Partial-to-Partial Shape Matching with Geometric Consistency
Viktoria Ehm Maolin Gao Paul Roetzer Marvin Eisenberger Daniel Cremers Florian Bernard
Finding correspondences between 3D shapes is an important and long-standing
problem in computer vision, graphics and beyond. A prominent challenge are
partial-to-partial shape matching settings, which occur when the shapes to
match are only observed incompletely (e.g. from 3D scanning). Although
partial-to-partial matching is a highly relevant setting in practice, it is
rarely explored. Our work bridges the gap between existing (rather artificial)
3D full shape matching and partial-to-partial real-world settings by exploiting
geometric consistency as a strong constraint. We demonstrate that it is indeed
possible to solve this challenging problem in a variety of settings. For the
first time, we achieve geometric consistency for partial-to-partial matching,
which is realized by a novel integer non-linear program formalism building on
triangle product spaces, along with a new pruning algorithm based on linear
integer programming. Further, we generate a new inter-class dataset for
partial-to-partial shape-matching. We show that our method outperforms current
SOTA methods on both an established intra-class dataset and our novel
inter-class dataset.