Learning Unorthogonalized Matrices for Rotation Estimation

Kerui Gu, Zhihao Li, Shiyong Liu, Jianzhuang Liu, Songcen Xu, Youliang Yan, Michael Bi Mi, Kenji Kawaguchi, Angela Yao

Primary Area: representation learning for computer vision, audio, language, and other modalities

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Keywords: geometry, optimization, pose estimation

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Abstract:

Estimating 3D rotations is a common procedure for 3D computer vision. The accuracy depends heavily on the rotation representation. Rotation matrices, recently,
have been popular due to their continuity, especially for pose estimation tasks. The
learning process usually incorporates orthogonalizations to generate orthonormal
matrices. We observe that common orthogonalization procedures like Gram-
Schmidt-based and SVD-based may slow down the training efficiency via a gradi-
ent analysis. To this end, we advocate removing orthogonalization from the learn-
ing process and learning unorthogonalized ‘Pseudo’ Rotation Matrices (PRoM).
To prove the superiority of PRoM over orthogonalization incorporated methods,
we conduct an optimization analysis to explicitly demonstrate that PRoM can con-
verge at a higher rate and to a better solution. By replacing the orthogonalization
incorporated representation with our proposed PRoM in various rotation-related
tasks, we can achieve state-of-the-art results on large-scale benchmarks

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Submission Number: 4833