Synthesis of solid textures based on a 2D example: application to the synthesis of 3D carbon structures observed by transmission electronic microscopy

We propose a novel parametric approach which aims at the synthesis of anisotropic solid textures from the analysis of a single 2D exemplar. This approach is an extension of the pyramidal scheme of Portilla and Simoncelli. It proceeds in three main steps: first, a 2D analysis of the example is performed which produces a set of reference statistics. Then, 3D reference statistics are inferred from the 2D ones thanks to specific anisotropy assumptions. The final step aims at the synthesis itself: the 3D target statistics are imposed on a random 3D block according to a specific multi resolution pyramidal scheme. The approach is applied to the synthesis of solid textures representative of the structure of dense pre-graphitic carbons. The samples are lattice fringe images obtained by high resolution transmission electronic microscopy (HRTEM). HRTEM samples with increasing structural order are used for the experimental evaluation. The produced solid textures exhibit anisotropy properties similar to those observed in the HRTEM samples. Such an approach can easily be extended to any 3D anisotropic structures showing stacks of layers such as wood grain images, seismic data, etc.