Combinatorial properties of scale space singular points

Authors:
Atsushi Imiya;Tomoya Sakai
Affiliations:
Institute of Media and Information Technology, Chiba University, Chiba, Japan;Institute of Media and Information Technology, Chiba University, Chiba, Japan
Venue:
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Year:
2006

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Abstract

Singular points in the linear scale space provide fundamental features for the extraction of dominant parts of an image. Employing the geometrical configuration of singular points, it is possible to construct a tree in scale space. This tree expresses a hierarchical structure of dominant parts. In this paper, we clarify the graphical grammar for the construction of this tree in the linear scale space and morphological scale space. Furthermore, we show a combinatorial structure of singular points in the linear scale space and morphological scale space using conformal mapping from Euclidean space to the spherical surface.