  This paper describes a novel approach for on demand volumetric texture
synthesis based on a deep learning framework that allows for the generation of
high quality 3D data at interactive rates. Based on a few example images of
textures, a generative network is trained to synthesize coherent portions of
solid textures of arbitrary sizes that reproduce the visual characteristics of
the examples along some directions. To cope with memory limitations and
computation complexity that are inherent to both high resolution and 3D
processing on the GPU, only 2D textures referred to as "slices" are generated
during the training stage. These synthetic textures are compared to exemplar
images via a perceptual loss function based on a pre-trained deep network. The
proposed network is very light (less than 100k parameters), therefore it only
requires sustainable training (i.e. few hours) and is capable of very fast
generation (around a second for $256^3$ voxels) on a single GPU. Integrated
with a spatially seeded PRNG the proposed generator network directly returns an
RGB value given a set of 3D coordinates. The synthesized volumes have good
visual results that are at least equivalent to the state-of-the-art patch based
approaches. They are naturally seamlessly tileable and can be fully generated
in parallel.
