Conformal Geometry and Its Applications on 3D Shape Matching, Recognition, and Stitching
IEEE Transactions on Pattern Analysis and Machine Intelligence
Space-time surface reconstruction using incompressible flow
ACM SIGGRAPH Asia 2008 papers
Technical Section: Dynamic harmonic fields for surface processing
Computers and Graphics
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
A framework for 3D analysis of facial morphology in fetal alcohol syndrome
MIAR'10 Proceedings of the 5th international conference on Medical imaging and augmented reality
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We present a novel fully automatic method for high resolution, non-rigid dense 3D point tracking. High quality dense point clouds of non-rigid geometry moving at video speeds are acquired using a phase-shifting structured light ranging technique. To use such data for the temporal study of subtle motions such as those seen in facial expressions, an efficient non-rigid 3D motion tracking algorithm is needed to establish inter-frame correspondences. The novelty of this paper is the development of an algorithmic framework for 3D tracking that unifies tracking of intensity and geometric features, using harmonic maps with added feature correspondence constraints. While the previous uses of harmonic maps provided only global alignment, the proposed introduction of interior feature constraints guarantees that non-rigid deformations will be accurately tracked as well. The harmonic map between two topological disks is a diffeomorphism with minimal stretching energy and bounded angle distortion. The map is stable, insensitive to resolution changes and is robust to noise. Due to the strong implicit and explicit smoothness constraints imposed by the algorithm and the high-resolution data, the resultingregistration/deformation field is smooth, continuous and gives dense one-to-one inter-frame correspondences. Our method is validated through a series of experiments demonstrating its accuracy and efficiency.