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


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.


 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},