3D Face Matching and Registration Based on Hyperbolic Ricci Flow
CVPR 2008 Workshop on 3D Face Processing
Wei Zeng, Xiaotian Yin, Yun Zeng, Yunkun Lai, Xianfeng Gu and Dimitris Samaras
3D surface matching is fundamental for shape analysis.
As a powerful method in geometric analysis, Ricci flow
can flexibly design metrics by prescribed target curvature.
In this paper we describe a novel approach for matching
surfaces with complicated topologies based on hyperbolic
Ricci flow. For surfaces with negative Euler characteristics,
such as a human face with holes (eye contours), the canonical
hyperbolic metric is conformal to the original and can
be efficiently computed. Then the surface can be canonically
decomposed to hyperbolic hexagons. By matching
the corresponding hyperbolic hexagons, the matching between
surfaces can be easily established. Compared to
existing methods, hyperbolic Ricci flow induces diffeomorphisms
between surfaces with complicated topologies with
negative Euler characteristics, while avoiding singularities.
Furthermore, all the boundaries are intrinsically mapped
to hyperbolic lines as alignment constraints. Finally, we
demonstrate the applicability of this intrinsic shape representation
for 3D face matching and registration.