Dense Non-rigid Point-Matching Using Random Projections

We present a robust and efficient technique for matching dense sets of points undergoing non-rigid spatial transformations. Our main intuition is that the subset of points that can be matched with high confidence should be used to guide the matching procedure for the rest. We propose a novel algorithm that incorporates these high-confidence matches as a spatial prior to learn a discriminative subspace that simultaneously encodes both the feature similarity as well as their spatial arrangement. Conventional subspace learning usually requires spectral decomposition of the pair-wise distance matrix across the point-sets, which can become inefficient even for moderately sized problems. To this end, we propose the use of random projections for approximate subspace learning, which can provide significant time improvements at the cost of minimal precision loss. This efficiency gain allows us to iteratively find and remove high-confidence matches from the point sets, resulting in high recall. To show the effectiveness of our approach, we present a systematic set of experiments and results for the problem of dense non-rigid image-feature matching.