NRDF: Neural Riemannian Distance Fields for Learning Articulated Pose Priors

Abstract

Faithfully modeling the space of articulations is a cru-cial task that allows recovery and generation of realistic poses, and remains a notorious challenge. To this end, we introduce Neural Riemannian Distance Fields (NRDFs), data-driven priors modeling the space of plausible articu-lations, represented as the zero-level-set of a neural field in a high-dimensional product-quaternion space. To train NRDFs only on positive examples, we introduce a new sam-pling algorithm, ensuring that the geodesic distances fol-low a desired distribution, yielding a principled distance field learning paradigm. We then devise a projection al-gorithm to map any random pose onto the level-set by an adaptive-step Riemannian optimizer, adhering to the product manifold of joint rotations at all times. NRDFs can compute the Riemannian gradient via backpropagation and by mathematical analogy, are related to Rieman-nian flow matching, a recent generative model. We conduct a comprehensive evaluation of NRDF against other pose priors in various downstream tasks, i.e., pose generation, image-based pose estimation, and solving inverse kinematics, highlighting NRDF's superior performance. Besides humans, NRDF's versatility extends to hand and animal poses, as it can effectively represent any articulation.