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2.2.B. Particularities of the Gradiet Procedure of the Local Maximum Detection of the Bell-Conformity.

During the given work several gradient procedures of search of local extremums have been tested. Their principal means consist in deployment of the frame corresponding to displacement of the central point of an approximating segment, along ridges of the conformity function. A characteristic example - the procedure circumscribed in [34]. However, use of such universal (that is why rather bulky) procedures does not justify itself in a situation when the preliminary count of specificity of the variables is possible,that simplifies extremum search. Specificity of the variables consists here in their well defined hierarchy. First of all the angle and cross position of a contiguous segment are arranged, a after them - parameters of branches. And only then moving in the longitudinal direction is carried out.

Such specificity of variables has allowed to use effectively at the second stage of experiments the gradient procedure in which moving on all variables of eight-parametrical conformity measure is carried out simultaneously and basically is independent. During searching delays are possible (misses of steps on some variables) if parameters with higher priority were not arranged yet. In final variant the following system of priorities was used: (+, A), (P1, P2), (D), (B1, B2, =) where - "+" and "=" designate moving in cross and longitudinal directions accordingly. The step on any variable increases half (with the count of restriction on maximum value - see further) if the it is executed in the same direction, as previous, and decreases otherwise. Thus it is considered, that those variables were arranged, the step on which became less, than 1/4 from the maximum admissible value on the given variable.

The last values were chosen from the most common reasons so that as a result of each step the new approximating segment not too overstepped the bounds of old onethe. Steps in a longitudinal direction (and on length of the branches) were limited to value B/2, and in cross - D/2. Steps on the angle and curvature should not oscillate ends of the segment on value bigger than D/2, i.e.  A*MAX(B1, B2)/0.7 and  P * (B/0.7)/2 should not exceed D/2. In order to prevent discretization disclosures of analysed contours, the value of parameter D was limited from below to the value ranging 0.5 - 2.5 distances between adjacent points of the raster. From above parameter D was limited by value B/2.

Particularly such restrictions are organized so, that at the approach to one of them it is authorized to make the following step only on half of the distance before this restriction. It simply enough ensures a possibility of increase of a step if a necessity of movement in the opposite direction exists. Initial steps on separate components were chosen equal to the half of their greatest possible values. Thus initial values of parameters B and D were accepted equal 10 and 4 accordingly, and as much as the possible admissible step value on D equal 0.5. Search procedure of the next conformity measure maximum stopped when steps on all variables became smaller, than 0.2 of their maximum possible admissible values.

As a rule, search of the maximums corresponding to contour segments required on the average 60-80 steps on theof declination angle and position in the cross direction at 8-12 steps in the longitudinal direction.

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