# Fractal Dimension-Based Methodology for Discriminating Original Paintings from Replicas
## 3 Material and Methods
### The DBC-RGB Algorithm
This discrepancy may be attributed to the fact that all three paintings by each artist in the Cleveland dataset are copies of a photograph rather than replicas of an original painting. While FD distributions are quite similar for paintings in the Princeton dataset, greater variability in FD distribution is observed in paintings by the same artist in the Cleveland dataset. One possible reason is that the artist in the first dataset was instructed to make the replica paintings as faithful to the originals as possible. However, for the second dataset, the artists were simply instructed to make copies of the water lily photograph, ensuring that the copies maintained the same style. The Cleveland dataset allowed us to test our methodology by comparing pairs of paintings by the same artist as well as similar paintings from different artists created under identical controlled conditions. This scenario closely resembles the typical forgery detection problem addressed in several recent studies [2,7]. Our results indicate that the methodology was able to identify significant differences in nearly all comparisons: 96.6% when comparing pairs of paintings from different artists (see Table 6) and 100% for inter-artist comparisons (see Table 7). Although accuracy metrics vary across studies, our results are comparable to or better than those in recent forgery detection research: 95% accuracy in [2] and a 96% hit rate in [7]. Previous studies that used the Princeton dataset [1,3,6] did not compare original paintings and replicas directly; instead, they used machine learning classifiers that were trained with the features extracted from each individual patch and tested by classifying individual patches as well. This analysis of original-replica paintings is different from the approach followed in [5] and in our study, so their results cannot be directly compared to ours and those obtained in [5]. Nevertheless, these studies based on machine learning classifiers provided metrics of accuracy for the classification of patches, and if we consider that an accuracy value above 75% for correctly classifying these patches is equivalent to a correct distinction between the original painting and its replica, then we can make a kind of comparison between the results of those previous studies based on machine learning and our results. In [1], a hidden Markov tree multiresolution model was used to extract the features for each patch, and their best classification technique correctly distinguished originals from replicas in three out of seven pairs of paintings in the Princeton dataset. In [3], the features computed for each patch were based on the histogram of oriented gradients technique, and they correctly classified seven out of seven pairs of paintings in the Princeton dataset, obtaining an equivalent result to ours. The last study analyzing the Princeton dataset was conducted in [6]. They extracted a total of 153 features for each patch, and their best result achieved correct classification in three out of seven pairs of paintings. Two other studies in forgery detection analyzed abstract paintings by the artist [PERSON] and fake paintings attempting to imitate his unique style [7; 8]. Although these studies did not try to differentiate between originals and replicas of the same painting, their results demonstrate that FD features provide strong discriminatory power between authentic and fake [PERSON] paintings. In these two studies, the FD was computed on the grayscale representation [7] or via black-and-white binarization [8] of the image of the painting. Our results using the FD at the color level of images suggest that their results could be further improved by applying FD computation algorithms such as DBC-RGB.