Projective Manifold Gradient Layer for Deep Rotation Regression

• URL: http://arxiv.org/abs/2110.11657v1
• Date: Fri, 22 Oct 2021 08:34:15 GMT
• Title: Projective Manifold Gradient Layer for Deep Rotation Regression
• Authors: Jiayi Chen, Yingda Yin, Tolga Birdal, Baoquan Chen, Leonidas Guibas, He Wang
• Abstract summary: Regressing rotations on SO(3) manifold using deep neural networks is an important yet unsolved problem. We propose a manifold-aware gradient that directly backpropagates into deep network weights.
• Score: 49.85464297105456
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Regressing rotations on SO(3) manifold using deep neural networks is an important yet unsolved problem. The gap between Euclidean network output space and the non-Euclidean SO(3) manifold imposes a severe challenge for neural network learning in both forward and backward passes. While several works have proposed different regression-friendly rotation representations, very few works have been devoted to improving the gradient backpropagating in the backward pass. In this paper, we propose a manifold-aware gradient that directly backpropagates into deep network weights. Leveraging the Riemannian gradient and a novel projective gradient, our proposed regularized projective manifold gradient (RPMG) helps networks achieve new state-of-the-art performance in a variety of rotation estimation tasks. The proposed gradient layer can also be applied to other smooth manifolds such as the unit sphere.

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