The objective of syntactic pattern recognition is to recognize not the input pattern but a story or sentence about that pattern. That allows for a much more robust recognition system. But, of course, there is a price to pay. Syntactic pattern recognition is much more difficult than statistical pattern recognition.
We have taken two quite different approaches to this problem.
A PCNN (Pulse Coupled Neural Network) does not recognize patterns. It creates them. Images are put in with a one-to-one correspondence between image pixels and neurons in the PCNN. Each neuron operates in an Integrate-and-fire mode. So if there were no coupling between neurons, firing speeds would be proportional to pixel brightness. If we allow some of the signal produced by firing to “leak” into neighboring cells, wonderful self organized behavior results. If one neuron fires when its neighbor is about to fire, the leaked signal can cause the neighboring cell to fire too. Soon coherent patterns of “auto waves” move across the input plane. For all but the simplest inputs, these patterns never quite repeat. They are chaotic. Thus, we create a 3D pattern (two spatial and one temporal) where only a 2D input existed. To simplify this information drastically, we integrated over the two spatial dimensions, leaving only a one-dimensional temporal pattern. It pulsates with patterns that can be shown to be syntactically related to the object shape. The patterns do not repeat perfectly, but they look very different for similar shaped objects (plus marks and crosses, for instance). We recognized those temporal syntactic patterns using statistical pattern recognition (“A Neural Bridge from Statistical to Syntactic Pattern Recognition,” Neural Networks Vol. 12, 519-5265, 1999, F. T. Allen, J. M. Kinser, and H. J. Caulfield). This allowed for much more robust recognition than purely statistical pattern recognition could achieve.
Our other approach is to use Fourier filtering (see Specialized Methods for Statistical Pattern Recognition) to recognize and locate reselected object features. To make it more robust, we used fuzzy outputs – measuring the degree to which the feature so located belong to the reference class. Then we told a simple story about the relationships (above, to the left of, close to, more-or-less horizontal with, etc.) those features; clearly the relationships too were fuzzy. Then we formed a score on the basis of the fuzzy relationships among the fuzzy features. That score was then thresholded to assign membership in the class of interest. ["Fuzzy Syntactical Pattern Recognition," Applied Optics, Vol. 29, pg. 2600-2602 (June 1990) H. John Caulfield and "Optical syntactic pattern recognition using fuzzy scoring," Opt. Lett. 21, 815-817 (1996), R. Srinivasan, J. Kinser, M. Schamschula, J. Shamir, and H. J. Caulfield]