Comparison of Algorithms for Fractional Differentiation of Images

Abstract

This paper brings analysis of frequently used algorithms for calculation of the fractional gradients of images. The measures used for the quantitative assessment of the considered algorithms are signal-to-noise ratio and effective average gradient. The results obtained on standard natural images show a distinctive trend in behavior over all images and superior algorithms for certain orders of differentiation. Both measures show similar behavior for the lower orders of differentiation whereas the higher orders of differentiation lead to different treatment of the considered algorithms.