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A Characterization of Discretized Polygonal Convex Regions by Discrete Moments

  • Joviša Žunić
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2905)

Abstract

For a given planar region P its discretization on a discrete planar point set \(\mathcal{S}\) consists of the points from \(\mathcal{S}\) which fall into P. If P is bounded with a convex polygon having n vertices and the number of points from \(P \cap \mathcal{S}\) is finite, the obtained discretization of P will be called discrete convexn-gon.

In this paper we show that discrete moments having the order up to n characterize uniquely the corresponding discrete convex n-gon if the discretizing set \(\mathcal{S}\) is fixed. In this way, as an example, the matching of discrete convex n-gons can be done by comparing \(\frac{1}{2} \cdot (n + 1) \cdot (n + 2)\) discrete moments what can be much efficient than the comparison “point-by-point” since a digital convex n-gon can consist of an arbitrary large number of points.

Keywords

Discrete shape coding moments pattern matching 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Joviša Žunić
    • 1
  1. 1.Computer ScienceCardiff UniversityCardiff, WalesU.K.

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