ANALYSIS OF FRESCHET AND HAUSDORF METRICS AND THEIR MODIFICATIONS FOR IMAGE COMPARISON

Abstract

This paper provides a comprehensive analysis of classical and modern metric approaches used for quantitative evaluation of image similarity, including the Fréchet and Hausdorff distances as well as their modifications – the Gromov-Fréchet and Gromov-Hausdorff metrics. The relevance of this research is determined by the wide use of image comparison methods in computer vision systems, where they form the basis for segmentation, classification, and object detection in various application domains, particularly in medicine. Images are represented as polygons, which unifies computational procedures and simplifies the formal description of distance measurement algorithms.

The properties of the considered metrics were compared, and computational experiments demonstrated that the Fréchet distance effectively reflects the similarity of polygon contours, while the Hausdorff distance is more suitable for comparing inner regions. The Gromov-based modifications provide minimal distances and more flexible results when dealing with objects of complex structure. Algorithmic solutions for each metric are described, with an emphasis on their computational complexity and possible practical applications. Special attention is given to isometric transformations, which reduce matching errors.

The results were validated through experiments implemented in Java with the OpenCV library, proving the adequacy and efficiency of the proposed approaches. The practical value of the research lies in the potential integration of the obtained results into automated medical diagnostic systems for the analysis of histological, cytological, and immunohistochemical images. The proposed algorithms may serve as a basis for developing effective segmentation and classification methods for biomedical data.