A closed-form solution to estimate uncertainty in non-rigid structure from motion

Semi-Definite Programming (SDP) with low-rank prior has been widely applied in Non-Rigid Structure from Motion (NRSfM). Based on a low-rank constraint, it avoids the inherent ambiguity of basis number selection in conventional base-shape or base-trajectory methods. Despite the efficiency in deformable shape reconstruction, it remains unclear how to assess the uncertainty of the recovered shape from the SDP process. In this paper, we present a statistical inference on the element-wise uncertainty quantification of the estimated deforming 3D shape points in the case of the exact low-rank SDP problem. A closed-form uncertainty quantification method is proposed and tested. Moreover, we extend the exact low-rank uncertainty quantification to the approximate low-rank scenario with a numerical optimal rank selection method, which enables solving practical application in SDP based NRSfM scenario. The proposed method provides an independent module to the SDP method and only requires the statistic information of the input 2D tracked points. Extensive experiments prove that the output 3D points have identical normal distribution to the 2D trackings, the proposed method and quantify the uncertainty accurately, and supports that it has desirable effects on routinely SDP low-rank based NRSfM solver.Comment: 9 pages, 2 figure

Invariant Teacher and Equivariant Student for Unsupervised 3D Human Pose Estimation

We propose a novel method based on teacher-student learning framework for 3D human pose estimation without any 3D annotation or side information. To solve this unsupervised-learning problem, the teacher network adopts pose-dictionary-based modeling for regularization to estimate a physically plausible 3D pose. To handle the decomposition ambiguity in the teacher network, we propose a cycle-consistent architecture promoting a 3D rotation-invariant property to train the teacher network. To further improve the estimation accuracy, the student network adopts a novel graph convolution network for flexibility to directly estimate the 3D coordinates. Another cycle-consistent architecture promoting 3D rotation-equivariant property is adopted to exploit geometry consistency, together with knowledge distillation from the teacher network to improve the pose estimation performance. We conduct extensive experiments on Human3.6M and MPI-INF-3DHP. Our method reduces the 3D joint prediction error by 11.4% compared to state-of-the-art unsupervised methods and also outperforms many weakly-supervised methods that use side information on Human3.6M. Code will be available at https://github.com/sjtuxcx/ITES.Comment: Accepted in AAAI 202

MHR-Net: Multiple-Hypothesis Reconstruction of Non-Rigid Shapes from 2D Views

We propose MHR-Net, a novel method for recovering Non-Rigid Shapes from Motion (NRSfM). MHR-Net aims to find a set of reasonable reconstructions for a 2D view, and it also selects the most likely reconstruction from the set. To deal with the challenging unsupervised generation of non-rigid shapes, we develop a new Deterministic Basis and Stochastic Deformation scheme in MHR-Net. The non-rigid shape is first expressed as the sum of a coarse shape basis and a flexible shape deformation, then multiple hypotheses are generated with uncertainty modeling of the deformation part. MHR-Net is optimized with reprojection loss on the basis and the best hypothesis. Furthermore, we design a new Procrustean Residual Loss, which reduces the rigid rotations between similar shapes and further improves the performance. Experiments show that MHR-Net achieves state-of-the-art reconstruction accuracy on Human3.6M, SURREAL and 300-VW datasets.Comment: Accepted to ECCV 202