# 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.
Keywords :
Type de document :
Rapport
[Research Report] RR-6684, INRIA. 2008, pp.24
Domaine :

Littérature citée [5 références]

https://hal.inria.fr/inria-00330584
Contributeur : Manuel Yguel <>
Soumis le : mardi 14 octobre 2008 - 21:03:12
Dernière modification le : vendredi 12 octobre 2018 - 01:18:13
Document(s) archivé(s) le : mardi 9 octobre 2012 - 13:00:24

### Fichier

RR-6684.pdf
Fichiers produits par l'(les) auteur(s)

### Identifiants

• 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〉

### Métriques

Consultations de la notice

## 343

Téléchargements de fichiers