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

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.

Mots clés: point registration; rigid body transformation; Mahalanobis distance; ICP; ECMPR; polynomial systems

Domaines: Robotique [cs.RO]

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⟩