Regularized vector field learning with sparse approximation for mismatch removal

• A sparse approximation is presented for vector-valued regularized least-squares.
• We derive a bound for the sparse approximation.
• Based on it, we give a new robust vector field learning algorithm called SparseVFC.
• We apply SparseVFC to mismatch removal and it achieves state-of-the-art performance.
• The proposed method has linear time and space complexities in the scale of samples.

In vector field learning, regularized kernel methods such as regularized least-squares require the number of basis functions to be equivalent to the training sample size, N  . The learning process thus has O(N3)O(N3) and O(N2)O(N2) in the time and space complexity, respectively. This poses significant burden on the vector learning problem for large datasets. In this paper, we propose a sparse approximation to a robust vector field learning method, sparse vector field consensus (SparseVFC), and derive a statistical learning bound on the speed of the convergence. We apply SparseVFC to the mismatch removal problem. The quantitative results on benchmark datasets demonstrate the significant speed advantage of SparseVFC over the original VFC algorithm (two orders of magnitude faster) without much performance degradation; we also demonstrate the large improvement by SparseVFC over traditional methods like RANSAC. Moreover, the proposed method is general and it can be applied to other applications in vector field learning.