Fuzzy partition of two-dimensional histogram and its application to thresholding

Abstract This paper proposes a thresholding approach by performing a fuzzy partition on a two-dimensional (2D) histogram of the image. The novel 2D fuzzy partition method and membership assignment are based on fuzzy relationship of two fuzzy sets characterized by a set of the best parameters (a, b, c) , which makes the image have the maximum fuzzy entropy. The threshold is selected as the crossover point of the fuzzy region [a, c] . The preprocessed moment arrays are employed to reduce the computation time of image entropy from O (8 N 2 ) to O (2 N ). The proposed approach has been tested on various images, and the results have demonstrated that the proposed 2D fuzzy approach outperforms the 2D nonfuzzy approach and the one-dimensional (1D) fuzzy partition approach.