The tie statistic and texture recognition

A statistic, called the tie statistic, is introduced and developed as a new measure for distinguishing between two probability density functions. Theorems and proofs establish an important relationship between the tie statistic (T) and the Kolmogorov variational distance and the Kolmogorov-Smirnov distance. Through these relationships, T can also be related to other popular discriminating measures such as the Matusita distance, the Bhattacharyya coefficient and the divergence measure.;The tie statistic provides a mapping technique to transform a feature space to an ordered space with simplified decision boundaries. The mapping process uses T to measure differences between probability density functions of features. The tie space mapping can then be used to evaluate the effectiveness of features in dichotomizing the decision space.;The texture recognition problem is explored using the tie statistic and the tie space mapping. A texture model is defined using features that measure gray level differences between pixels. Unknown samples are compared to the known texture models using the tie statistic and classification decisions are made based on values of the tie mapped features. The decision process incorporates single features or pairs of features. Decision techniques are also explored using the fusion of all available feature information.