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Proceedings Paper • Open Access

Shape simplification through polygonal approximation in the Fourier domain
Author(s): Mark Andrews; Ramakrishna Kakarala

Paper Abstract

Fourier descriptors have long been used to describe the underling continuous contours of two-dimensional shapes. Approximations of shapes by polygons is a natural step for efficient algorithms in computer graphics and computer vision. This paper derives mathematical relationships between the Fourier descriptors of the continuous contour, and the corresponding descriptors of a polygon obtained by connecting samples on the contour. We show that the polygon's descriptors may be obtained analytically in two ways: first, by summing subsets of the contour's descriptors; and second, from the discrete Fourier transform (DFT) of the polygon's vertices. We also analyze, in the Fourier domain, shape approximation using interpolators. Our results show that polygonal approximation, with its potential benefits for efficient analysis of shape, is achievable in the Fourier descriptor domain.

Paper Details

Date Published: 8 February 2015
PDF: 9 pages
Proc. SPIE 9406, Intelligent Robots and Computer Vision XXXII: Algorithms and Techniques, 94060D (8 February 2015); doi: 10.1117/12.2078148
Show Author Affiliations
Mark Andrews, The Univ. of Auckland (New Zealand)
Ramakrishna Kakarala, Nanyang Technological Univ. (Singapore)

Published in SPIE Proceedings Vol. 9406:
Intelligent Robots and Computer Vision XXXII: Algorithms and Techniques
Juha Röning; David Casasent, Editor(s)

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