Metric tensor and christoffel symbols based 3D object categorization

Abstract

In this paper we propose to address the problem of 3D object categorization. We model 3D object as a piecewise smooth Riemannian manifold and propose metric tensor and Christoffel symbols as a novel set of features. The proposed set of features captures the local and global geometry of 3D objects by exploiting the uniqueness and compatibility of the features. The metric tensor represents a geometrical signature of the 3D object in a Riemannian manifold. To capture global geometry we propose to use combination of metric tensor and Christoffel symbols, as Christoffel symbols measure the deviations in the metric tensor. The categorization of 3D objects is carried out using polynomial kernel SVM classifier. The effectiveness of the proposed framework is demonstrated on 3D objects obtained from different datasets and achieved comparable results.