A Natural Discrete Model of a Drawing, Certain of Its Asymptotic Properties, and Prediction of the Slave-Scan Process

The author studies an ensemble of drawings as a discrete source of signals which are obtained by scanning along lines. The quantized function of a discrete argument which describes the lines in the drawing is taken to be the angle of inclination of the tangent to the line as a function of the arc length; this corresponds to an approximation of the lines in the drawings by broken lines in the discrete model which consist of links of fixed length, where each link is oriented along some one of $N$ fixed directions. The author analyzes the combined effect of the parameter $N$ and of the statistic of the initial drawings on the distribution of the transition probabilities of the source and the average number of readings. The theoretical level is established for the reduction of signal volume by predicting whether the direction of the preceding step will be preserved in the next step of the scan.