The goal of this paper is to implement an extension of the accelerated version of Wei and Levoy's algorithm [1] to the synthesis of 3D volumetric textures. This algorithm derives from Markov Random Fields texture models and generates a 3D textured block one pixel at a time with the goal of maintaining coherence of the evolving region with nearby pixels. The novelty lies in the fact that the 3D synthesis process is constrained by a single 2D sample. We accelerate the algorithm using Tree-Structured Vector Quantization, implemented for both single resolution and multiresolution texture synthesis. This approach is applied with success to the synthesis of volumetric textures from Transmission Electronic Microscopy images of dense carbons. The resulting 3D textures will be used as targets for the atomistic modelling of such materials.