Geometry-Aware Hierarchical Bayesian Learning on Manifolds

Yonghui Fan, Yalin Wang; Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision (WACV), 2022, pp. 1786-1795

Bayesian learning with Gaussian processes demonstrates encouraging regression and classification performance 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 inputs. In this paper, we propose a hierarchical Bayesian learning model to address this challenge. We implicitly introduce the geometry-awareness and the intra-kernel convolution to the kernel so that the prior becomes geometry sensitive without using any hand-crafted feature descriptors. We implement a hierarchical feature aggregation architecture by concatenating multiple Gaussian processes together. Furthermore, we incorporate the feature learning of neural networks with the feature aggregation of Bayesian models to investigate the feasibility of jointly learning inferences 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 learning methods