Part of Advances in Neural Information Processing Systems 33 (NeurIPS 2020)

*David Mohlin, Josephine Sullivan, Gérald Bianchi*

This paper focuses on estimating probability distributions over the set of 3D ro-
tations (SO(3)) using deep neural networks. Learning to regress models to the
set of rotations is inherently difficult due to differences in topology between
R^N and SO(3). We overcome this issue by using a neural network to out-
put the parameters for a matrix Fisher distribution since these parameters are
homeomorphic to R^9 . By using a negative log likelihood loss for this distri-
bution 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 applica-
ble datasets, namely Pascal3D+, ModelNet10-SO(3). Our code is available at
https://github.com/Davmo049/Public*prob*orientation*estimation*with*matrix
_fisher*distributions

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