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Proceedings Paper

Differentialless geometry of plane curves
Author(s): Longin Jan Latecki; Azriel Rosenfeld
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Paper Abstract

We introduce a class of planar arcs and curves, called tame arcs, which is general enough to describe the boundaries of planar real objects. A tame arc can have smooth parts as well as sharp corners; thus a polygonal arc is tame. On the other hand, this class of arcs is restrictive enough to rule out pathological arcs which have infinitely many inflections or which turn infinitely often: a tame arc can have only finitely many inflections, and its total absolute turn must be finite. In order to relate boundary properties of discrete objects obtained by segmenting digital images to the corresponding properties of their continuous originals, the theory of tame arcs is based on concepts that can be directly transferred from the continuous to the discrete domain. A tame arc is composed of a finite number of supported arcs. We define supported digital arcs and motivate their definition by the fact that hey can be obtained by digitizing continuous supported arcs. Every digital arc is tame, since it contains a finite number of points, and therefore it can be decomposed into a finite number of supported digital arcs.

Paper Details

Date Published: 20 October 1997
PDF: 11 pages
Proc. SPIE 3168, Vision Geometry VI, (20 October 1997); doi: 10.1117/12.279677
Show Author Affiliations
Longin Jan Latecki, Univ. of Hamburg (Germany)
Azriel Rosenfeld, Univ. of Maryland/College Park (United States)

Published in SPIE Proceedings Vol. 3168:
Vision Geometry VI
Robert A. Melter; Angela Y. Wu; Longin Jan Latecki, Editor(s)

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