Authors: Žunić, Joviša 
Title: On discrete triangles characterization
Journal: Computer Vision and Image Understanding
Volume: 90
Issue: 2
First page: 169
Last page: 189
Issue Date: 1-Jan-2003
Rank: M21a
ISSN: 1077-3142
DOI: 10.1016/S1077-3142(03)00007-9
For a given real triangle T its discretization on a discrete point set S consists of points from S which fall into T. If the number of such points is finite the obtained discretization of T will be called discrete triangle. In this paper we show that all discrete triangles from a fixed discretizing set are determined uniquely by their 10 discrete moments which have the order up to 3. Of a particular interest is the case when S is the integer grid, i.e., S = Z2. The discretization of a real triangle on Z2 is called digital triangle. It turns out that the proposed characterization preserves a coding of digital triangles from an integer grid of a given size, say m × m, within an script O sign (log m) amount of memory space per coded digital triangle. That is the theoretical minimum. A possible extension of the proposed coding scheme for digital triangles to the coding digital convex k-gons and arbitrary digital convex shapes is discussed, as well.
Keywords: Coding | Digital shape | Digital triangle | Discrete moments | Moments
Publisher: Elsevier

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