Probabilistic orientation estimation with matrix Fisher distributions

D. Mohlin; G. Bianchi; J. Sullivan

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arXiv · 2006.09740

Probabilistic orientation estimation with matrix Fisher distributions

D. Mohlin·G. Bianchi·J. Sullivan

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Abstract

This paper focuses on estimating probability distributions over the set of 3D rotations ($SO(3)$) using deep neural networks. Learning to regress models to the set of rotations is inherently difficult due to differences in topology between $\mathbb{R}^N$ and $SO(3)$. We overcome this issue by using a neural network to output the parameters for a matrix Fisher distribution since these parameters are homeomorphic to $\mathbb{R}^9$. By using a negative log likelihood loss for this distribution we get a loss which is convex with respect to the network outputs. By optimizing this loss we improve state-of-the-art on several challenging applicable datasets, namely Pascal3D+, ModelNet10-$SO(3)$ and UPNA head pose.

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D. Mohlin, G. Bianchi, J. Sullivan. 2020-06-17. Probabilistic orientation estimation with matrix Fisher distributions. https://arxiv.org/abs/2006.09740

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