A Statistical Manifold Framework for Point Cloud Data

이용현(서울대), 김승연(서울대), 최진원(카카오엔터프라이즈), 박종우(서울대)

International Conference on Machine Learning (ICML)



Many problems in machine learning involve data sets in which each data point is a point cloud in R^D. A growing number of applications require a means of measuring not only distances between point clouds, but also angles, volumes, derivatives, and other more advanced concepts. To formulate and quantify these concepts in a coordinate-invariant way, we develop a Riemannian geometric framework for point cloud data. By interpreting each point in a point cloud as a sample drawn from some given underlying probability density, the space of point cloud data can be given the structure of a statistical manifold – each point on this manifold represents a point cloud – with the Fisher information metric acting as a natural Riemannian metric. Two autoencoder applications of our framework are presented: (i) smoothly deforming one 3D object into another via interpolation between the two corresponding point clouds; (ii) learning an optimal set of latent space coordinates for point cloud data that best preserves angles and distances, and thus produces a more discriminative representation space. Experiments with large-scale standard benchmark point cloud data show greatly improved classification accuracy vis-´a-vis existing methods.