Common theoretical formulation of the pattern recognition,identification, and detection problems

Patterns are formalized as operators, which may be compared on the basis of an equivalence relation, of a metricd, and of probability measures. The general pattern recognition problem for metric and probabilistic patterns is then formulated, referring to the formalism of U. Grenander; identification and detection are shown to be special cases hereof. A list of possible distancesd between patterns is then given, including a suggested distance between line patterns; wider applications of some of these distances are suggested. This paper has a theoretical concern, but it nevertheless aims at letting pattern recognition draw benefit from techniques which are similar in theory, but which are curiously still considered as distinct in practice.