King Sun Fu, who was an engineer working in Pattern Recognition and not an oriental potentate, was one of the first to note that significant pattern recognition is syntactic and his works may be consulted for examples, some rather artificial, of cases where syntactic methods can be applied. Perhaps the classic case is an attempt to segment handwritten characters into stroke primitives, and then to extract the syntax of the sequence of primitives. The primitives were extracted by eye, and may not have been the best choice.
The difficulties engendered by the segmentation problem have stimulated attempts to go to higher dimensions than one and to apply to more complicated entities than symbol strings, the same kind of syntactic ideas. A directed graph is a set of nodes with arcs going between some of them, an arrow showing the direction of the arc. A graph is a directed graph with arcs always going both ways, or alternatively with the arrows left off altogether. It is easy to see that you can glue some such objects together to get others, and that there are thus some generalisations of concatenation for strings. It is plain that some sort of segmentation and decomposition of graphs (directed or not) can be done and that rules for allowing some subgraphs to be rewritten to others, just as in the standard rewrite grammars, are possible. What is not apparent is whether the things arise in nature with such decompositions built in. It is not plain how you make a predictor or a context, and without these you cannot easily get chunking or stochastic equivalences. The opportunities for Pure Mathematicians to occupy their time with little profit to the rest of us would seem to be excellent, but people have thought that before and been horribly wrong.
Huffman, Clowes and later Waltz have analysed the way in which trihedral edges in line drawings can be constrained when the drawings depict solid objects such as cuboids. This is a nice example of syntax arising naturally in the world, but the simplifications needed to make the subject tractable reduce the inference problem to triviality.
McLaughlin and Alder have shown how some structure in a silhouette of a hand, namely that it is built up out of fingers and a palm, can be extracted automatically and used to distinguish between left and right hand palm prints. The method has also been used to classify aeroplane silhouettes and to learn the rotation, scale and translation transformations. This will be discussed at greater length in the next chapter.