Ricci flow-based spherical parameterization and surface registration

Abstract

This paper presents an improved Euclidean Ricci flow method for spherical parameterization. We subsequently invent a scale space processing built upon Ricci energy to extract robust surface features for accurate surface registration. Since our method is based on the proposed Euclidean Ricci flow, it inherits the properties of Ricci flow such as conformality, robustness and intrinsicalness, facilitating efficient and effective surface mapping. Compared with other surface registration methods using curvature or sulci pattern, our method demonstrates a significant improvement for surface registration. In addition, Ricci energy can capture local differences for surface analysis as shown in the experiments and applications.

Fast spherical quasiconformal parameterization of genus-$0$ closed surfaces with application to adaptive remeshing

“…In [10], Springborn et al computed spherical conformal parameterization using discrete conformal equivalence. Later, several flow-based methods were developed for spherical conformal parameterization, including the surface Ricci flow [11,12], mean curvature flow [13], and Willmore flow [14]. In [15], Lai et al proposed a harmonic energy minimization approach for folding-free spherical conformal parameterization.…”

Spherical volume-preserving Demons registration

“…In general, a manifold cannot be mapped to another domain without any distortions. Thus, different mapping methods focus on preserving certain local geometries like angle [3,4] or area [5,6]. To date, more and more volumetric measurements are derived from a rich line of multimodal imaging, e.g.…”