NRDF: Neural Riemannian Distance Fields for Learning Articulated Pose Priors
Authors: Yannan He, Garvita Tiwari, Tolga Birdal, Jan Eric Lenssen, Gerard Pons-Moll

Faithfully modeling the space of articulations is a crucial 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 articulations 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 sampling algorithm ensuring that the geodesic distances follow a desired distribution yielding a principled distance field learning paradigm. We then devise a projection algorithm 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 Riemannian 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.