BEO GDV-IMAGE RECOGNITION SYSTEM
A.Kuznetsov, K.Korotkov, B.Krylov
For automatic classification of BEO-grams we have constructed a self-learning system of pattern recognition. It is able to judge what class an object belongs to and also creates the automatic descriptions of the particular class. The system is based on the attributes of Beo-grams divided into several groups:
The integral characteristics describe the image in general quantitative terms:
• total area of the image S , defined as the number of pixels with the brightness higher than a fixed threshold bs;
• the areas Si of the shades of gray, defined as the number of pixels within the brightness interval [ bi-1 , bi ] ;
• the integral brightness of the image: Σx Σy b(x,y) / S;
• the length of the image’s perimeter L .
The spectral parameters describe the image in common statistical terms, like:
• the square of the brightness and fragmental spectrums;
• mean values and dispersions;
• quantil parameters (low and high quartils, medians of the spectrums).
The fractal characteristics:
• the form coefficient q = L*L/ S ;
• the Mandelbrot fractal coefficient.
The structural characteristics, describe the general outlook of the image, e.g.:
• the number and the average length of the streamers;
• the number and the area of the spots;
• distributions of above mentioned values;
• parameters of the inscribed ellipse.
The crown characteristics, dealing with the form of the crown of the discharge, with the square distribution of described concentric ellipses etc.
All these parameters are being calculated in the GDV programs and some of them presented in the “GDV Processor” and “GDV Analysis” programs. For every type of the attributes, there are specific methods of their processing. The attributes used in the description of GDV-images are en masse stochastic, and accordingly the apparatus of the theory of mathematical statistics is used. The system can be effective if the vocabulary of the selected attributes is extensive enough, so all the attributes described above are taken into consideration. System life cycle consists of several phases.
At first stage, an educative set of images is introduced to the system, with every image a-priori assigned to a class by the teacher:
[ ω11 , ω12 , ω13 , … ] ⊂ Ω1 … [ ωk1 , ωk2 , ωk3 , … ] ⊂ Ωm
Every object ωij of the educative set is represented by the concrete values of the same attributes:
ωij = { x′1 , x′2 , … , x′n }
Mathematically processing the subsets of attributes, the system can form “statistical portraits” of every class, i.e. the specific form of distribution laws Φi and its parameters (βi, δi):
[ ω11 , ω12 , ω13 , … ] ⊂ Ω1 ==> Φ1 (β1 , δ1 ; x 1, x 2 , … , x n ) …
[ ωk1 , ωk2 , ωk3 , … ] ⊂ Ωk ==> Φk (βk , δk ; x 1, x 2 , … , x n )
The second stage assumes the examination of the system.
At this stage the test objects are introduced to the system. With known functions Φi for every given object ωt = { x′1 , x′ 2 , … , x′n } it is possible to estimate a statistical risk of the decision that object ωt belongs to class Ωi . The class with the minimum risk Ωl could be selected as the most perspective candidate for the final decision. Comparing this decision with a-priori known, the teacher evaluates the system’s performance.
If a teacher considers the system to operate with the acceptable quality, he launches it into autonomic exploitation (the third stage). Otherwise the teacher has to proceed with the education procedure, or the problem cannot be solved by the used mathematical approach.
Described principles have been practically implemented into program complex. The system was tested on the samples of water with different chemical stuffs with low concentrations. The total number of the attributes under consideration was 17; the educative set for the learning system consisted of 175 samples; the rule base of the knowledge-based system included 47 rules. The control group consisted of 25 samples, 5 of each type.
After the education and rules correction both systems were able to distinguish between the samples without any mistakes. The results encouraged launching wide series of experiments in different segments of applications. At the next stage the system was able distinguish between Aura BEO-grams of different people.
See also: Korotkov’s images