Texture transfer during shape transformation

Abstract

Mappings between surfaces have a variety of uses, including texture transfer, multi-way morphing, and surface analysis. Given a 4D implicit function that defines a morph between two implicit surfaces, this article presents a method of calculating a mapping between the two surfaces. We create such a mapping by solving two PDEs over a tetrahedralized hypersurface that connects the two surfaces in 4D. Solving the first PDE yields a vector field that indicates how points on one surface flow to the other. Solving the second PDE propagates position labels along this vector field so that the second surface is tagged with a unique position on the first surface. One strength of this method is that it produces correspondences between surfaces even when they have different topologies. Even if the surfaces split apart or holes appear, the method still produces a mapping entirely automatically. We demonstrate the use of this approach to transfer texture between two surfaces that may have differing topologies.

Differential Geometry Based Multiscale Models

“…Recently, we have proposed an evolution operator based single-step method for image denoising and enhancement (Sun et al, 2006a). Surface gradient flows derived from the optimization of certain functionals defined on the surface are commonly used for applications ranging from surface diffusion (Taubin, 1995), denoising of acquired surface data from 3D scanners (Desbrun et al, 1999), harmonic analysis and structure definition of data (Coifman et al, 2005), shape optimization and surface design (Kobbelt, 2000; Bobenko and Schröder, 2005), minimal surfaces (Pinkall and Polthier, 1993), texture transfer (Dinh et al, 2005), to dynamic evolution of surfaces (Grinspun et al, 2003). Such flows can be either extrinsic, where the embedding of the surface itself changes, as in the mean curvature flow; or intrinsic, where properties such as metric tensor defined on the surface evolve, as in the Ricci flow.…”

3D shape and texture morphing using 2D projection and reconstruction

“…Dinh [22] provides a means to transfer texture across topologies using an implicit function. Unfortunately this function provides limited control over the movement of specific features.…”

Comparative Visualization of Molecular Surfaces Using Deformable Models

“…The problem of establishing shape correspondence between surfaces of arbitrary genus while being able to track points is an actively researched field. In [DYT05], explicit point tracking is performed based on a prior implicit morph. Other work suggests morphing between objects of arbitrary genus by combining distance field interpolation with point tracking [WCX*13].…”