Fractal characterization of restored paintings

Abstract

The fractal dimension (FD) is a quantitative measure of complexity that has been effectively used over the past two decades to analyze paintings for several purposes, including forgery detection, artist classification, characterization of pictorial genres, and analysis of historical periods. However, the potential of FD to characterize the variations that may occur during restoration processes, such as consolidation, cleaning, and reintegration, remains largely unexplored. In this study, we present a novel methodology that combines FD computation on color images with a sliding window approach to generate detailed FD maps of paintings before and after restoration. We applied this methodology to a dataset of twenty-four restored paintings, which includes three types of alterations: craquelure, paint losses, and aged varnishes. Statistical comparisons of FD distributions before and after restoration were conducted using the Wilcoxon rank-sum test and Levene’s test. Our results show a consistent decrease in FD after restoration in paintings affected by craquelure or paint losses, and an increase in FD in aged-varnish paintings following restoration. Additionally, most paintings exhibited increased variance in FD after restoration, regardless of the type of damage. The difference FD maps, obtained by subtracting the post-restoration FD map from the pre-restoration one, revealed the specific areas where restoration had the greatest impact. These findings suggest that the proposed FD-based methodology offers a valuable, image-based tool for restorers, serving as a complementary resource to traditional restoration techniques for assessing the extent of alterations and monitoring applied treatments.