Statistical-Mechanical Modeling of Digital Halftoning

Statistical-mechanical modeling of digital halftoning is proposed. The digital halftoning dealt with here is achieved by making use of the threshold mask, and for each pixel, the halftoned pixel is determined as black (set to one) if the original grayscale pixel is greater than or equal to the mask value and is determined as white (set to zero) vice versa. Basically, our method is a kind of the so-called model-based digital halftoning technique and we use the information about the original grayscale image to generate the threshold mask. To determine the optimal value of the mask on each pixel for a given original grayscale image, we first assume that the human-eyes might recognize the black and white binary halftoned image as the corresponding grayscale one by linear filters. Then, the energy function is constructed as the distance between the original and the recognized images which is written in terms of the threshold mask. By minimizing the energy function via simulated annealing, we obtain the optimal threshold mask and the resultant halftoned binary dots simultaneously. From the power-spectrum analysis, we find that the resultant binary dots image is physiologically plausible from the view point of human-eyes modulation properties. Key words—Image processing, Model-based digital halftoning technique, Statistical mechanics, Markov Chain Monte Carlo methods, Simulated annealing, Computer vision, Combinatorial optimization problem, Power-spectrum, Human visual systems