Syntactic Analysis of Region Boundaries and Other Curves

Abstract

Encodings of curves as sequences of arcs are particularly suited for syntactic descriptions. If each arc is labeled by a symbol from a finite alphabet, then the curve is mapped into a string over such an alphabet and the classical theory of formal languages [8.1] is directly applicable. Much of the early work in syntactic pattern recognition has used representations based on the chain code or its variants (for a review see [8.2]). A recent example of its use can be found in the work of JARVIS [8.3]. Under this formalism each symbol corresponds to an arc of very short length and the symbol name signifies the direction of a linear segment approximating the arc (see Sec.7.5). This has the advantage of obtaining encodings very easily, but it places the burden for noise removal on the syntactic analyzer. It also requires the use of syntactic methodology for checking relatively simple geometrical properties, like length equality. These disadvantages may be overcome if we preprocess the input curves and obtain encodings in terms of symbols which represent higher order structures rather than small arc segments. Piecewise polynomial approximations offer one possibility, since they remove much of the noise and make information regarding simple properties, like length, readily available. However, they cannot be represented in terms of a finite alphabet, and, for certain applications, they may offer an encoding which is still too “elementary”. In this chapter we shall describe techniques which overcome these problems and produce curve descriptions in terms of finite alphabets, but with each symbol representing a more complex part of a curve than a short arc or an arc which is nearly linear.