Gestalt Ensemble:
Conceptualization  and Modeling of Visual Patterns
Micro-cannical Ensemble
Canonical Ensemble
Grand-Canonical ensemble
An input texton pattern
t=0, inital sample from a Gibbs model
a random sample after t = 72 sweeps
a random sample after t=200 sweeps.

C. E. Guo, S.C. Zhu and Y.N. Wu, "Visual learning by integrating descriptive and generative models", Int'l J. of Computer Vision, 53(1), 5-29, 2003.

S.C. Zhu, "Statistical modeling and conceptualization of visual patterns", IEEE Trans. on PAMI, vol. 25, no.6, pp. 691-712, 2003.

As David Marr pointed out in his primal sketch, natural images consist of enormous visual patterns of stochastic nature. A global visual pattern emerges from a large number of small elements through hierarchic and local (Markov) interactions. As we know, the subject of statistical physics is to study the microscopic properties of massive elements, and thus is a well suited theoretical foundation for studying visual patterns. For example, we can conceptulize a visual pattern to an ensemble which is a set of image instance with a certain frequency. A model of visual pattern is then an estimate/learning of this frequency from observations.

There happens to be three physical ensembles: micro-canonical ensemble, canonical ensemble, and grand-canonical ensemble. These three ensembles correspond to what we called the Julesz, Gibbs, and Gestalt ensembles respectively in visual modeling. In the following we show a few examples of learning texton patterns which are spatially organized textons. We learn a Gestalt ensemble from an observed pattern (computed in a texton finding procedure), and we draw random samples from this model to verify the learned model.

An input texton pattern
t=0, inital sample from a Gibbs model
a random sample after t = 72 sweeps
a random sample after t=200 sweeps.
An input texton pattern
t=0, inital sample from a Gibbs model
a random sample after t = 15 sweeps
a random sample after t=130 sweeps.