Unsupervised Deep Learning for Structured Shape Matching

Abstract

We present a novel method for computing correspondences across 3D shapes using unsupervised learning. Our method computes a non-linear transformation of given descriptor functions, while optimizing for global structural properties of the resulting maps, such as their bijectivity or approximate isometry. To this end, we use the functional maps framework, and build upon the recent FMNet architecture for descriptor learning. Unlike that approach, however, we show that learning can be done in a purely unsupervised setting, without having access to any ground truth correspondences. This results in a very general shape matching method that we call SURFMNet for Spectral Unsupervised FMNet, and which can be used to establish correspondences within 3D shape collections without any prior information. We demonstrate on a wide range of challenging benchmarks, that our approach leads to state-of-the-art results compared to the existing unsupervised methods and achieves results that are comparable even to the supervised learning techniques. Moreover, our framework is an order of magnitude faster, and does not rely on geodesic distance computation or expensive post-processing.

ZoomOut

“…Our method is also much simpler than BCICP (see Appendix B for an overview of the source code of BCICP and our method). Interestingly, we also note that the method in [Roufosse et al 2018] overfits severely when trained directly on functional maps of size 120 and results in an average error of 97.5. In contrast, training on smaller functional maps and using our upsampling leads to average error of 21.7.…”

“…To demonstrate that our algorithm works with different initializations, we use three different types of descriptors to compute the initial functional maps (with size 20 × 20) for the three datasets: (1) WKS; (2) descriptors derived from two landmarks (see the two spheres highlighted in the middle of Figure 17); (3) Learned SHOT descriptors [Roufosse et al 2018]: the descriptors computed by a non-linear transformation of SHOT, using an unsupervised deep learning method trained on a mixed subset of the remeshed and resampled SCAPE and FAUST dataset. For the experiments with WKS descriptors, we also use the orientation-preserving operators [Ren et al 2018] to disambiguate the symmetry of the WKS descriptors.…”

Consistent ZoomOut: Efficient Spectral Map Synchronization

“…• SHREC'07: for the tests involving this dataset, we always use the maps computed using BIM [KLF11] as initialization. • SCAPE (dense): we pick 18 shapes from this dataset, and use a learning-based framework, SURFMNet [RSO19], to compute the densely pairwise maps as initialization. • FAUST (sparse): we use the provided maps in [RPWO18], which contains 300 pairs of maps among the whole 100 shapes.…”

MapTree

“…While computing a functional map reduces to solving a least squares system, the conversion from a functional map to a point-wise map is not trivial and can lead to errors and noise [Ezuz and Ben-Chen 2017;Rodolà et al 2015]. To improve accuracy, several desirable map attributes have been promoted via regularizers for the functional map estimation rst using geometric insights [Burghard et al 2017;Eynard et al 2016;Litany et al 2017b;Nogneng and Ovsjanikov 2017;Ren et al 2018;Shoham et al 2019;Wang et al 2018a,b], and more recently using learning-based techniques [Halimi et al 2019;Roufosse et al 2019]. Nevertheless, despite signicant progress, the reliance on descriptors and decoupling of continuous optimization and pointwise map conversion remains common to all existing methods.…”