Alpha-rooting and Correlation Method of Image Enhancement

This paper analyzes the known method of the Fourier transforms-based alpha-rooting in image enhancement and describes a new method of alpha-rooting, by using the autocorrelation function of the image. The alpha-rooting in the frequency-domain can be described by the Taylor series, as well as in the spatial domain, by using the inverse 2-D DFT. In such a series, the alpha-rooting is the convolution of the image with the series of the autocorrelation functions. The application of the Taylor series in alpha-rooting allows to use the parameterized filters even for parameter alpha in a much larger interval than [0,1]. Examples of application of these two filters for enhancement of the grayscale images are given.