Applications of Multidimensional Search to Structural Feature Identification

Abstract

Shape recognition by fast syntactic methods is possible when there exists a natural linear (one-dimensional) order on component shapes. This may not be available for “structural” shape descriptions taking the form of unordered, variable-length sets of simpler shapes. In this case, it is tempting to fall back on slower exhaustive correlation, graph matching, and relaxation methods. However, if the structural shapes are themselves “simple”, it is possible to apply multi-dimensional search techniques for asymptotically fast feature identification. I exploit the fact that many simple shape types may be parameterized as points in low-dimensional spaces where distance models dissimilarity. During training, shapes are clustered heuristically within each class, then among all classes, giving a small set of characteristic shape distributions. Each of these is then associated with a binary feature variable taking the value one when any input shape falls within the distribution. This mapping from a structural description into a bit-vector is an example of a “feature identification” method. Selecting such a mapping is slow and heuristic, but fully automated, applicable uniformly to many shape types, and controlled by only a few natural statistical parameters. A mapping, once selected, can be applied quickly using kD-trees. Large-scale, statistically-significant trials have shown the technique to be superior to simpler fixed mappings, in an OCR context.