Image Modeling continued observed feature statistics Haobs we

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

Image Modeling - continued Image Synthesis Algorithm Compute {Hobs} from an observed texture image • Initialize Isyn as any image, and T as T 0 • 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 •

A Texture Synthesis Example Observed image Initial synthesized image

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

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

A Texture Synthesis Example - continued ? Synthesized images from different initial conditions

Texture Synthesis Examples - continued Observed image ? A random texture image Synthesized image

Texture Synthesis Examples - continued Observed image ? An Synthesized image with periodic structures

Texture Synthesis Examples - continued Mud image Synthesized image ? A mud image with some animal foot prints

Texture Synthesis Examples - continued Observed image Synthesized image ? A random texture image with elements

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

Texture Synthesis Examples - continued Original cheetah skin patch ? A cheetah skin image Synthesized image

Texture Synthesis Examples - continued Observed image ? An Synthesized image consisting of circles

Texture Synthesis Examples - continued Observed image ? An Synthesized image consisting of crosses

Texture Synthesis Examples - continued Observed image ? A Synthesized image pattern with long-range structures