Hierarchical Functional Maps between Subdivision Surfaces

We propose a novel approach for computing correspondences between subdivision surfaces with different control polygons. Our main observation is that the multi-resolution spectral basis functions that are open used for computing a functional correspondence can be compactly represented on subdivision surfaces, and therefore can be efficiently computed. Furthermore, the reconstruction of a pointwise map from a functional correspondence also greatly benefits from the subdivision structure. Leveraging these observations, we suggest a hierarchical pipeline for functional map inference, allowing us to compute correspondences between surfaces at fine subdivision levels, with hundreds of thousands of polygons, an order of magnitude faster than existing correspondence methods. We demonstrate the applicability of our results by transferring high-resolution sculpting displacement maps and textures between subdivision models.