(A) patch-based approach to synthesizing textures on 3D surfaces using global conformal parameterization

Abstract

In recent years, texture synthesis on surfaces has been intensively studied as a strong alternative of texture mapping in many applications. The general framework of this stream of research is relying on iterative synthesis of texture patterns, based on local parameterization of the surface. This strategy successfully deals with the well-known problems of texture mapping, such as discontinuities at the boundary, distortions, and trivial repetitions. However, for anisotropic textures, a closer look at the textured surfaces still reveals texture discontinuities even with the state of the art approaches. Such artifacts are more apparent for textures with monotone spatial color variations. In this thesis, we deal with the texture discontinuity issue by generalizing the 2D patch-based texture synthesis scheme. First, for maximal alignment among adjacent patches, a smooth vector field is constructed along the surface using global conformal parameterization. Second, we synthesize texture patterns on the patches with two celebrated schemes, the graphcut technique and the Poisson diffusion. The former is to find optimal seams between the patches, and the latter is to diffuse color discontinuity across seams. Finally, the resulting texture images are rearranged in a compact form, for reducing the memory requirement in the rendering time.