A robust method for vector field learning with application to mismatch removing

We propose a method for vector field learning with outliers, called vector field consensus (VFC). It could distinguish inliers from outliers and learn a vector field fitting for the inliers simultaneously. A prior is taken to force the smoothness of the field, which is based on the Tiknonov regularization in vector-valued reproducing kernel Hilbert space. Under a Bayesian framework, we associate each sample with a latent variable which indicates whether it is an inlier, and then formulate the problem as maximum a posteriori problem and use Expectation Maximization algorithm to solve it. The proposed method possesses two characteristics: 1) robust to outliers, and being able to tolerate 90% outliers and even more, 2) computationally efficient. As an application, we apply VFC to solve the problem of mismatch removing. The results demonstrate that our method outperforms many state-of-the-art methods, and it is very robust.