COMET · foundations of COmputational similarity geoMETtry

Similarity is one of the most fundamental notions encountered in problems practically in every branch of science, and is especially crucial in image sciences such as computer vision and pattern recognition. The need to quantify similarity or dissimilarity of some data is central to broad categories of problems involving comparison, search, matching, alignment, or reconstruction. The most common way to model a similarity is using metrics (distances). Such constructions are well-studied in the field of metric geometry, and there exist numerous computational algorithms allowing, for example, to represent one metric using another by means of isometric embeddings.However, in many applications such a model appears to be too restrictive: many types of similarity are non-metric