IEEE Transactions on Pattern Analysis and Machine Intelligence
Geodesic Active Regions and Level Set Methods for Supervised Texture Segmentation
International Journal of Computer Vision
Learning in Gibbsian Fields: How Accurate and How Fast Can It Be?
IEEE Transactions on Pattern Analysis and Machine Intelligence
Modeling Visual Patterns by Integrating Descriptive and Generative Methods
International Journal of Computer Vision
Composite Texture Descriptions
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
A Compact Model for Viewpoint Dependent Texture Synthesis
SMILE '00 Revised Papers from Second European Workshop on 3D Structure from Multiple Images of Large-Scale Environments
What Do Features Tell about Images?
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
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Research on texture has been pursued along two different lines. The first line of research, pioneered by Julesz (1962), seeks the essential ingredients in terms of features and statistics in human texture perception. This leads us to a mathematical definition of texture as a Julesz ensemble. A Julesz ensemble is the maximum set of images that share the same value of some basic feature statistics as the image \math, or equivalently it is a uniform distribution on this set. The second line of research studies statistical models, in particular, Markov random field (MRF) and FRAME models (Zhu, Wu, and Mumford 1997), to characterize texture patterns locally.In this article, we bridge the two lines by the fundamental principle of equivalence of ensembles in statistical mechanics (Gibbs, 1902). We prove that 1). The conditional probability of an arbitrary image patch given its environment, under the Julesz ensemble or the uniform model, is inevitably a FRAME (MRF) model, and 2). The limit of the FRAME (MRF) model, which we called the Gibbs ensemble, is equivalent to a Julesz ensemble as \math. Thus the advantages of the two methodologies can be fully utilized.