Progressive match expansion via coherent subspace constraint

In this paper a quasi-dense matching algorithm called Progressive match Expansion via Coherent Subspace (PECS) is proposed. Our algorithm starts from a set of sparse seeds and iteratively expands potential matches in the region around the seeds until no more matches could be found. The main difference from previous methods is that our method computes a coherent non-rigid transformation to relate the matching pixels instead of using local planar affine model to approximate the real scene surface within the expanding region. The points in the expanding region are treated as a whole and all the matches satisfying the transformation are found at once. First, dense SIFT descriptors are extracted and a subspace encoding the feature similarity between two point sets is computed. This embedding pulls two points closer if they have similar features and makes the non-rigid transformation learning more robust. Second, a coherent non-rigid transformation in the subspace is computed to move one point set towards the other and the spatially aligned two points denote a match. The proposed model is robust to scenes with non-smooth surface and experiment results reveal the good performance in both 2D image matching and 3D reconstruction.