Outline

1. Outline • Texture modeling - continued • FRAME model for textures

2. Texture Modeling • The structures of images • The structures in images are due to the inter-pixel relationships • The key issue is how to characterize the relationships Visual Perception Modeling

3. FRAME Model • FRAME model • Filtering, random field, and maximum entropy • A well-defined mathematical model for textures by combining filtering and random field models Visual Perception Modeling

4. Maximum Entropy • Maximum entropy • Is an important principle in statistics for constructing a probability distribution on a set of random variables • Suppose the available information is the expectations of some known functions n(x), that is • Let W be the set of all probability distributions p(x) which satisfy the constraints Visual Perception Modeling

5. Maximum Entropy – cont. • Maximum Entropy – continued • According to the maximum entropy principle, a good choice of the probability distribution is the one that has the maximum entropy subject to Visual Perception Modeling

6. Maximum Entropy – cont. • Maximum Entropy – continued • By Lagrange multipliers, the solution for p(x) is • where Visual Perception Modeling

7. Maximum Entropy – cont. • Maximum Entropy – continued • are determined by the constraints • But a closed form solution is not available general • Numerical solutions Visual Perception Modeling

8. Maximum Entropy – cont. • Maximum Entropy – continued • The solutions are guaranteed to exist and be unique by the following properties Visual Perception Modeling

9. FRAME Model • Texture modeling • The features can be anything you want n(x) • Histograms of filter responses are a good feature for textures Visual Perception Modeling

10. FRAME Model – cont. • The FRAME algorithm • Initialization Input a texture image Iobs Select a group of K filters SK={F(1), F(2), ...., F(K)} Compute {Hobs(a), a = 1, ....., K} Initialize Initialize Isyn as a uniform white noise image Visual Perception Modeling

11. FRAME Model – cont. • The FRAME algorithm – continued • The algorithm Repeat calculate Hsyn(a), a=1,..., K from Isyn and use it as Update by Apply Gibbs sampler to flip Isyn for w sweeps until Visual Perception Modeling

12. FRAME Model – cont. • The Gibbs sampler Visual Perception Modeling

13. FRAME Model – cont. • Filter selection • In practice, we want a small number of “good” filters • One way to do that is to choose filters that carry the most information • In other words, minimum entropy Visual Perception Modeling

14. FRAME Model – cont. • Filter selection algorithm • Initialization Visual Perception Modeling

15. FRAME Model – cont. Visual Perception Modeling

16. FRAME Model – cont. Visual Perception Modeling

17. FRAME Model – cont. Visual Perception Modeling

18. FRAME Model – cont. Visual Perception Modeling

19. FRAME Model – cont. Visual Perception Modeling

20. FRAME Model – cont. Visual Perception Modeling

21. FRAME Model – cont. Visual Perception Modeling