SOLO: Efficient 3D Rigid-Body Motion Registration.pdf

Robust PCA is used to initialize a low-rank shape representation of the rigid body, finding the global optimal solution while its complexity is comparable to singular value decomposition. In the online update stage, a sparse subspace projection method projects new observations onto the low-dimensional shape model, correcting possible sparse data corruption. The overall algorithm, called Sparse Online Low-rank projection and Outlier rejection (SOLO), is illustrated in Figure 1. SOLO provides provable global optimality to compensate missing data, image corruption, and erroneous feature tracks, and is more efficient to recover rigid-body motion from a video sequence in an online fashion. The algorithm is guaranteed to converge to the global optimum if the ambient space dimension is sufficiently high, and has minimal heuristic parameters to tune. Recent progress in convex optimization has led to very efficient numerical implementation of RPCA with computational complexity comparable to classical SVD. The proposed solution consists of two steps: initialization and online update. In the initialization step, RPCA is used to estimate a low-rank representation of the rigid-body motion within the first several image frames, establishing a global shape model of the rigid body. In the online update step, the sparse subspace projection method projects new observations onto the low-dimensional shape model, simultaneously correcting possible sparse data corruption. The overall algorithm is called Sparse Online Low-rank projection and Outlier rejection (SOLO).