Pyramid-based texture analysis/synthesis
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Periodicity, Directionality, and Randomness: Wold Features for Image Modeling and Retrieval
IEEE Transactions on Pattern Analysis and Machine Intelligence
Texture Classification Using Windowed Fourier Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Minimax entropy principle and its application to texture modeling
Neural Computation
Prior Learning and Gibbs Reaction-Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
A non-parametric multi-scale statistical model for natural images
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Embedding Gestalt Laws in Markov Random Fields
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fundamental Limits of Bayesian Inference: Order Parameters and Phase Transitions for Road Tracking
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recognizing Surfaces Using Three-Dimensional Textons
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
The Earth Mover''s Distance as a Metric for Image Retrieval
The Earth Mover''s Distance as a Metric for Image Retrieval
Real-time texture synthesis by patch-based sampling
ACM Transactions on Graphics (TOG)
Order Parameters for Detecting Target Curves in Images: When Does High Level Knowledge Help?
International Journal of Computer Vision - Special issue on statistical and computational theories of vision: Part II
Statistical Modeling of Texture Sketch
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
Gabor Feature Space Diffusion via the Minimal Weighted Area Method
EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
Binary Partitioning, Perceptual Grouping, and Restoration with Semidefinite Programming
IEEE Transactions on Pattern Analysis and Machine Intelligence
Natural Image Statistics for Natural Image Segmentation
International Journal of Computer Vision
Steganographic capacity of images, based on image equivalence classes
MM&Sec '01 Proceedings of the 2001 workshop on Multimedia and security: new challenges
Primal sketch: Integrating structure and texture
Computer Vision and Image Understanding
Optimal dimension reduction for image retrieval with correlation metrics
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Skin detection using pairwise models
Image and Vision Computing
A computational approach to fisher information geometry with applications to image analysis
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Non linear temporal textures synthesis: a monte carlo approach
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
Automatic image inpainting by heuristic texture and structure completion
MMM'10 Proceedings of the 16th international conference on Advances in Multimedia Modeling
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In the past thirty years, research on textures has been pursued along two different lines. The first line of research, pioneered by Julesz (1962, IRE Transactions of Information Theory, IT-8:84–92), seeks essential ingredients in terms of features and statistics in human texture perception. This leads us to a mathematical definition of textures in terms of Julesz ensembles (Zhu et al., IEEE Trans. on PAMI, Vol. 22, No. 6, 2000). A Julesz ensemble is a set of images that share the same value of some basic feature statistics. Images in the Julesz ensemble are defined on a large image lattice (a mathematical idealization being Z2) so that exact constraint on feature statistics makes sense. The second line of research studies Markov random field (MRF) models that characterize texture patterns on finite (or small) image lattice in a statistical way. This leads us to a general class of MRF models called FRAME (Filter, Random field, And Maximum Entropy) (Zhu et al., Neural Computation, 9:1627–1660). In this article, we bridge the two lines of research by the fundamental principle of equivalence of ensembles in statistical mechanics (Gibbs, 1902, Elementary Principles of Statistical Mechanics. Yale University Press). We show that 1). As the size of the image lattice goes to infinity, a FRAME model concentrates its probability mass uniformly on a corresponding Julesz ensemble. Therefore, the Julesz ensemble characterizes the global statistical property of the FRAME model; 2). For a large image randomly sampled from a Julesz ensemble, any local patch of the image given its environment follows the conditional distribution specified by a corresponding FRAME model. Therefore, the FRAME model describes the local statistical property of the Julesz ensemble, and is an inevitable texture model on finite (or small) lattice if texture perception is decided by feature statistics. The key to derive these results is the large deviation estimate of the volume of (or the number of images in) the Julesz ensemble, which we call the entropy function. Studying the equivalence of ensembles provides deep insights into questions such as the origin of MRF models, typical images of statistical models, and error rates in various texture related vision tasks (Yuille and Coughlan, IEEE Trans. on PAMI, Vol. 2, No. 2, 2000). The second thrust of this paper is to study texture distance based on the texture models of both small and large lattice systems. We attempt to explain the asymmetry phenomenon observed in texture “pop-out” experiments by the asymmetry of Kullback-Leibler divergence. Our results generalize the traditional signal detection theory (Green and Swets, 1988, Signal Detection Theory and Psychophysics, Peninsula Publishing) for distance measures from iid cases to random fields. Our theories are verified by two groups of computer simulation experiments.