  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
