Rigid Transformation Estimation in Point Registration Procedures: Study of the Use of Mahalanobis DistancesReport as inadecuate




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





Author: Manuel Yguel -

Source: https://hal.archives-ouvertes.fr/



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