Fast communication: The use of total least squares data fitting in the shape-from-moments problem

Authors:
M. Schuermans;P. Lemmerling;L. De Lathauwer;S. Van Huffel
Affiliations:
Katholieke Universiteit Leuven, ESAT-SCD, Kasteelpark Arenberg 10, B-3001 Leuven-Heverlee, Belgium;Katholieke Universiteit Leuven, ESAT-SCD, Kasteelpark Arenberg 10, B-3001 Leuven-Heverlee, Belgium;Katholieke Universiteit Leuven, ESAT-SCD, Kasteelpark Arenberg 10, B-3001 Leuven-Heverlee, Belgium and ETIS (CNRS, ENSEA, UCP), UMR 8051, Cergy-Pontoise, France;Katholieke Universiteit Leuven, ESAT-SCD, Kasteelpark Arenberg 10, B-3001 Leuven-Heverlee, Belgium
Venue:
Signal Processing
Year:
2006

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Abstract

In this paper we discuss the problem of recovering the vertices of a planar polygon from its measured complex moments. Because the given, measured moments can be noisy, the recovered vertices are only estimates of the true ones. The literature offers many algorithms for solving such an estimation problem. We will restrict our discussion to the Total Least Squares (TLS) data fitting models HTLS and STLS and the matrix pencil method GPOF. We show the close link between the HTLS and the GPOF method. We use the HTLS method to compute starting values for the STLS method. We compare the accuracy of these three methods on simulated data.