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 nonparametric Parzen-windowing. Optimization is handled 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 nonparametric neighborhood-search-based algorithm.

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.

The goal of this paper is to evaluate non-parametric algorithms that achieve 3D texture synthesis from a single 2D sample. The algorithms under study are variants of the algorithm proposed by Wei and Levoy [1]. Several authors have proposed different algorithms that intend to better reproduce, in the output texture, the diversity learned in the input sample. Hence, we turn our attention to the improved algorithm proposed by Kopf et al. [2] and the particular histogram matching approach of Chen and Wang [3]. In addition, we propose to visit the voxels during synthesis according to the 3D extension of space filling curves. We investigate the algorithms capability to reproduce anisotropic textures. In particular we are interested in laminar textures, i.e. textures made of anisotropic sheets stacked along a given direction. Examples of such textures are snapshots of dense carbons observed by high resolution transmission electronic microscopy (HRTEM). Beyond the traditional subjective evaluation of the synthesized textures, we propose a genuine quantitative benchmark for the analysis of the synthesized textures which consists in comparing input and output gray level statistics and patterns morphology.