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Rigid Transformation Estimation in Point Registration Procedures: Study of the Use of Mahalanobis Distances

Manuel Yguel 1
1 E-MOTION - Geometry and Probability for Motion and Action
Inria Grenoble - Rhône-Alpes, LIG - Laboratoire d'Informatique de Grenoble
Abstract : This document explores the problem of the estimation of the rigid body transformation that minimizes the sum of squares between matched points of dimension $n$ where Mahalanobis distances are used. This problem is stated as a constrained minimization problem and the Lagrange multipliers framework is used. The solution is given as a system of polynomial equations. Among the solution of that system is the solution of the estimation problem. The 2-D and the 3-D cases are explicitely studied and simplified equations are given for those cases. In addition results are given concerning the optimal choice of the Lagrange multiplier.
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https://hal.inria.fr/inria-00330584
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Submitted on : Tuesday, October 14, 2008 - 9:03:12 PM
Last modification on : Friday, October 25, 2019 - 2:01:18 AM
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Manuel Yguel. Rigid Transformation Estimation in Point Registration Procedures: Study of the Use of Mahalanobis Distances. [Research Report] RR-6684, INRIA. 2008, pp.24. ⟨inria-00330584⟩

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