Mahalanobis Distance Based Iterative Closest Point

This paper proposes an extension to the standard iterative closest point method (ICP). In contrast to ICP, our approach (ICP-M) uses the Mahalanobis distance to align a set of shapes thus assigning an anisotropic independent Gaussian noise to each point in the reference shape. The paper introduces the notion of a mahalanobis distance map upon a point set with associated covariance matrices which in addition to providing correlation weighted distance implicitly provides a method for assigning correspondence during alignment. This distance map provides an easy formulation of the ICP problem that permits a fast optimization. Initially, the covariance matrices are set to the identity matrix, and all shapes are aligned to a randomly selected shape (equivalent to standard ICP). From this point the algorithm iterates between the steps: (a) obtain mean shape and new estimates of the covariance matrices from the aligned shapes, (b) align shapes to the mean shape. Three different methods for estimating the mean shape with associated covariance matrices are explored in the paper. The proposed methods are validated experimentally on two separate datasets (IMM face dataset and femur-bones). The superiority of ICP-M compared with ICP in recovering the underlying correspondences in the face dataset is demonstrated.