4,809 research outputs found
Robust Rotation Synchronization via Low-rank and Sparse Matrix Decomposition
This paper deals with the rotation synchronization problem, which arises in
global registration of 3D point-sets and in structure from motion. The problem
is formulated in an unprecedented way as a "low-rank and sparse" matrix
decomposition that handles both outliers and missing data. A minimization
strategy, dubbed R-GoDec, is also proposed and evaluated experimentally against
state-of-the-art algorithms on simulated and real data. The results show that
R-GoDec is the fastest among the robust algorithms.Comment: The material contained in this paper is part of a manuscript
submitted to CVI
A Gradient Descent Algorithm on the Grassman Manifold for Matrix Completion
We consider the problem of reconstructing a low-rank matrix from a small
subset of its entries. In this paper, we describe the implementation of an
efficient algorithm called OptSpace, based on singular value decomposition
followed by local manifold optimization, for solving the low-rank matrix
completion problem. It has been shown that if the number of revealed entries is
large enough, the output of singular value decomposition gives a good estimate
for the original matrix, so that local optimization reconstructs the correct
matrix with high probability. We present numerical results which show that this
algorithm can reconstruct the low rank matrix exactly from a very small subset
of its entries. We further study the robustness of the algorithm with respect
to noise, and its performance on actual collaborative filtering datasets.Comment: 26 pages, 15 figure
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