Generalized Fourier Descriptors with Applications

Authors: Fethi Smach Cedric Lemaître JeanPaul Gauthier Johel Miteran Mohamed Atri

Publish Date: 2007/12/01

Volume: 30, Issue: 1, Pages: 43-71

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Abstract

This paper is about generalized Fourier descriptors and their application to the research of invariants under group actions A general methodology is developed crucially related to Pontryagin’s Tannaka’s Chu’s and Tatsuuma’s dualities from abstract harmonic analysis Application to motion groups provides a general methodology for pattern recognition This methodology generalizes the classical basic method of Fourierinvariants of contours of objects In the paper we use the results of this theory inside a SupportVectorMachine context for 3D objectsrecognition As usual in practice we classify 3D objects starting from 2D information However our method is rather general and could be applied directly to 3D data in other contextsOur applications and comparisons with other methods are about humanface recognition but also we provide tests and comparisons based upon standard databases such as the COIL database Our methodology looks extremely efficient and effective computations are rather simple and low costThe paper is divided in two parts first the part relative to applications and computations in a SVM environment The second part is devoted to the development of the general theory of generalized Fourierdescriptors with several new results about their completeness in particular These results lead to simple formulas for motioninvariants of images that are “complete” in a certain sense and that are used in the first part of the paper The computation of these invariants requires only standard FFT estimations and one dimensional integration

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