Fuzzy thresholding: mathematical framework, bound functions and weighted moving average technique

Abstract

The problem of histogram sharpening and thresholding by minimising greylevel fuzziness is considered. The earlier work on the said problem consists only of algorithms without mathematical justification of the findings. For example, the choices of appropriate membership function and the optimum value of its window size (band width) for detecting thresholds were made experimentally with iterative manner. The present work provides a complete theoretical formulation of the same and establishes the criteria regarding the choices of membership function and its window size (band width). The variation in membership function is seen to be restricted by bound functions, thus enabling the method of segmentation more flexible but effective. Finally, the method can be viewed as a weighted moving average technique, greyness ambiguity being the weights.