Feature-based syntactic and metric shape recognition

We present a syntactic and metric two-dimensional shape recognition scheme based on shape features. The principal features of a shape can be extracted and semantically labeled by means of the chordal axis transform (CAT), with the resulting generic features, namely torsos and limbs, forming the primitive segmented features of the shape. We introduce a context-free universal language for representing all connected planar shapes in terms of their external features, based on a finite alphabet of generic shape feature primitives. Shape exteriors are then syntactically represented as strings in this language. Although this representation of shapes is not complete, in that it only describes their external features, it effectively captures shape embeddings, which are important properties of shapes for purposes of recognition. The elements of the syntactic strings are associated with attribute feature vectors that capture the metrical attributes of the corresponding features. We outline a hierarchical shape recognition scheme, wherein the syntactical representation of shapes may be 'telescoped' to yield a coarser or finer description for hierarchical comparison and matching. We finally extend the syntactic representation and recognition to completely represent all planar shapes, albeit without a generative context-free grammar for this extension.