Determining the shape of a pattern class from sampled points in R²

Abstract

An important problem in pattern recognition is determining the shape of a pattern class from its sampled points. A procedure which provides multivalued shape has been suggested here for a pattern class in R². The procedure can be viewed in two phases. Phase I deals with the decomposition of sample set into some groups of nearly rectangular shape. Phase II determines each of the sub-classes corresponding to the groups separately, aggregates them and obtains the multivalued shape of the pattern class. The effectiveness of the procedure has been demonstrated on some artificially generated data sets or pattern classes as well as on the Indian Telugu vowel speech data set. The convergence of the estimated set to the original set has been verified successfully using two different metrics between sets. One is the well-known Hausdorff metric. The other is a new metric which has been defined in the paper.