Markov-Gibbs Texture Modelling with Learnt Freeform Filters

Energy-based Markov–Gibbs random field (MGRF) image models describe images by statistics of local features. But finding features sufficient to describe a texture class has proven challenging. Modern MGRF models learn (extract) parametrised features rather than rely on hand-selected statistics; well-known examples include Fields of Experts (FoE) and Boltzmann machines, which use features built on linear filters. However due to computational cost and learning difficulties these families of texture models have been limited to fixed numbers of small filters only capturing short-range details directly, and are typically only concerned with means and covariances of filter responses. In contrast, the FRAME approach iteratively selected large fixed filters from a set. This paper unifies and extends these, FoE and other MGRF models with a procedure to learn heterogeneous parametrised features including large sparse (non-contiguous) filters which can capture long-range structure directly. The learning procedure combines iterative feature selection, arbitrary learnt filter shapes, and a filter pre-training step which improves speed and results. Synthesis of a variety of textures shows promising abilities of the proposed models to capture both fine details and larger-scale structure with just a few small and efficient filters.