Filtering and luminance correction for aged photographs

We virtually restore faded black and white photographic prints by the method of decomposing the image into a smooth component that contains edges and smoothed homogeneous regions, and a rough component that may include grain noise but also fine detail. The decomposition into smooth and rough components is achieved using a rational filter. Two approaches are considered; in one, the smooth component is histogram-stretched and then gamma corrected before being added back to a homomorphically filtered version of the rough component; in the other the image is initially gamma corrected and shifted towards white. Each approach presents improvements with respect to the previously separately explored techniques of gamma correction alone, and the stretching of the smooth component together with the homomorphical filtering of the rough component, alone. After characterizing the image with the help of the scatter plot of a 2D local statistic of the type (local intensity, local contrast), namely (local average, local standard deviation), the effects of gamma correction are studied as the effects on the scatter plot, on the assumption that the quality of the image is related to the distribution of data on the scatter plot. Also, the correlation coefficient between the local average and the local deviation on the one hand, and the global average of the image play important descriptor roles.