Shaohua Pan

Shaohua Pan, Xinyu Yi, Yan Zhou et al.

Combining sparse IMUs and a monocular camera is a new promising setting to perform real-time human motion capture. This paper proposes a diffusion-based solution to learn human motion priors and fuse the two modalities of signals together seamlessly in a unified framework. By delicately considering the characteristics of the two signals, the sequential visual information is considered as a whole and transformed into a condition embedding, while the inertial measurement is concatenated with the noisy body pose frame by frame to construct a sequential input for the diffusion model. Firstly, we observe that the visual information may be unavailable in some frames due to occlusions or subjects moving out of the camera view. Thus incorporating the sequential visual features as a whole to get a single feature embedding is robust to the occasional degenerations of visual information in those frames. On the other hand, the IMU measurements are robust to occlusions and always stable when signal transmission has no problem. So incorporating them frame-wisely could better explore the temporal information for the system. Experiments have demonstrated the effectiveness of the system design and its state-of-the-art performance in pose estimation compared with the previous works. Our codes are available for research at https://shaohua-pan.github.io/diffcap-page.

Shaohua Pan, Qi Ma, Xinyu Yi et al.

Either RGB images or inertial signals have been used for the task of motion capture (mocap), but combining them together is a new and interesting topic. We believe that the combination is complementary and able to solve the inherent difficulties of using one modality input, including occlusions, extreme lighting/texture, and out-of-view for visual mocap and global drifts for inertial mocap. To this end, we propose a method that fuses monocular images and sparse IMUs for real-time human motion capture. Our method contains a dual coordinate strategy to fully explore the IMU signals with different goals in motion capture. To be specific, besides one branch transforming the IMU signals to the camera coordinate system to combine with the image information, there is another branch to learn from the IMU signals in the body root coordinate system to better estimate body poses. Furthermore, a hidden state feedback mechanism is proposed for both two branches to compensate for their own drawbacks in extreme input cases. Thus our method can easily switch between the two kinds of signals or combine them in different cases to achieve a robust mocap. %The two divided parts can help each other for better mocap results under different conditions. Quantitative and qualitative results demonstrate that by delicately designing the fusion method, our technique significantly outperforms the state-of-the-art vision, IMU, and combined methods on both global orientation and local pose estimation. Our codes are available for research at https://shaohua-pan.github.io/robustcap-page/.

Xinyu Yi, Yuxiao Zhou, Marc Habermann et al.

Human and environment sensing are two important topics in Computer Vision and Graphics. Human motion is often captured by inertial sensors, while the environment is mostly reconstructed using cameras. We integrate the two techniques together in EgoLocate, a system that simultaneously performs human motion capture (mocap), localization, and mapping in real time from sparse body-mounted sensors, including 6 inertial measurement units (IMUs) and a monocular phone camera. On one hand, inertial mocap suffers from large translation drift due to the lack of the global positioning signal. EgoLocate leverages image-based simultaneous localization and mapping (SLAM) techniques to locate the human in the reconstructed scene. On the other hand, SLAM often fails when the visual feature is poor. EgoLocate involves inertial mocap to provide a strong prior for the camera motion. Experiments show that localization, a key challenge for both two fields, is largely improved by our technique, compared with the state of the art of the two fields. Our codes are available for research at https://xinyu-yi.github.io/EgoLocate/.

Ting Tao, Yitian Qian, Shaohua Pan

This paper is concerned with the column $\ell_{2,0}$-regularized factorization model of low-rank matrix recovery problems and its computation. The column $\ell_{2,0}$-norm of factor matrices is introduced to promote column sparsity of factors and low-rank solutions. For this nonconvex discontinuous optimization problem, we develop an alternating majorization-minimization (AMM) method with extrapolation, and a hybrid AMM in which a majorized alternating proximal method is proposed to seek an initial factor pair with less nonzero columns and the AMM with extrapolation is then employed to minimize of a smooth nonconvex loss. We provide the global convergence analysis for the proposed AMM methods and apply them to the matrix completion problem with non-uniform sampling schemes. Numerical experiments are conducted with synthetic and real data examples, and comparison results with the nuclear-norm regularized factorization model and the max-norm regularized convex model show that the column $\ell_{2,0}$-regularized factorization model has an advantage in offering solutions of lower error and rank within less time.

Ting Tao, Shaohua Pan, Shujun Bi

This paper is concerned with the squared F(robenius)-norm regularized factorization form for noisy low-rank matrix recovery problems. Under a suitable assumption on the restricted condition number of the Hessian for the loss function, we derive an error bound to the true matrix for the non-strict critical points with rank not more than that of the true matrix. Then, for the squared F-norm regularized factorized least squares loss function, under the noisy and full sample setting we establish its KL property of exponent $1/2$ on its global minimizer set, and under the noisy and partial sample setting achieve this property for a class of critical points. These theoretical findings are also confirmed by solving the squared F-norm regularized factorization problem with an accelerated alternating minimization method.

Shujun Bi, Ting Tao, Shaohua Pan

This paper is concerned with the factorization form of the rank regularized loss minimization problem. To cater for the scenario in which only a coarse estimation is available for the rank of the true matrix, an $\ell_{2,0}$-norm regularized term is added to the factored loss function to reduce the rank adaptively; and account for the ambiguities in the factorization, a balanced term is then introduced. For the least squares loss, under a restricted condition number assumption on the sampling operator, we establish the KL property of exponent $1/2$ of the nonsmooth factored composite function and its equivalent DC reformulations in the set of their global minimizers. We also confirm the theoretical findings by applying a proximal linearized alternating minimization method to the regularized factorizations.

Yulan Liu, Shujun Bi, Shaohua Pan

This paper proposes a mechanism to produce equivalent Lipschitz surrogates for zero-norm and rank optimization problems by means of the global exact penalty for their equivalent mathematical programs with an equilibrium constraint (MPECs). Specifically, we reformulate these combinatorial problems as equivalent MPECs by the variational characterization of the zero-norm and rank function, show that their penalized problems, yielded by moving the equilibrium constraint into the objective, are the global exact penalization, and obtain the equivalent Lipschitz surrogates by eliminating the dual variable in the global exact penalty. These surrogates, including the popular SCAD function in statistics, are also difference of two convex functions (D.C.) if the function and constraint set involved in zero-norm and rank optimization problems are convex. We illustrate an application by designing a multi-stage convex relaxation approach to the rank plus zero-norm regularized minimization problem.

Weimin Miao, Shaohua Pan, Defeng Sun

For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation matrix completion in various fields such as the financial market and the low-rank density matrix completion from the quantum state tomography. To seek a solution of high recovery quality beyond the reach of the nuclear norm, in this paper, we propose a rank-corrected procedure using a nuclear semi-norm to generate a new estimator. For this new estimator, we establish a non-asymptotic recovery error bound. More importantly, we quantify the reduction of the recovery error bound for this rank-corrected procedure. Compared with the one obtained for the nuclear norm penalized least squares estimator, this reduction can be substantial (around 50%). We also provide necessary and sufficient conditions for rank consistency in the sense of Bach (2008). Very interestingly, these conditions are highly related to the concept of constraint nondegeneracy in matrix optimization. As a byproduct, our results provide a theoretical foundation for the majorized penalty method of Gao and Sun (2010) and Gao (2010) for structured low-rank matrix optimization problems. Extensive numerical experiments demonstrate that our proposed rank-corrected procedure can simultaneously achieve a high recovery accuracy and capture the low-rank structure.