This project investigates the computational conformal geometric methods applied for computer vision. The research team develops novel algorithms for shape analysis, surface matching and registration based on Ricci flow, and compared with conventional vision methods thoroughly.
The basic of idea of the research is to conformally deform all surfaces as one of three canonical shapes, and then perform matching and registering these 3D surfaces in 2D planes. The research team uses the Ricci for shape analysis to preserve the intrinsic geometric characteristics, and to map the surfaces to the canonical shapes.. Ricci flow is the process to deform the metric proportional to the curvature, such that the curvature evolves according to a heat diffusion process. The research team conducts thoroughly comparison with conventional vision methods through extensive experiments using real world datasets. The research benefits many computer vision and visualization applications with methods for computing and visualizing conformal structures and conformal invariants on surfaces. The project also provides opportunity for training students in the areas of differential geometry, hyperbolic geometry, Riemannian geometry, computer vision.
