Efficient computation of scale-space features for deformable shape correspondences

With the rapid development of fast data acquisition techniques, 3D scans that record the geometric and photometric information of deformable objects are routinely acquired nowadays. To track surfaces in temporal domain or stitch partially-overlapping scans to form a complete model in spatial domain, robust and efficient feature detection for deformable shape correspondences, as an enabling method, becomes fundamentally critical with pressing needs. In this paper, we propose an efficient method to extract local features in scale spaces of both texture and geometry for deformable shape correspondences. We first build a hierarchical scale space on surface geometry based on geodesic metric, and the pyramid representation of surface geometry naturally engenders the rapid computation of scale-space features. Analogous to the SIFT, our features are found as local extrema in the scale space. We then propose a new feature descriptor for deformable surfaces, which is a gradient histogram within a local region computed by a local parameterization. Both the detector and the descriptor are invariant to isometric deformation, which makes our method a powerful tool for deformable shape correspondences. The performance of the proposed method is evaluated by feature matching on a sequence of deforming surfaces with ground truth correspondences.