Geometry-Aware Hierarchical Bayesian Learning on Manifolds

TL;DR

This paper introduces a hierarchical Bayesian learning model tailored for 3D manifold-valued vision data, effectively aggregating geometric features without hand-crafted descriptors, and explores joint neural-Bayesian learning.

Contribution

It proposes a geometry-aware kernel and hierarchical Bayesian network for efficient feature aggregation on manifolds, and investigates combining neural networks with Bayesian models.

Findings

Outperforms existing Bayesian methods on manifold data

Demonstrates the feasibility of joint neural and Bayesian learning on manifolds

Shows potential for improved geometric feature inference

Abstract

Bayesian learning with Gaussian processes demonstrates encouraging regression and classification performances in solving computer vision tasks. However, Bayesian methods on 3D manifold-valued vision data, such as meshes and point clouds, are seldom studied. One of the primary challenges is how to effectively and efficiently aggregate geometric features from the irregular inputs. In this paper, we propose a hierarchical Bayesian learning model to address this challenge. We initially introduce a kernel with the properties of geometry-awareness and intra-kernel convolution. This enables geometrically reasonable inferences on manifolds without using any specific hand-crafted feature descriptors. Then, we use a Gaussian process regression to organize the inputs and finally implement a hierarchical Bayesian network for the feature aggregation. Furthermore, we incorporate the feature learning of neural networks with the feature aggregation of Bayesian models to investigate the feasibility of jointly learning on manifolds. Experimental results not only show that our method outperforms existing Bayesian methods on manifolds but also demonstrate the prospect of coupling neural networks with Bayesian networks.