Geometric texture transfer via local geometric descriptors

Geometric Texture Transfer, aimed to add fine grained details to surfaces, can be seen as a realistic advanced geometry modelling technique. At this aim, we investigate and advocate the use of local geometric descriptors as alternative descriptors to the vertex coordinates for surface representation. In particular, we consider the Laplacian coordinates, the normal-controlled coordinates and the mean value encoding, which are well prone to facilitate the transfer of source geometric texture details onto a target surface while preserving the underlying global shape of the target surface. These representations, in general, encode the underlying geometry by describing relative position of a vertex with respect to its local neighborhood, with different levels of invariance to rigid transformations and uniform scaling. We formulate the geometric texture transfer task as a constrained variational nonlinear optimization model that combines an energy term on the shape-from-operator inverse model with constraints aimed to preserve the original underlying surface shape. In contrast to other existing methods, which rely on the strong assumptions of bijectivity, equivalency in local connectivity, and require massive tesselations, we simply map the geometric texture on the base surface, under the only assumption of boundary matching. The proposed geometric texture transfer optimization model is then efficiently solved by nonlinear least squares numerical methods. Experimental results show how the nonlinear texture transfer variational approach based on mean value coordinates overcomes the performance of other alternative descriptors.