creation bifurcation of the extreme points and saddle points does not influence subsequent deep structure analysis of the Gaussian scale-space, which coincides with claims given in the current literature in a rigorous and concise way.

Keywords: CREATION AND ANNIHILATION; CRITICAL POINTS; DEEP STRUCTURE; GAUSSIAN SCALE-SPACE MODEL; NORMAL FORM

Document Type: Research Article

DOI: http://dx.doi.org/10.1166/asl.2012.2286

Publication date: March 1, 2012

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  • ADVANCED SCIENCE LETTERS is an international peer-reviewed journal with a very wide-ranging coverage, consolidates research activities in all areas of (1) Physical Sciences, (2) Biological Sciences, (3) Mathematical Sciences, (4) Engineering, (5) Computer and Information Sciences, and (6) Geosciences to publish original short communications, full research papers and timely brief (mini) reviews with authors photo and biography encompassing the basic and applied research and current developments in educational aspects of these scientific areas.
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