📝 Abstract:
Learned methods for dense correspondence between deformable shapes are accurate within a dataset but lose much of that accuracy across datasets. This thesis studies how to reduce that loss, starting from FanNet, a mesh convolution that orders vertex neighborhoods along geodesic spokes. We first extend FanNet with three geometry-aware components: a deformable fan convolution with learnable offsets, an attention that reweights neighbors using a Fourier encoding of relative position, and an auxiliary loss tying feature distances to geodesic distances. In paired comparisons over four to twelve matched seeds, none improves on the baseline, although several looked promising on a few seeds. We then adapt image masking, a common data augmentation in computer vision, to supervised and unsupervised shape correspondence: during training, the input descriptors of all vertices inside a randomly placed ball are zeroed, and nothing else changes. On FanNet trained on FAUST and tested on SCAPE the error falls by 12.3% on average and is lower on all twelve seeds. Added to GeomFmaps and Hybrid ULRSSM in the same setting, the masking also lowers their mean error at the last evaluation point, by 17.6% and 23.1%. Zeroing the descriptors of the same number of scattered vertices gives no reliable gain on FanNet or Hybrid ULRSSM, so the masked vertices have to be grouped together. On FanNet and Hybrid ULRSSM the masked models lose less accuracy late in training, consistent with a regularizing effect; the benefit is limited by the receptive field and by test-time refinement.