Uniform texture synthesis and texture mapping using global parameterization

Abstract

Texture mapping and texture synthesis are two popular methods for the decoration of surfaces with visual detail. Here, an existing challenge is to preserve, or at least balance, two competing metrics: scale and angle. In this paper we present two methods for this, both based on global conformal parameterization. First, we describe a texture synthesis algorithm for surfaces with arbitrary topology. By using the conformal parameterization, the 3D surface texture synthesis problem can be converted to a 2D image synthesis problem, which is more intuitive, easier, and conceptually simpler. While the conformality of the parameterization naturally preserves the angles of the texture, in this paper we provide a multi-scale technique to also maintain a more uniform area scaling factor. A second novel contribution is to employ the global parameterization to simultaneously preserve orthogonality and size in texture mapping. For this, we show that a conformal factor-driven mass-spring method offers a convenient way to trade off these two qualitative metrics. Our algorithms are simple, efficient and automatic, and they are theoretically sound and universal to general surfaces as well.

Indirection mapping for quasi-conformal relief texturing

“…We see convergence on the order of two minutes for meshes up to 1024 × 1024, wheras previous work reports convergence in about an hour [Wang et al 2005] for comparable complexity. Although it is not necessary to run a preprocessing step extremely fast, minutes of preprocessing accommodate an artist's workflow better than hours.…”

“…al [2001] relaxed pieces of the texture itself to eliminate wasted space in the texture map. We instead use relaxation in a manner similar to Wang et al [2005] by relaxing the texture coordinates and holding the mesh geometry fixed. Compared to previous multiscale optimizers [Wang et al 2005;Lévy et al 2002], the new surface distance metric presented in section 3.5 brings the coarse-scale approximation much closer to the fine-scale solution to dramatically speed convergence.…”

Optimizing the parameters for patch-based texture synthesis

“…Moreover, patch-based texture synthesis has found many interesting applications, e.g. using directional textures for example-based painting and synthesis [Wang et al 2004], and synthesizing 3D surface textures via texturing mapping [Wang et al 2005]. …”

Evaluation and optimization of central vision compensation techniques

“…Conformal mapping is a unique warping since it preserves the local angles between pixels (after warping), and is accordingly referred to also as an angle-preserving transformation. The original idea behind texture mapping and texture synthesis was initially that of enhancing an image by adding 2-D visual effects or a wrapping to it [51]. Recent applications include the ability to generate conformal, bijective spatial transformations of a 2-D image convex polygon and some types of curves (e.g.…”

“…Wang et al (as displayed in Figure 6), which involves creating and optimizing texture mapping algorithms for surfaces with arbitrary (including non-trivial or complex) shapes [19,25,51]. The authors describe how this method simplifies 3-D surface texture synthesis into that of a 2-D image synthesis.…”