Non-Rigid Structure Estimation in Trajectory Space from Monocular Vision

Abstract

In this paper, the problem of non-rigid structure estimation in trajectory space from monocular vision is investigated. Similar to the Point Trajectory Approach (PTA), based on characteristic points’ trajectories described by a predefined Discrete Cosine Transform (DCT) basis, the structure matrix was also calculated by using a factorization method. To further optimize the non-rigid structure estimation from monocular vision, the rank minimization problem about structure matrix is proposed to implement the non-rigid structure estimation by introducing the basic low-rank condition. Moreover, the Accelerated Proximal Gradient (APG) algorithm is proposed to solve the rank minimization problem, and the initial structure matrix calculated by the PTA method is optimized. The APG algorithm can converge to efficient solutions quickly and lessen the reconstruction error obviously. The reconstruction results of real image sequences indicate that the proposed approach runs reliably, and effectively improves the accuracy of non-rigid structure estimation from monocular vision.

Capturing Complex 3D Human Motions with Kernelized Low-Rank Representation from Monocular RGB Camera

“…Furthermore, the performance of our marker-less algorithm is illustrated on the Human3.6M. We compare our approach, which is denoted as TUNS (temporal union of nonlinear subspaces) in the remainder of this section, against six NRSfM baselines: point tracking algorithm PTA [ 5 ], the trajectory-sapce method CSF [ 6 ], the block matrix method BMM [ 8 ], the temporal union of subspaces TUS [ 31 ], the accelerated proximal gradient optimization APG [ 9 ] and the consensus NRSfM of CNR [ 14 ]. For PTA [ 5 ], CSF [ 6 ], BMM [ 8 ], CNR [ 14 ], we use authors’ implementation in experiments.…”

“…For PTA [ 5 ] and CSF [ 6 ], we manually set the rank of the subspace to the value yielding the best results. For TUS [ 31 ] and APG [ 9 ], since there are not publicly available implementations, our re-implementations are adopted in comparison. We test such re-implementations and get similar results to what the authors reported in [ 9 , 31 ].…”

“…Consequently, it is less effective when recovering the complex motion. APG [ 9 ] inherently uses the single subspace, whereas it performs better than BMM [ 8 ] since a more effective rank-minimisation technique is employed. The part-based method CNR [ 14 ], which is more adept at handling complex shape configurations, yields better reconstruction of subject 86 than the subject 56, since sequences of subject 86 have more points than subject 56.…”

“…Based on this, a prior-free method [ 8 ] was introduced to estimate the 3D non-rigid structures and camera rotations by only exploiting the low-rank shape assumption. In Wang et al [ 9 ], they use the low-rank assumption in a similar way, but an Accelerated Proximal Gradient (APG) algorithm solver is employed to solve the resulting problem. Furthermore, the method in Gotardo and Martinez [ 10 ] combined the shape basis model and trajectory basis model, and revealed trajectories of the shape basis coefficients.…”