  We present an unsupervised data-driven approach for non-rigid shape matching.
Shape matching identifies correspondences between two shapes and is a
fundamental step in many computer vision and graphics applications. Our
approach is designed to be particularly robust when matching shapes digitized
using 3D scanners that contain fine geometric detail and suffer from different
types of noise including topological noise caused by the coalescence of
spatially close surface regions. We build on two strategies. First, using a
hierarchical patch based shape representation we match shapes consistently in a
coarse to fine manner, allowing for robustness to noise. This multi-scale
representation drastically reduces the dimensionality of the problem when
matching at the coarsest scale, rendering unsupervised learning feasible.
Second, we constrain this hierarchical matching to be reflected in 3D by
fitting a patch-wise near-rigid deformation model. Using this constraint, we
leverage spatial continuity at different scales to capture global shape
properties, resulting in matchings that generalize well to data with different
deformations and noise characteristics. Experiments demonstrate that our
approach obtains significantly better results on raw 3D scans than
state-of-the-art methods, while performing on-par on standard test scenarios.
