Non-causal non-parametric multi-scale Markov Random Field synthesis of volumetric textures from a unique 2D sample

We propose a genuine 3D texture synthesis algorithm based on a probabilistic 2D Markov Random Field conceptualization. We intend to reproduce, in the volumetric texture, the interactions between pixels learned non-parametrically in an input 2D image. Optimization is handled voxel by voxel by a deterministic algorithm, deciding for each voxel the most probable grey level. Variants are proposed regarding the heuristic strategies used for the simultaneous handling of the orthogonal slices containing the voxel. Voxel relaxation and scale handling policies are al so investigated. The procedures are materialized on various textures to identify their strengths and weaknesses.