Scale-Space hierarchy of singularities

Authors:
Tomoya Sakai;Atsushi Imiya
Affiliations:
Institute of Media and Information Technology, Chiba University, Japan;Institute of Media and Information Technology, Chiba University, Japan
Venue:
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
Year:
2005

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Abstract

This paper clarifies the nature of hierarchical relationships among singularities in the Gaussian scale-space. The hierarchy of the singular points is essentially provided by ‘stationary curves' and flux curves of ‘figure field'. They are defined, respectively, as the trajectories of stationary points across scale, and as the gradient field of the scale-space image at fixed scale. The figure field also reveals an important fact that a stationary point at infinity is involved in catastrophe events of local minimum points. These mathematical properties define the scale-space hierarchy, which is qualitatively described as a tree.