Gibbs texture modelling

The natural textures came from the well-known collection "VisTex" of the MIT Media Laboratory,
and the artificial images are simulated as samples of specific Gibbs random fields with multiple pairwise
pixel interactions. All details are given in my relevant publications. Most of the initial results in simulating,
retrieving, and segmenting textures with a generic Markov-Gibbs random field model have been detailed
in my monograph published in the series "Computational Imaging and Vision":

G.L.Gimel'farb : Image Textures and Gibbs Random Fields . Dordrecht : Kluwer Academic, 1999. 250pp.

Perhaps, two small hints can be helpful concerning the above images: there are two simulated and one
natural texture in every triple, and the natural texture is either the leftmost or the center one in the first row
and either the rightmost or the center one in the second row. Now, what is your choice?

Yes, you are almost right, the leftmost upper and the rightmost bottom images are natural (if I did not mix
the file names). But you may agree that all these textures are fairly similar...

Therefore, at least in a few cases it is possible to roughly mimic our visual perception of an image texture...

Markov-Gibbs texture models permit us to discriminate between different types of textures depending on how closely
they can be simulated using such a model. In particular, we can define such texture types as, for instance,

• stochastic textures that are efficiently modelled by accounting for only pairwise pixel interactions
• regular mosaics that are formed by spatial replication of a single forming element (texel)

Bunch sampling

This new approach to fast realistic synthesis of large-size textures by smart sampling of a small-size training image
has been developed in 2002 - 2005 together with my masters and PhD student, Dongxiao Zhou, under the RSNZ
Marsden Fund Grant UOA122. The sampling, based on the Gibbs texture model, allows us to estimate both the
characteristic geometry of a bunch acting as a structural texture element (called texel by R. M. Haralick or texton
by B. Julesz) and the placement rule that governs relative positioning of different interdependent bunches.

training image MIT VisTex "Grass0001"

Synthetic texture "Grass0001"

training image Brodatz's "D003 Croc skin"

Synthetic rectified prototype "D003 Croc skin"

Bunch sampling is quite successful for many spatially homogeneous textures, allows us to rectify some weakly
inhomogeneous textures (i.e. synthesise their homogeneous prototrypes) , but it fails if the images are strongly
inhomogeneous (geometrically and/or photometrically) or if the training image is too small to reveal the long-range
geometric structure of pairwise pixel interactions. These features are exemlified by results of such synthesis in the
thesis of Dr. Dongxiao Zhou^*) for various natural textures from the Brodatz's database, MIT Media Lab.'s VisTex
collection, and other sources. This approach bridges the gap between the computationally intensive probabilistic
synthesis by random sampling of the Markov - Gibbs model and the fast heuristic block / patch sampling when
each goal image may have false inter-block borders and verbatim replicas of the training blocks and needs special
post-processing to restore its realistic visual appearance. Bunch sampling escapes both these shortcomings.