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

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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Reports (Research report)
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Cited literature [5 references]

https://hal.inria.fr/inria-00330584
Contributor : Manuel Yguel Connect in order to contact the contributor
Submitted on : Tuesday, October 14, 2008 - 9:03:12 PM
Last modification on : Wednesday, October 26, 2022 - 8:16:45 AM
Long-term archiving on: : Tuesday, October 9, 2012 - 1:00:24 PM

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RR-6684.pdf
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• HAL Id : inria-00330584, version 1

### Citation

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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