  Currently, Markov-Gibbs random field (MGRF) image models which include
high-order interactions are almost always built by modelling responses of a
stack of local linear filters. Actual interaction structure is specified
implicitly by the filter coefficients. In contrast, we learn an explicit
high-order MGRF structure by considering the learning process in terms of
general exponential family distributions nested over base models, so that
potentials added later can build on previous ones. We relatively rapidly add
new features by skipping over the costly optimisation of parameters.
  We introduce the use of local binary patterns as features in MGRF texture
models, and generalise them by learning offsets to the surrounding pixels.
These prove effective as high-order features, and are fast to compute. Several
schemes for selecting high-order features by composition or search of a small
subclass are compared. Additionally we present a simple modification of the
maximum likelihood as a texture modelling-specific objective function which
aims to improve generalisation by local windowing of statistics.
  The proposed method was experimentally evaluated by learning high-order MGRF
models for a broad selection of complex textures and then performing texture
synthesis, and succeeded on much of the continuum from stochastic through
irregularly structured to near-regular textures. Learning interaction structure
is very beneficial for textures with large-scale structure, although those with
complex irregular structure still provide difficulties. The texture models were
also quantitatively evaluated on two tasks and found to be competitive with
other works: grading of synthesised textures by a panel of observers; and
comparison against several recent MGRF models by evaluation on a constrained
inpainting task.
