Algorithms for fast convolutions on motion groups
type: Item
instance of: scholarly article
title: Algorithms for fast convolutions on motion groups
zbMATH Open document ID: 0966.65120
author: Alexander B. Kyatkin
author: Gregory S. Chirikjian
published in: Applied and Computational Harmonic Analysis
publication date: 2001-08-16T00:00:00Z
review text: The authors develop fast algorithms for the computation of convolution integrals on the motion group of the 3D Euclidean space (special Euclidean group \(\text{SE}(3)\)). Using irreducible unitary representations of \(\text{SE}(3)\) in operator form, the Fourier transform of functions on the motion group can be written as an integral over the product space \(\text{SE}(3)\otimes S^2\). The integral form of the Fourier transform matrix elements allows the application of FFT methods developed for \(\mathbb{R}^3\), \(S^2\) and \(\text{SO}(3)\). The authors provide an algorithm for the fast computation of Fourier transforms on \(\text{SE}(3)\) and discuss its complexity. Furthermore, they consider the Fourier transform for the 3D discrete motion group. The paper doesn't contain numerical results.
Mathematics Subject Classification ID: 65T50
Mathematics Subject Classification ID: 43A30
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 1512548
zbMATH Keywords: fast Fourier transform
zbMATH Keywords: fast algorithms
zbMATH Keywords: convolution integrals
zbMATH Keywords: Fourier transforms
zbMATH Keywords: complexity
zbMATH Keywords: discrete motion group
reviewed by: Gabriele Steidl
MaRDI profile type: Publication
full work available at URL: acha.2000.0321
OpenAlex ID: W2056653204
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DOI: 10.1006/ACHA.2000.0321
description: scientific article; zbMATH DE number 1512548