Digitization of the Image Rectilinear Boundaries on a Square Graticule

摘要

The quantization of image rectilinear boundaries on a square graticule is considered. A mathematical model of the process is obtained in the form of a discrete Markov chain with a degenerate matrix of the transition probabilities. A complete spectral analysis of behavior of the vectors of probabilities of the states of the chain is carried out, and a representation for a current element of the code of quantized boundary is found. An autocorrelation function of the quantization process is investigated. It is shown that the code of a quantized boundary has a property of periodicity. Behavior of the quantization errors is considered with respect to the angle of inclination of the boundary, and conditions of attainment maximum and minimum are determined for them. A matched filter is synthesized, and the filtration of the code of a quantized boundary is investigated. Resonance phenomena which arise in filtration and which are accompanied by total suppression of the quantization errors are described. The problems are solved which are related to an ideal reconstruction of the shape of the boundary from its code and with optimization of the quantization.