Information Geometric Framework For Point Cloud Data

TL;DR

This paper presents an information geometric approach to compare 3D point clouds by modeling them as probability distributions using GMMs and measuring their similarity with a modified KL divergence, capturing geometric features effectively.

Contribution

The paper introduces a novel framework that applies information geometry to point cloud comparison, integrating GMMs and a modified divergence for improved geometric analysis.

Findings

Effective comparison across diverse shape datasets

Captures geometric features more accurately

Applicable to audio signal analysis as well

Abstract

In this paper, we introduce a novel method for comparing 3D point clouds, a critical task in various machine learning applications. By interpreting point clouds as samples from underlying probability density functions, the statistical manifold structure is given to the space of point clouds. This manifold structure will help us to use the information geometric tools to analyze the point clouds. Our method uses the Gaussian Mixture Model (GMM) to find the probability density functions and the Modified Symmetric KL divergence to measure how similar the corresponding probability density functions are. This method of comparing the point clouds takes care of the geometry of the objects represented by the point clouds. To demonstrate the effectiveness of our approach, we take up five distinct case studies:(i) comparison of basic geometric shapes, (ii) comparison of 3D human body shapes within the MP FAUST dataset, (iii) comparison of animal shapes, (iv) comparison of human and animal datasets and (v) comparison of audio signals.