Probabilistic orientation estimation with matrix Fisher distributions
This work addresses a specific challenge in computer vision for tasks requiring robust orientation estimation, representing an incremental improvement over existing methods.
The paper tackles the problem of estimating probability distributions over 3D rotations using deep neural networks by employing matrix Fisher distributions to handle topological differences, resulting in improved state-of-the-art performance on datasets like Pascal3D+, ModelNet10-SO(3), and UPNA head pose.
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.