Producing fuzzy inclusion and entropy measures and their application on global image thresholding

Abstract

In this presentation, we continue and expand our previous work on fuzzy subsethood and entropy measures. After a minor alteration to the axioms of fuzzy inclusion, we are able to produce new possible fuzzy inclusion and entropy indicators. We believe that these measures could be used in applications which require or properly exploit fuzzy inclusion and entropy measurements (e.g., image processing, feature selection, fuzzy controllers, similarity measures). Possibly they could offer us more information or lead to alternative ways of solving specific problems of these areas of research. We back up this by introducing a general method of global image thresholding which effectively uses some of these measures. Unlike other common techniques of global image thresholding, this method does not depend on histogram concativity analysis nor does it rely on optimizing some statistical measure (e.g. variance minimization) of the gray-level information. It only needs specific attributes of the image which are measured by some of our fuzzy inclusion and entropy indicators. It’s more of an adaptable process rather than a “strict” procedure and we believe that it can be easily adjusted to meet the needs of different domains or fields of research.