Point matching based on affine invariant centroid trees

Abstract

Object detection can be formulated as a point matching problem when objects are modeled by point sets. Moments, which have been widely used for point matching, are limited to affine transformations as their support point sets cannot keep invariant. To address this problem, we developed an affine invariant centroid tree (AICT) to obtain a rigorous affine invariant support point set (SPS). The algorithm is constructed by a recursive process: the point set is first divided by the vector from the certain point to the centroid of the point set, and the centroids of subsets are used to generate vectors for renewed partitions. In addition, the centroids of the subsets are stored to form an AICT. The AICT represents the inherent structure of the point set. It is highly tolerant to noise and outliers due to the partitions on the whole point set. More importantly, it is affine invariant owing to the affine invariance of partition. Therefore, we can get rigorous affine invariant descriptors while moments are combined with AICT. The experimental results on synthesized and real data verify that our proposed algorithm outperforms the state-of-the-art point matching methods including shape context, iterative closet point, and the method adopting thin plate spline for rigid robust point matching (TPS-RPM).