Shape simplification through polygonal approximation in the fourier domain
Date of Issue2015
SPIE 9406, Intelligent Robots and Computer Vision XXXII: Algorithms and Techniques
School of Computer Engineering
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.
DRNTU::Engineering::Computer science and engineering::Theory of computation::Analysis of algorithms and problem complexity
© 2015 Society of Photo-optical Instrumentation Engineers. This paper was published in Proceedings of SPIE 9406, Intelligent Robots and Computer Vision XXXII: Algorithms and Techniques and is made available as an electronic reprint (preprint) with permission of Society of Photo-optical Instrumentation Engineers. The paper can be found at the following official DOI: [http://dx.doi.org/10.1117/12.2078148]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.