Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifold

Single image pose estimation is a fundamental problem in many vision and\nrobotics tasks, and existing deep learning approaches suffer by not completely\nmodeling and handling: i) uncertainty about the predictions, and ii) symmetric\nobjects with multiple (sometimes infinite) correct poses. To this end, we\nintroduce a method to estimate arbitrary, non-parametric distributions on\nSO(3). Our key idea is to represent the distributions implicitly, with a neural\nnetwork that estimates the probability given the input image and a candidate\npose. Grid sampling or gradient ascent can be used to find the most likely\npose, but it is also possible to evaluate the probability at any pose, enabling\nreasoning about symmetries and uncertainty. This is the most general way of\nrepresenting distributions on manifolds, and to showcase the rich expressive\npower, we introduce a dataset of challenging symmetric and nearly-symmetric\nobjects. We require no supervision on pose uncertainty -- the model trains only\nwith a single pose per example. Nonetheless, our implicit model is highly\nexpressive to handle complex distributions over 3D poses, while still obtaining\naccurate pose estimation on standard non-ambiguous environments, achieving\nstate-of-the-art performance on Pascal3D+ and ModelNet10-SO(3) benchmarks.\n