Normalizing Flows on the Product Space of SO Manifolds for Probabilistic Human Pose Modeling

Normalizing flows have proven their efficacy for density estimation in Euclidean space, but their application to rotational representations, crucial in various domains such as robotics or human pose modeling, remains underexplored. Probabilistic models of the human pose can benefit from approaches that rigorously consider the rotational nature of human joints. For this purpose, we introduce HuProSO3, a normalizing flow model that operates on a high-dimensional product space of SO(3) manifolds, modeling the joint distribution for human joints with three degrees of freedom. HuProSO3's advantage over state-of-the-art approaches is demonstrated through its superior modeling accuracy in three different applications and its capability to evaluate the exact likelihood. This work not only addresses the technical challenge of learning densities on SO(3) manifolds, but it also has broader implications for domains where the probabilistic regression of correlated 3D rotations is of importance.

Sample-Specific Output Constraints for Neural Networks

Neural networks reach state-of-the-art performance in a variety of learning tasks. However, a lack of understanding the decision making process yields to an appearance as black box. We address this and propose ConstraintNet, a neural network with the capability to constrain the output space in each forward pass via an additional input. The prediction of ConstraintNet is proven within the specified domain. This enables ConstraintNet to exclude unintended or even hazardous outputs explicitly whereas the final prediction is still learned from data. We focus on constraints in form of convex polytopes and show the generalization to further classes of constraints. ConstraintNet can be constructed easily by modifying existing neural network architectures. We highlight that ConstraintNet is end-to-end trainable with no overhead in the forward and backward pass. For illustration purposes, we model ConstraintNet by modifying a CNN and construct constraints for facial landmark prediction tasks. Furthermore, we demonstrate the application to a follow object controller for vehicles as a safety-critical application. We submitted an approach and system for the generation of safety-critical outputs of an entity based on ConstraintNet at the German Patent and Trademark Office with the official registration mark DE10 2019 119 739.