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Outline

Outline. Texture modeling - continued Julesz ensemble. FRAME Model – review. FRAME model Filtering, random field, and maximum entropy A well-defined mathematical model for textures by combining filtering and random field models

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Outline

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  1. Outline • Texture modeling - continued • Julesz ensemble

  2. FRAME Model – review • FRAME model • Filtering, random field, and maximum entropy • A well-defined mathematical model for textures by combining filtering and random field models • Maximum entropy is used when constructing the probability distribution on the image space • Minimum entropy is used when selecting filters from a large bank of filters • Together this is called min-max entropy principle Visual Perception Modeling

  3. FRAME Model – review • Maximum Entropy Distribution • Given the expectations of some functions, the maximum entropy solution for p(x) is • where Visual Perception Modeling

  4. FRAME Model – review • Maximum Entropy – continued • are determined by the constraints • Gradient ascend to maximize Visual Perception Modeling

  5. Julesz Ensemble • The original texture modeling question • What features and statistics are characteristics of a texture pattern, so that texture pairs that share the same features and statistics cannot be told apart by pre-attentive human visual perception? --- Julesz, 1962 Visual Perception Modeling

  6. Summary of Existing Texture Features Visual Perception Modeling

  7. Existing Feature Statistics Visual Perception Modeling

  8. Most General Feature Statistics Visual Perception Modeling

  9. Julesz Ensemble – cont. • Definition • Given a set of normalized statistics on lattice  a Julesz ensemble W(h) is the limit of the following set as   Z2 and H  {h} under some boundary conditions Visual Perception Modeling

  10. Julesz Ensemble – cont. • Feature selection • A feature can be selected from a large set of features through information gain, or the decrease in entropy Visual Perception Modeling

  11. Julesz Ensemble – cont. Visual Perception Modeling

  12. Julesz Ensemble – cont. • Sampling the Julesz ensemble • In the Julesz ensemble, a texture type is defined as all the images sharing the observed statistics and features • It is an inverse problem in order to generate texture images or verify the statistics • The problem is again the dimensionality • If the image size is 256x256 and each pixel can have 8 values, there are 865536 different images • Markov chain Monte-Carlo algorithms Visual Perception Modeling

  13. Julesz Ensemble – cont. • Given observed feature statistics {H(a)obs}, we associate an energy with any image I as • Then the corresponding Gibbs distribution is • The q(I) can be sampled using a Gibbs sampler or other Markov chain Monte-Carlo algorithms Visual Perception Modeling

  14. Image Synthesis Algorithm • Compute {Hobs} from an observed texture image • Initialize Isyn as any image, and T as T0 • Repeat Randomly pick a pixel v in Isyn Calculate the conditional probability q(Isyn(v)| Isyn(-v)) Choose new Isyn(v) under q(Isyn(v)| Isyn(-v)) Reduce T gradually • Until E(I) < e Visual Perception Modeling

  15. Observed image Initial synthesized image A Texture Synthesis Example Visual Perception Modeling

  16. Temperature Image patch Energy Conditional probability A Texture Synthesis Example Visual Perception Modeling

  17. Average spectral histogram error A Texture Synthesis Example - continued Visual Perception Modeling

  18. Observed image Synthesized image Texture Synthesis Examples - continued Visual Perception Modeling

  19. Observed image Synthesized image Texture Synthesis Examples - continued Visual Perception Modeling

  20. Mud image Synthesized image Texture Synthesis Examples - continued Visual Perception Modeling

  21. Observed image Synthesized image Texture Synthesis Examples - continued Visual Perception Modeling

  22. Observed image Synthesized image Texture Synthesis Examples - continued Visual Perception Modeling

  23. Synthesized image Original cheetah skin patch Texture Synthesis Examples - continued Visual Perception Modeling

  24. Observed image Synthesized image Texture Synthesis Examples - continued Visual Perception Modeling

  25. Observed image Synthesized image Texture Synthesis Examples - continued Visual Perception Modeling

  26. Observed image Synthesized image Texture Synthesis Examples - continued Visual Perception Modeling

  27. An Synthesis Example for Fun Visual Perception Modeling

  28. Cross image Heeger and Bergen’s Our result Comparison with Texture Synthesis Method - continued • An example from Heeger and Bergen’s algorithm Visual Perception Modeling

  29. Julesz Ensemble – cont. • Remarks • The results shown here are based on histograms of filter responses • However, the Julesz ensemble applies to any features/statistics of your choice • You can also define Julesz ensemble for images other than textures Visual Perception Modeling

  30. Julesz Ensemble – cont. • Applications • This essentially provides a framework to systematically verify the sufficiency of chosen features/statistics • Normally, features/statistics are evaluated empirically. In other words, features are evaluated on a limited number of images Visual Perception Modeling

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