Application of Analytical Methods and Computer Algebra Tools for Calculating Invariant Characteristics of Random Point Images

When solving a number of problems related to image processing, one of the most important points is the correct choice of features that determine the degree of “abnormality” of the image under study. The paper proposes a set of several classification features of random point images for their use in the tasks of detecting anomalous clumps in the processed data stream or, on the contrary, detecting areas and fragments with increased inter-element spread. Numerical values of features are calculated over the ensemble of analyzed images. Their significant difference from the pre-calculated theoretical values that correspond to random point images can help identify the presence of a regular component or an “abnormal” component in the processed data array. Theoretical and software calculations performed using specialized computer algebra tools are presented in the paper. The discussed classification features and probabilistic dependencies are stable invariants characterizing a random point image.