Möbius voting for surface correspondence
ACM SIGGRAPH 2009 papers
Recent Advances in Computational Conformal Geometry
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Surface Quasi-Conformal Mapping by Solving Beltrami Equations
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Generalized Koebe's method for conformal mapping multiply connected domains
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Shape analysis of planar objects with arbitrary topologies using conformal geometry
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
Facial cartography: interactive scan correspondence
SCA '11 Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
3D shape restoration via matrix recovery
ACCV'10 Proceedings of the 2010 international conference on Computer vision - Volume part II
Conformal geometry based supine and prone colon registration
MICCAI'10 Proceedings of the Second international conference on Virtual Colonoscopy and Abdominal Imaging: computational challenges and clinical opportunities
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3D surface matching is fundamental for shape registration, deformable 3D non-rigid tracking, recognition and classification. In this paper we describe a novel approach for generating an efficient and optimal combined matching from multiple boundary-constrained conformal parameterizations for multiply connected domains (i.e., genus zero open surface with multiple boundaries), which always come from imperfect 3D data acquisition (holes, partial occlusions, change of pose and non-rigid deformation between scans). This optimality criterion is also used to assess how consistent each boundary is, and thus decide to enforce or relax boundary constraints across the two surfaces to be matched. The linear boundary-constrained conformal parameterization is based on the holomorphic differential forms, which map a surface with n boundaries conformally to a planar rectangle with (n - 2) horizontal slits, other two boundaries as constraints. The mapping is a diffeomorphism and intrinsic to the geometry, handles an open surface with arbitrary number of boundaries, and can be implemented as a linear system. Experimental results are given for real facial surface matching, deformable cloth non-rigid tracking, which demonstrate the efficiency of our method, especially for 3D non-rigid surfaces with significantly inconsistent boundaries.