Shape simplification through polygonal approximation in the fourier domain

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...

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Main Authors: Andrews, Mark, Kakarala, Ramakrishna
Other Authors: Röning, Juha
Format: Conference or Workshop Item
Language:English
Published: 2015
Subjects:
Online Access:https://hdl.handle.net/10356/106994
http://hdl.handle.net/10220/25238
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1069942020-05-28T07:19:05Z Shape simplification through polygonal approximation in the fourier domain Andrews, Mark Kakarala, Ramakrishna Röning, Juha Casasent, David School of Computer Engineering SPIE 9406, Intelligent Robots and Computer Vision XXXII: Algorithms and Techniques DRNTU::Engineering::Computer science and engineering::Theory of computation::Analysis of algorithms and problem complexity 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. Published version 2015-03-11T08:37:01Z 2019-12-06T22:22:40Z 2015-03-11T08:37:01Z 2019-12-06T22:22:40Z 2015 2015 Conference Paper Andrews, M., & Kakarala, R. (2015). Shape simplification through polygonal approximation in the Fourier domain. Proceedings of SPIE 9406, Intelligent Robots and Computer Vision XXXII: Algorithms and Techniques, 9406. https://hdl.handle.net/10356/106994 http://hdl.handle.net/10220/25238 10.1117/12.2078148 en © 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. 9 p. application/pdf
institution Nanyang Technological University
building NTU Library
country Singapore
collection DR-NTU
language English
topic DRNTU::Engineering::Computer science and engineering::Theory of computation::Analysis of algorithms and problem complexity
spellingShingle DRNTU::Engineering::Computer science and engineering::Theory of computation::Analysis of algorithms and problem complexity
Andrews, Mark
Kakarala, Ramakrishna
Shape simplification through polygonal approximation in the fourier domain
description 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.
author2 Röning, Juha
author_facet Röning, Juha
Andrews, Mark
Kakarala, Ramakrishna
format Conference or Workshop Item
author Andrews, Mark
Kakarala, Ramakrishna
author_sort Andrews, Mark
title Shape simplification through polygonal approximation in the fourier domain
title_short Shape simplification through polygonal approximation in the fourier domain
title_full Shape simplification through polygonal approximation in the fourier domain
title_fullStr Shape simplification through polygonal approximation in the fourier domain
title_full_unstemmed Shape simplification through polygonal approximation in the fourier domain
title_sort shape simplification through polygonal approximation in the fourier domain
publishDate 2015
url https://hdl.handle.net/10356/106994
http://hdl.handle.net/10220/25238
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