Algorithms for Estimate Calculations Designed for the Case of 2D Support Sets. Part 1: Rectangular Support Sets

摘要

Most of the advanced data processing and analysis technologies designed for solving domain-specific problems employ the automation and optimization techniques of decision-making based on "real" (incomplete, indirect, heterogeneous, inconsistent, erroneous, etc.) information. The methods of mathematical theory of pattern recognition play an important role here. To carry out image recognition, we need an image representation that corresponds to the requirements of the efficient recognition algorithm chosen for the task. A vast majority of the efficient image recognition algorithms only work with image descriptions or models. To completely use the information contained in images, it is necessary to overcome the principal discrepancy between the nature of images and the data-extraction techniques based on symbol models of images. Thus, there is a practical need for an efficient recognition algorithm that directly deals with images and their fragments. Moreover, the algorithm should provide the possibility of posing and solving the problem of choosing the best recognition algorithm. This class of algorithms-algorithms of estimate calculations based on 2D information (2D-AEC)-was defined by I. Gurevich as a special type of the classical model of the recognition algorithms based on estimate calculations (AEC) introduced by Yu. Zhuravlev. Generally, the AEC model can cope with the spatial (2D) image structure. The principal feature of the 2D-AEC is the use of the proximity of objects in spatial support sets, i.e., in images and their fragments. The range of the problems of 2D-AEC includes the enumeration and investigation of spatial support sets as well as definition of the subclasses of algorithms (corresponding to the types of the support sets) which allow one to produce efficient formulas that model the work of the algorithms. In this work, we find these formulas for the particular subclass of 2D-AEC-algorithms of estimate calculations with rectangular support sets.