Sparse Online Low-Rank Projection and Outlier Rejection (SOLO) for 3-D Rigid-Body Motion Registration

TL;DR

This paper introduces SOLO, a real-time, robust algorithm for 3-D rigid-body motion registration using low-rank matrix techniques, suitable for portable devices, and validated through simulations and real-world tests.

Contribution

The paper presents a novel online motion registration method combining Robust PCA and sparse subspace projection for improved speed and robustness.

Findings

Achieves one to two orders of magnitude speed-up over RANSAC.

Maintains high registration accuracy under noise and data corruption.

Validated with extensive simulations and real-world experiments.

Abstract

Motivated by an emerging theory of robust low-rank matrix representation, in this paper, we introduce a novel solution for online rigid-body motion registration. The goal is to develop algorithmic techniques that enable a robust, real-time motion registration solution suitable for low-cost, portable 3-D camera devices. Assuming 3-D image features are tracked via a standard tracker, the algorithm first utilizes Robust PCA to initialize a low-rank shape representation of the rigid body. Robust PCA finds the global optimal solution of the initialization, while its complexity is comparable to singular value decomposition. In the online update stage, we propose a more efficient algorithm for sparse subspace projection to sequentially project new feature observations onto the shape subspace. The lightweight update stage guarantees the real-time performance of the solution while maintaining good registration even when the image sequence is contaminated by noise, gross data corruption, outlying features, and missing data. The state-of-the-art accuracy of the solution is validated through extensive simulation and a real-world experiment, while the system enjoys one to two orders of magnitude speed-up compared to well-established RANSAC solutions. The new algorithm will be released online to aid peer evaluation.