## Analytical Computer Calculations in Image Analysis: Correct Reading of Random Discrete-point Fields

A.L. Reznik and V.M. Efimov (Russia)

### Keywords

Random discrete-point image, scanning, computer analytical calculations, integral, algorithm, probability.

### Abstract

The present paper is devoted to questions arising during the registration of random two-dimensional discrete point fields of a various physical nature. For determination of coordinates of point sources forming such image, the sizes of the integrating aperture of the photo-reading device (integrator) are chosen depending on required accuracy of measurement. In order to prevent errors, which can happen if some point objects (2 or greater) get to the driven aperture-"window", the multithreshold integrators are applied. To solve applied tasks, in which the similar schemes of registration are used, engineers and practical researchers need know reliability of the received data. Unfortunately, the exact analytical formulas describing probability of correct reading, are known only for the elementary case, when the integrator has one threshold level [1-2]. The research of multithreshold reading leads up, as a rule, to difficult probability problems related to random division of an interval [3-6] (a lot of them are not decided on today). In this paper the original nontraditional algorithms are offered, and its essence is, that the exact formulas for probability of correct multithreshold reading are obtained with the help of analytical computer transformations. Figure 1. The scheme of television scanning of a field LL by the integrator - aperture . To determine the coordinates of impulse-point objects according to the scheme shown in a Fig. 1, the television reading of the random image is carried out within the limits of a field by the sizes LL. The coordinates of points-sources forming the researched image, are registered at that moment, when a total signal inside the aperture of integration x crosses the next threshold level. At slot-hole (one-dimensional case, Fig.2) or television (two-dimensional case) reading of the discrete-point images by the integrators having a bounded number of threshold levels k, major characteristic is probability that the specified reading is carried out without errors. (The reading is considered correct, if in a slot-hole or in square aperture x never will appear more than k point objects during the scanning).

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