Ignorance functions. An application to the calculation of the threshold in prostate ultrasound images

In this paper, we define the concept of an ignorance function and use it to determine the best threshold with which to binarize an image. We introduce a method to construct such functions from t-norms and automorphisms. By means of these new measures, we represent the degree of ignorance of the expert when given one fuzzy set to represent the background and another to represent the object. From this ignorance degree, we assign interval-valued fuzzy sets to the image in such a way that the best threshold is given by the interval-valued fuzzy set with the lowest associated ignorance. We prove that the proposed method provides better thresholds than the fuzzy classical methods when applied to transrectal prostate ultrasound images. The experimental results on ultrasound and natural images also allow us to determine the best choice of the function to represent the ignorance.