A study of character recognition using geometric moments under conditions of simple and non-simple loss

Abstract

The theory of Loss Functions Is a fundamental part of Statistical Decision Theory and of Pattern Recognition. However It is a subject which few have studied In detail. This thesis is an attempt to develop a simple character recognition process In which losses may be Implemented when and where necessary. After a brief account of the history of Loss Functions and an Introduction to elementary Decision Theory, some examples have been constructed to demonstrate how various decision boundaries approximate to the optimal boundary and what Increase In loss would be associated with these sub-optimal boundaries. The results show that the Euclidean and Hamming distance discriminants can be sufficiently close approximations that the decision process may be legitimately simplified by the use of these linear boundaries. Geometric moments were adopted for the computer simulation of the recognition process because each moment is closely related to the symmetry and structure of a character, unlike many other features. The theory of Moments is discussed, in particular their geometrical properties. A brief description of the programs used in the simulation follows. Two different data sets were investigated, the first being hand-drawn capitals and the second machine-scanned lower case type script. This latter set was in the form of a message, which presented interesting programming problems in itself. The results from the application of different discriminants to these sets under conditions of simple loss are analysed and the recognition efficiencies are found to vary between about 30% and. 99% depending on the number of moments being used and the type of discriminant. Next certain theoretical problems are studied. The relations between the rejection rate, the error rate and the rejection threshold are discussed both theoretically and practically. Also an attempt is made to predict theoretically the variation of efficiency with the number of moments used in the discrimination. This hypothesis is then tested on the data already calculated and shown to be true within reasonable limits. A discussion of moment ordering by defining their re-solving powers is undertaken and it seems likely that the moments normally used unordered are among the most satisfactory. Finally, some time is devoted towards methods of improving recognition efficiency. Information content is discussed along with the possibilities inherent in the use of digraph and trigraph probabilities. A breakdown of the errors in the recognition system adopted here is presented along with suggestions to improve the technique. The execution time of the different decision mechanisms is then inspected and a refined 2-Stage method is produced. Lastly the various methods by which a decision mechanism might be improved are united under a common loss matrix, formed by a product of matrices each of which represents a particular facet of the recognition problem.