Projective texture atlas construction for 3D photography

The use of attribute maps for 3D surfaces is an important issue in geometric modeling, visualization and simulation. Attribute maps describe various properties of a surface that are necessary in applications. In the case of visual properties, such as color, they are also called texture maps. Usually, the attribute representation exploits a parametrization g: U subset of R-2 -> R-3 of a surface in order to establish a two-dimensional domain where attributes are defined. However, it is not possible, in general, to find a global parametrization without introducing distortions into the mapping. For this reason, an atlas structure is often employed. The atlas is a set of charts defined by a piece-wise parametrization of a surface, which allows local mappings with small distortion. Texture atlas generation can be naturally posed as an optimization problem where the goal is to minimize both the number of charts and the distortion of each mapping. Additionally, specific applications can impose other restrictions, such as the type of mapping. An example is 3D photography, where the texture comes from images of the object captured by a camera [4]. Consequently, the underlying parametrization is a projective mapping. In this work, we investigate the problem of building and manipulating texture atlases for 3D photography applications. We adopt a variational approach to construct an atlas structure with the desired properties. For this purpose, we have extended the method of Cohen-Steiner et al. [6] to handle the texture mapping setup by minimizing distortion error when creating local charts. We also introduce a new metric tailored to projective maps that is suited to 3D photography.