Ricci Flow for 3D Shape Analysis
Eleventh IEEE International Conference on Computer Vision (ICCV 2007)
Xianfeng Gu, Sen Wang, Junho Kim, Yun Zeng, Yang Wang, Dimitris Samaras
Ricci flow is a powerful curvature flow method in geometric analysis.
This work is the first application of surface Ricci flow in computer
vision. We show that previous methods based on conformal geometries,
such as harmonic maps and least-square conformal maps, which can
only handle 3D shapes with simple topology are subsumed by our Ricci
flow based method which can handle surfaces with arbitrary topology.
Because the Ricci flow method is intrinsic and depends on the
surface metric only, it is invariant to rigid motion, scaling, and
isometric and conformal deformations. The solution to Ricci flow is
unique and its computation is robust to noise. Our Ricci flow based
method can convert all 3D problems into 2D domains and offers a
general framework for 3D surface analysis. Large non-rigid
deformations can be registered with feature constraints, hence we
introduce a method that constrains Ricci flow computation using
feature points and feature curves. Finally, we demonstrate the
applicability of this intrinsic shape representation through
standard shape analysis problems, such as 3D shape matching and
registration.