E.P. Petrov, N.L. Harina, E.D. Rzhanikova

Now the considerable part of a visual information is presented in a digital form. Therefore the analog mathematical models of halftone images become inadequate to the digital halftone images, each element of which accepts a finite number of states in discrete instants. For the development of a new algorithms of digital halftone images processing (compression, filtration) the mathematical models reflecting the specifics of digital halftone images presented by g-digit binary numbers are necessary. The digital halftone images mathematical models offered in the work is based on adequacy of simulated digital halftone images to the real ones. The digital halftone images on the average are close to two-dimensional Markov chains with several states as for their statistical characteristics. Therefore a two-dimensional Markov chain which is presented by superposition of two orthogonal one-dimensional Markov chains with several states is used as a basis of the development of digital halftone images mathematical model, provided that digital halftone image is created on the asymmetrical half-plane. It is supposed that the digital halftone image is received by progressive scanning. The developed MM can form a basis of synthesis of a digital halftone images non-linear filtration algorithms in white Gaussian noise and digital halftone images compression algorithms without any information loss (fig. 5).