Statistics for image sharpening

Sharpening filters increase the depth of digital images by adding a fraction of their gradient. This portion is tuned by a coefficient which is usually selected according to rules of thumb or subjective evaluation. This paper proposes statistical measures for designing such a parameter in a nearly automatic way, avoiding subjective evaluations. The proposed measures are based on the distance between sharpened and equalized images, which serve as an early reference, and test statistics of uniformity of the luminance histogram. More complex measures, based on the trade-off between skewness and kurtosis, and variance and autocovariance of the sharpened image, are also studied. Numerical applications to various kinds of digital images show that the proposed measures provide similar and acceptable solutions.