Information Geometric Framework for Point Cloud Analysis

This paper introduces a novel method for comparing three dimensional point clouds, a critical task in various applications such as computer vision, pattern recognition etc. In this method, point cloud is interpreted as samples from an underlying probability distribution-Gaussian Mixture Model. Then, a rigorous mathematical foundation is established by proving that the space of Gaussian Mixture Models form a statistical manifold. The statistical manifold structure of Gaussian Mixture Model enables us to use the information geometric tools for similarity measure. The similarity or distance measures between Gaussian Mixture Models plays a crucial role in many applications. In this paper, the Modified Symmetric Kullback-Leibler Divergence is used for the similarity measure. This method of comparing the point clouds takes care of the geometry of the objects represented by the point clouds. The experimental result on comparison (i) of basic geometric shapes, (ii) of three-dimensional human body shapes within a comprehensive human body shape dataset, (iii) of animal shapes and (iv) of point clouds of same objects produced from the dense point clouds in Point Cloud Upsampling Adversarial Network dataset indicate that the information geometric method achieves superior performance compared with the state-of-the-art methods and valuable insights are derived from the results.