G. Bianchi

David Mohlin, Gerald Bianchi, Josephine Sullivan

In this paper we describe a probabilistic method for estimating the position of an object along with its covariance matrix using neural networks. Our method is designed to be robust to outliers, have bounded gradients with respect to the network outputs, among other desirable properties. To achieve this we introduce a novel probability distribution inspired by the Huber loss. We also introduce a new way to parameterize positive definite matrices to ensure invariance to the choice of orientation for the coordinate system we regress over. We evaluate our method on popular body pose and facial landmark datasets and get performance on par or exceeding the performance of non-heatmap methods. Our code is available at github.com/Davmo049/Public_prob_regression_with_huber_distributions

D. Mohlin, G. Bianchi, J. Sullivan

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.