Pattern Linguistic Analysis Invariant for Plane Transformations

Pattern analysj s using syntacti c methods is discussed briefly to introduce the ideas of the linguistic nature of the attributes and of possi-bl e invariance properties versus usual geometrica] t ran sformations. A linguistic operator invariant for projec-ti ons from plane to plane is proposed and appli ed to the analysis of point patterns X. From knowled ge of the operator "result" or "attribute", it is possible to obtain the convex envelope, reconsti­ tute X, compare X to another pattern X' and more generally, to obtai n the possible common subpat-terns. Thi s last process showy that a threshold exists, under which a pattern comparison is not reliable. Linguistic operators invari ant tor plane similarities are also consi dered. §1. INTRODUCTION J.I. FORMALIZATION OF PATTERN RECOGNITION OPERATIONS Except for some very simple recognitions, many "recogni ti on 1 eve] r," have i o be di st inguished in a pattern recogniti on problem. Recognition operations have to be performed to get from one level to the next. Most of the time, they may be described under a common formaliza-tion : a. Let a pattern X he a set of "primitive" pat­ terns, each of which has a name to which are associated numerical values-b. One or more anatysi s operat ors to operate on X through algorithms ; the result of & is u x. A c. A recognition decision i s performed by compa­ ring u X w i th informat ion previously stored. If this phase is successful, a pattern "feature" is extracted. Thi s feature has EL name ; nunieri cal values may be associated with it. The recogni z ed features are the new primitive patterns. Their set i s the pattern on which the operators of the next level will operate. This scheme is valid obviously for the first J evel extract ion of simple features where X is the set of sampl es obtai ned t hrough a measuring instru rnent such as an optical or acoustical device. Most of the time, the operators & are linear operators. For example, let X be a one dimensional "signal", i is the name of the primitive measure or sample, x the munerical value associated with it. The operators &p are defined by the set of numerical values (α 1 , α 2 .. .α q). The result u p X is the numerical value obtainea …