Image Modeling - continued

1. Image Modeling - continued • 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

2. Image Modeling - continued 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

3. A Texture Synthesis Example Observed image Initial synthesized image

4. Temperature Image patch Energy Conditional probability A Texture Synthesis Example • Energy and conditional probability of the marked pixel

5. Average spectral histogram error A Texture Synthesis Example - continued • A white noise image was transformed to a perceptually similar texture by matching the spectral histogram

6. A Texture Synthesis Example - continued • Synthesized images from different initial conditions

7. Observed image Synthesized image Texture Synthesis Examples - continued • A random texture image

8. Texture Synthesis Examples - continued • An image with periodic structures Observed image Synthesized image

9. Texture Synthesis Examples - continued • A mud image with some animal foot prints Mud image Synthesized image

10. Texture Synthesis Examples - continued • A random texture image with elements Observed image Synthesized image

11. Texture Synthesis Examples - continued • An image consisting of two regions • Note that wrap-around boundary conditions were used Observed image Synthesized image

12. Synthesized image Original cheetah skin patch Texture Synthesis Examples - continued • A cheetah skin image

13. Texture Synthesis Examples - continued • An image consisting of circles Observed image Synthesized image

14. Texture Synthesis Examples - continued • An image consisting of crosses Observed image Synthesized image

15. Observed image Synthesized image Texture Synthesis Examples - continued • A pattern with long-range structures