We propose a genuine 3D texture synthesis algorithm based on a probabilistic 2D Markov Random Field conceptualization, capable of capturing the visual characteristics of a texture into a unique statistical texture model. We intend to reproduce, in the volumetric texture, the interactions between pixels learned in an input 2D image. The learning is done by non-parametric Parzen-windowing. Optimization is handled voxel by voxel by a relaxation algorithm, aiming at maximizing the likelihood of each voxel in terms of its local conditional probability function. Variants are proposed regarding the relaxation algorithm and the heuristic strategies used for the simultaneous handling of the orthogonal slices containing the voxel. The procedures are materialized on various textures through a comparative study and a sensitivity analysis, highlighting the variants strengths and weaknesses. Finally, the probabilistic model is compared objectively with a non-parametric neighborhood-search based algorithm.