LAM: Locality affine-invariant feature matching

Abstract False match removal is a crucial and fundamental task in photogrammetry and computer vision. This paper proposes a robust and efficient mismatch-removal algorithm based on the concepts of local barycentric coordinate (LBC) and matching coordinate matrices (MCMs), called locality affine-invariant matching (LAM). LAM is suitable for both rigid and nonrigid image matching problems. We define a novel LBC system based on area ratios, which is invariant to local affine transformations. We also present the MCMs based on the coordinates of matches, whose degeneracy is able to indicate the correctness of correspondences. Our LAM method first builds a mathematical model based on the LBCs to extract good matches that preserve local neighborhood structures. Then, LAM constructs local MCMs using the extracted reliable correspondences and identifies the correctness for the remaining matches via minimizing the rank of the MCMs. LAM has linear space and linearithmic time complexities. Extensive experiments on both rigid and nonrigid real datasets demonstrate the power of the proposed method; i.e., LAM is more robust to complex transformations compared to other methods and is two orders of magnitude faster than RANSAC under low inlier rates. The source code of the proposed LAM method will be publicly available in http://www.escience.cn/people/lijiayuan/index.html .