Numerical Criteria for Assessing the Similarity of Multidimensional Geometric Objects

Abstract

The possibility of using statistical numerical criteria for comparison of geometrical objects represented as point sets has been investigated. This approach can be easily generalized to the multidimensional space and can be an effective tool for comparison of multidimensional geometrical objects. If to any continuous process to correspond the continuous geometrical object, the offered approach can be effectively used for an expert estimation of a degree of similarity of objects, processes and the phenomena in many branches of a science and engineering. Based on the results we can conclude that the choice of criterion for assessing the degree of similarity depends on the conditions of the comparing geometric objects problem. In case of superposition of geometrical objects on each other the determination coefficient gives more qualitative results, and in case of comparison of geometrical objects received by means of transformation the Pearson correlation coefficient gives more qualitative results. Considering that Pearson correlation coefficient showed high stability when comparing transformed geometric objects, its use in solving a wide range of problems of expert analysis of biometric data and identity identification, diagnosis of diseases of various etymologies, recognition of handwritten and printed text, acoustic and radio signals is promising.