A thresholding method based on two-dimensional fractional differentiation

In this paper, we present a new thresholding technique based on two-dimensional fractional differentiation, that was obtained through the extension of the one-dimensional fractional differentiation. A new geometric interpretation of the two-dimensional fractional differentiation is also presented in the paper. The proposed method exploits the properties and the interpretations of the two-dimensional fractional differentiation. It is based on the assumption that there is a dependency between the pixels’ gray-levels, that is translated into a correlation between pixels describing the same object. The effectiveness of the proposed method is demonstrated by using examples from real-world and synthetic images.