L. V. Bokut, A. Ya. Kuleshov

Recognition and classification of gray image objects on their contour representation are actual investigations for solving different scientific and applied problems of national economy. Now strict and complete theory of pattern recognition is not constructed yet. The structure of the recognition process is multilevel, it includes the following operations: preliminary processing, segmentation on homogeneous areas, identification, automatic classification of the investigated objects on their contour representation and visualization of the received results. At each level signs are selected, extracted or calculated, which are used to build model of the image. It should be noted that there are no effective gray image analysis algorithms and methods of clear selection of signs yet, without which no complicating decision rules will not allow the desired effect. The most informative part of gray image is the contour representation. In the absence of training samples to classify objects measures of similarity or proximity are widely applied. So our article deals with the issues of hierarchical approach application to problems of recognition, pattern recognition without using the training sample, determining the similarity measure of recognized objects and the experimental results. Definition of similarity measure and classification of objects on their contour representation by using the modified theoretical correlation relation of their vector models are proposed. In general in cluster analysis and automatic classification a given set of objects is decomposed on subsets according to the properties of objects. In doing so they require that subset include objects, which are in some ways more similar to objects from the same subset, than objects from other subsets. A concept of the object homogeneity is determined by the rule to specify value which characterizes or the distance between objects, or the degree of proximity (the similarities) of the same objects. As a measure of proximity (similarity) of contour representation of the investigated objects the authors suggested the modified theoretical correlation relation. It is determined by ratio of the sum of the intergroup variance and investigated objects to the sum of their total variance. As invariant information signs we use the weight values of the direction vectors for normalized vector model , the differences of which are multiplied by a factor of location of deducted weight value of the investigated object. It identifies a very similar forms of contour representations of the investigated objects the modified theoretical correlation relation of which is close to the unit. To classify the investigated objects on their contour representation relatively standard or the investigated object, which is considered as standard, the authors used similarity measure threshold indicators which are determined by error integral values and the calculated values of the modified theoretical correlation relation. The proposed modified theoretical correlation relation, serving as a proximity measure of the investigated objects, was examined on its correspondence to the basic mathematical requirements. The modified theoretical correlation relation has properties of symmetry, the maximum similarity of the object with itself, monotonous decrease, simple computational procedures and can be used as a measure of the similarity of the investigated gray image objects for automatic classification. Using the absolute value of the sum of intergroup variance of standard and the investigated object increases robustness of the algorithm for determining the proximity measure to the investigated objects of different configurations and orientation.