Constrained Texture Mapping and Foldover-Free Condition

Abstract

Abstract-Texture mapping has been widely used in image processing and graphics to enhance the realism of CG scenes. However to perfectly match the feature points of a 3D model with the corresponding pixels in texture images, the parameterisation which maps a 3D mesh to the texture space must satisfy the positional constraints. Despite numerous research efforts, the construction of a mathematically robust foldover-free parameterisation subject to internal constraints is still a remaining issue. In this paper, we address this challenge by developing a two-step parameterisation method. First, we produce an initial parameterisation with a method traditionally used to solve structural engineering problems, called the bar-network. We then derive a mathematical foldover-free condition, which is incorporated into a Radial Basis Function based scheme. This method is therefore able to guarantee that the resulting parameterization meets the hard constraints without foldovers.Index Terms-Foldover, constrained texture mapping, parameterization. I. INTRODUCTIONTexture mapping is an effective means in image processing and graphics to achieve improved visual realism. Existing research has largely concentrated on the production of planar parameterization [1]- [7] in order to map a 3D mesh to the planar domain. Most recent works are concerned with texture distortion reduction when mapping a planar image (texture) to a curved surface. Although this is an important issue, in practice the animator is also challenged with other problems in texture mapping. One of them is to register a texture map accurately with the features of a 3D model. For example, if one is to texture map a human face, in addition to reducing texture distortion, one has to ensure the important feature points and lines on the 3D model match those on the texture plane during the mapping process, such as the eyes, nose, eyebrows and lips. In another word, one needs to accurately register the 3D features with their 2D counterparts.With the current production practice, this registration operation is almost completely manual. Once a texture map is generated by animation software, the animator has to painstakingly tweak the unwrapped mesh on the texture plane to align the key feature points on the texture image with the 3D features. He/she has to manually move many vertices around each feature in order to avoid texture distortion being concentrated and visible. This is a timeconsuming task. Manuscript received September 18, 2012; revised December 7, 2012. The authors are with the National Center for Computer Animation, Bournemouth University, Poole, UK. (email:cnyuhc@yahoo.com, xyang@bournemouth.ac.uk, jzhang@bournemouth.ac.uk).Attempts have been made to formulate it as a constrained optimization problem [3]- [5], [7] where the important features in the texture images are to be located correctly on the 3D surface. Despite varying degree of success, a key issue yet to be solved is there is currently no robust solution to controlling the spread of the mesh points such th...