TY - GEN
T1 - Geometry-Aware Hierarchical Bayesian Learning on Manifolds
AU - Fan, Yonghui
AU - Wang, Yalin
N1 - Funding Information:
In this work, we propose the GAC kernel that carries properties of geometry-awareness and intra-kernel convolution. Our methods show strong feature aggregation capability in various tasks on manifolds. We hope our work may inspire future Bayesian and NN+Bayesian studies on manifolds. Acknowledgements This work was funded by grants R01EY032125 and R21AG065942.
Publisher Copyright:
© 2022 IEEE.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - Learning and Optimization Biometrics
KW - Statistical Methods
KW - Vision for Graphics
UR - http://www.scopus.com/inward/record.url?scp=85126108914&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85126108914&partnerID=8YFLogxK
U2 - 10.1109/WACV51458.2022.00280
DO - 10.1109/WACV51458.2022.00280
M3 - Conference contribution
AN - SCOPUS:85126108914
T3 - Proceedings - 2022 IEEE/CVF Winter Conference on Applications of Computer Vision, WACV 2022
SP - 2743
EP - 2752
BT - Proceedings - 2022 IEEE/CVF Winter Conference on Applications of Computer Vision, WACV 2022
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 22nd IEEE/CVF Winter Conference on Applications of Computer Vision, WACV 2022
Y2 - 4 January 2022 through 8 January 2022
ER -