An optimization approach for extracting and encoding consistent maps in a shape collection

We introduce a novel approach for computing high quality point-topoint maps among a collection of related shapes. The proposed approach takes as input a sparse set of imperfect initial maps between pairs of shapes and builds a compact data structure which implicitly encodes an improved set of maps between all pairs of shapes. These maps align well with point correspondences selected from initial maps; they map neighboring points to neighboring points; and they provide cycle-consistency, so that map compositions along cycles approximate the identity map. The proposed approach is motivated by the fact that a complete set of maps between all pairs of shapes that admits nearly perfect cycleconsistency are highly redundant and can be represented by compositions of maps through a single base shape. In general, multiple base shapes are needed to adequately cover a diverse collection. Our algorithm sequentially extracts such a small collection of base shapes and creates correspondences from each of these base shapes to all other shapes. These correspondences are found by global optimization on candidate correspondences obtained by diffusing initial maps. These are then used to create a compact graphical data structure from which globally optimal cycle-consistent maps can be extracted using simple graph algorithms. Experimental results on benchmark datasets show that the proposed approach yields significantly better results than state-of-theart data-driven shape matching methods. © 2012 ACM.

Huang Q-X, Zhang G-X, Gao L, Hu S-M, Butscher A, et al. (2012) An optimization approach for extracting and encoding consistent maps in a shape collection. ACM Transactions on Graphics 31: 1. Available:

The authors would like to acknowledge the support of NSF grants FODAVA 808515 and CCF 1011228, ONR MURI N0001470710747, the Max Planck Center for Visual Computing and Communications, the KAUST Academic Excellence Alliance, and a Google Research Award. Prof. Shi-Min Hu was supported by the National Basic Research Project 2011CB30220, the Natural Science Foundation Project 61120106007 and the National High Technology Research and Development Program Project 2012AA011802.

Association for Computing Machinery (ACM)

ACM Transactions on Graphics


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