Partial-to-Partial Shape Matching with Geometric Consistency
This addresses a practical but rarely explored problem in computer vision and graphics for applications like 3D scanning, though it appears incremental in advancing from full to partial shape matching.
The paper tackles the problem of partial-to-partial 3D shape matching, where shapes are incompletely observed, by introducing a method that enforces geometric consistency through a novel integer non-linear program and pruning algorithm. The method outperforms state-of-the-art approaches on both intra-class and new inter-class datasets.
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.