On Characterization of Discrete Triangles by Discrete Moments

  • Joviša Žunić
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2301)

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 = Z 2. 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 x m within an O(log m) amount of memory space per coded digital triangle. That is the theoretical minimum.

Keywords

Digital triangle digital shape coding moments 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Joviša Žunić
    • 1
  1. 1.Computer ScienceCardiff UniversityCardiffUK

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