Fractal Dimension-Based Methodology for Discriminating Original Paintings from Replicas

Abstract

Discriminating between original paintings and replicas is a challenging task. In recent years, the fractal dimension (FD) has been used as a quantitative measure of self-similarity to analyze differences between paintings. However, while the FD parameter has proven effective, previous studies often did not utilize all available image information, typically requiring binarization or grayscale analysis and the manual selection of painting regions. This study introduces a novel, color-FD-based method for differentiating original paintings from replicas. Our approach employs a sliding window approach combined with recent color-FD computation techniques. To assess the effectiveness of our FD methodology, we used two public datasets where originals and replicas were produced by the same artist under identical conditions, ensuring maximum similarity. Statistical comparisons were performed using the nonparametric Wilcoxon rank-sum test. Our method identified significant differences between original and replica paintings for 18 out of 19 pairs across both datasets, outperforming previous studies using the same datasets. As expected, our method discriminates more effectively between paintings by different artists (hit rate of 96.6%) than between originals and replicas by the same artist (hit rate of 91.7%). These findings indicate that combining the FD of color images with a sliding window approach is a promising tool for forgery detection.