Qixing Huang, Fan Wang, Leonidas Guibas, Functional map networks for analyzing and exploring large shape collections, ACM Transactions on Graphics (TOG), Volume 33, Issue 4, July 2014

Abstract:

The construction of networks of maps among shapes in a collection enables a variety of applications in data-driven geometry processing. A key task in network construction is to make the maps consistent with each other. This consistency constraint, when properly defined, leads not only to a concise representation of such networks, but more importantly, it serves as a strong regularizer for correcting and improving noisy initial maps computed between pairs of shapes in isolation. Up-to-now, however, the consistency constraint has only been fully formulated for point-based maps or for shape collections that are fully similar. In this paper, we introduce a framework for computing consistent functional maps within heterogeneous shape collections. In such collections not all shapes share the same structure --- different types of shared structure may be present within different (but possibly overlapping) sub-collections. Unlike point-based maps, functional maps can encode similarities at multiple levels of detail (points or parts), and thus are particularly suitable for coping with such diversity within a shape collection. We show how to rigorously formulate the consistency constraint in the functional map setting. The formulation leads to a powerful tool for computing consistent functional maps, and also for discovering shared structures, such as meaningful shape parts. We also show how to adapt the procedure for handling very large-scale shape collections. Experimental results on benchmark datasets show that the proposed framework significantly improves upon state-of-the-art data-driven techniques. We demonstrate the usefulness of the framework in shape co-segmentation and various shape exploration tasks.

Bibtex:

@article{hwg-fmnaelsc-14,
 author = {Huang, Qixing and Wang, Fan and Guibas, Leonidas},
 title = {Functional Map Networks for Analyzing and Exploring Large Shape Collections},
 journal = {ACM Trans. Graph.},
 issue_date = {July 2014},
 volume = {33},
 number = {4},
 month = jul,
 year = {2014},
 issn = {0730-0301},
 pages = {36:1--36:11},
 articleno = {36},
 numpages = {11},
 url = {http://doi.acm.org/10.1145/2601097.2601111},
 doi = {10.1145/2601097.2601111},
 acmid = {2601111},
 publisher = {ACM},
 address = {New York, NY, USA},
 keywords = {functional maps, shape analysis, shape exploration},
}