Abstract: Group point objects (GPO) are multitudes of isolated background-contrasting dots united by one common feature. Many apps use a method of mutual arrangement of group point objects. Implementation of well-known methods for recognizing GPOs gets difficult when an observer has only part of GPOs constituting one of famous classes within his or her sight. Possible deviations of point objects from their standard positions additionally complicate the task to recognize partially marked GPOs. In their research the authors perform recognition of GPOs based on most similar local description of configuration with adjacent elements of GPOs. Cylindrical sections of the abstract vector field with sources in GPO elements and restricted scale of long-range interaction are used as local descriptions. Local descriptions of GPO configuration are viewed as discrete complex-valued codes. The module and argument of each reference correspond to the strength and direction of the vector field action. Similarity of such description of forms on the basis of the dot product module ensures invariance to GPO observation angle and does not depend on GPO shift in picture. Recognition features prove efficiency of the reviewed method for recognizing partially masked GPOs in a practically significant scope of random fluctuations in GPO element coordinates. 

Abstract: The issues arising in the implementation of the technical approach to the recognition of the group point object (GPO) images on the basis of the binding elements of the continuous associated images (CAI) are considered. The basic CAI formation models of the point scene defocusing are analyzed. For bell-shaped and rectangular impulse response obtained defocusing filter selection rules limiting circuit CAI level with maximum fault tolerance quantization of the image brightness. Concretize methodology harmonization CAI model parameters with the density of the GPO members. For clarity and simplify the operator interface work with models CAI highlight - radius of the filter impulse response the ratio of the radius with a threshold localize spatially compact objects is obtained. Synthesized numerical method for the formation of base procedure ASO, characterized by one - two orders of magnitude higher performance than with an approach based on the fast Fourier transform for compact GPO. The method is based on the filtering properties of the deltoid brightness distribution GPO elements and limitations of the low pass filter window size based on the number of quantization levels of its impulse response. The results are aimed at ensuring the quality of the detection procedures, permits and GPO recognition in noisy images, set in a one-dimensional, two-dimensional and three-dimensional spaces in their technical implementation.