Authors: Žunić, Joviša 
Title: On characterization of discrete triangles by discrete moments
Journal: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume: 2301
First page: 232
Last page: 243
Conference: 10th International Conference on Discrete Geometry for Computer Imagery, DGCI 2002; Bordeaux; France; 3 April 2002 through 5 April 2002
Issue Date: 1-Jan-2002
Rank: M22
ISBN: 978-3-540-43380-5
ISSN: 0302-9743
DOI: 10.1007/3-540-45986-3_21
Abstract: 
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 the discrete moments having the order up to 3 characterize uniquely the corresponding discrete triangle if the discretizationing set S is fixed. Of a particular interest is the case when S is the integer grid, i.e., S = Z2. Then the discretization of a triangle T 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 O(logm) amount of memory space per coded digital triangle. That is the theoretical minimum.
Keywords: Coding | Digital shape | Digital triangle | Moments
Publisher: Springer Link

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