Probabilistic Inference to the Problem of Inverse-halftoning based on Statistical Mechanics of the Q-Ising Model

On the basis of statistical mechanics of the Q-Ising model, we formulate the problem of inverse-halftoning using the maximizer of the posterior marginal (MPM) estimate for halftone images obtained by the threshold mask method. Then, we estimate the performance of the method in terms of the mean square error and the histogram of the gray-level using the Markov-chain Monte Carlo simulation. The simulation for a set of snapshots of the Q-Ising model reveals the results that the MPM estimate works effectively for the problem of inverse-halftoning, if we appropriately set the parameters of the model prior expressed by the Boltzmann factor of the Q-Ising model. We then clarify that the model prior shifts the gray-level images from both sides to the middle range of the gray-level in the procedure of inverse-halftoning. Also, these properties are confirmed by the MCMC method even for real-world images.