Discrete and Continuous Similarity Measures and Shape Analysis

Paul G. Mezey

ABSTRACT: Precise description of shapes and the numerical evaluation of shape similarity measures are some of the tools of modeling approaches in many areas of natural sciences. Various branches of algebraic and differential topology provide the foundation for most of the more recent developments. Several approaches involve discrete mathematical methods, some others use continuum techniques, and a combination of these approaches appears especially fruitful in applications. Some of the more recent applications in molecular shape analysis and similarity evaluation are reviewed, with special emphasis on functional groups and local ranges of novel molecular structures and biologically important macromolecules.