Texture Synthesis by a Generic MGRF Model

Conventional identification of a generic MGRF model via MCMC algorithms also synthesises texture.

Figure 7.1: Texture synthesis by a generic MGRF model.

[Sample D17]

[t=0 (IRF)]

[t=10]

[t=20]

[t=30]

[t=40]

[t=50]

[t=60]

[t=70]

[t=80]

[t=90]

[t=100]

[t=110]

[t=130]

[t=170]

[t=190]

Recall Eq. (6.3.6). At each step $t$ of the stochastic approximation, the potentials $\mathbf{V}^{[t]}$ and then the posterior probability distribution $Pr^{[t]}({g} \mid \mathbf{V}^{[t]})$ are computed by Eqs. 6.3.6 and 6.1.3 respectively. Then, an image ${g}^{[t+1]}$ is generated by sampling the distribution $Pr^{[t]}({g} \mid \mathbf{V}^{[t]})$ via either Gibbs sampling or Metropolis algorithm. During the process, a sequence of images, $\{{g}^{[t]}:t=1..n\}$, are generated along with the Markov chain. When the Markov chain attains convergence, the generated image is expected to resemble the training texture because their joint probability distributions of selected signal statistics are close to each other. This approach to texture synthesis is based on the assumption that visual similarity of textures follows the proximity of their signal statistics [35].

Figure 7.1 shows a sequence of images generated along the Markov chain during the identification of a generic MGRF model given a training texture D17. As one can see, initialised with a white noise image, the process generates new images that gradually resemble the training sample. After the $100th$ step, each synthetic image appears more or less within a certain proximity to the training texture and shows little improvement over the previous one. This indicates that the Markov chain attains an state of equilibrium and therefore texture synthesis is completed.