Two novel methods for image feature extraction based on fractional differentiation are presented in this paper. The first method is the feature extraction of fusing multi-direction CRONE operators. In this method, the fractional differential CRONE mask is generalized to eight directions at first for extracting image features; then the extracted features are tested by the statistic method and fu...

Throughout this paper, G will denote a nondegenerate continuous collection of atriodic continuous curves (i.e. arcs or simple closed curves) filling up a compact metric continuum M. As is well known, we may regard G itself as a compact metric continuum, with the elements of the collection G as the points of the space G and with G, as a space, the image of M under an open continuous mapping whos...

In mathematics classes where the natural numbers are studied, several surprising results can be shown about the relative “sizes” of infinite sets, such as the fact the there is a oneto-one mapping between the natural numbers N and the even numbers, showing that they are both countably infinite, with the “same size”. Similar logic also shows that there is a mapping from the natural numbers N ont...

In mathematics classes where the natural numbers are studied, several surprising results can be shown about the relative “sizes” of infinite sets, such as the fact the there is a oneto-one mapping between the natural numbers N and the even numbers, showing that they are both countably infinite, with the “same size”. Similar logic also shows that there is a mapping from the natural numbers N ont...