Fractional differentiation and non-Pareto multiobjective optimization for image thresholding

Various techniques have previously been proposed for single-stage thresholding of images to separate objects from the background. Although these global or local thresholding techniques have proven effective on particular types of images, none of them is able to produce consistently good results on a wide range of existing images. Here, a new image histogram thresholding method, called TDFD, based on digital fractional differentiation is presented for gray-level image thresholding. The proposed method exploits the properties of the digital fractional differentiation and is based on the assumption that the pixel appearance probabilities in the image are related. To select the best fractional differentiation order that corresponds to the best threshold, a new algorithm based on non-Pareto multiobjective optimization is presented. A new geometric regularity criterion is also proposed to select the best thresholded image. In order to illustrate the efficiency of our method, a comparison was performed with five competing methods: the Otsu method, the Kapur method, EM algorithm based method, valley emphasis method, and two-dimensional Tsallis entropy based method. With respect to the mode of visualization, object size and image contrast, the experimental results show that the segmentation method based on fractional differentiation is more robust than the other methods.