# Fractal Dimension-Based Methodology for Discriminating Original Paintings from Replicas
## 3 Material and Methods  
### Test Datasets  
To assess the efficacy of FD in distinguishing original paintings from replicas, we used two publicly accessible datasets derived from controlled experiments. A notable feature of both datasets is that the originals and replicas were produced by the same artist under identical conditions, ensuring maximum similarity between the paintings. The images in both datasets were obtained from their authors at a very high resolution under the same acquisition conditions for original paintings and replicas, so no further pre-processing was necessary to apply our methodology to them.  
The first dataset, which was created by the Machine Learning and Image Processing for Art Investigation Research Group at Princeton University (USA), can be found at [[https://web.math.princeton.edu/ipai/datasets.html](https://web.math.princeton.edu/ipai/datasets.html)]([https://web.math.princeton.edu/ipai/datasets.html](https://web.math.princeton.edu/ipai/datasets.html)) (accessed on 1 May 2025). We refer to this dataset as the Princeton dataset throughout this paper. It has been thoroughly described in previous studies [1,3,5], so we provide only a brief overview here. The Princeton dataset consists of seven original paintings by the artist [PERSON] and their respective replicas, which were painted by the same artist two weeks later (see Figure 1). The original paintings were created using various brushes, canvases, and paints, while the replicas were generated under identical conditions and with the same materials as the corresponding originals. Table 1 shows the relevant data for each original-replica pair within the dataset.  
The second dataset was generated as part of the study by [PERSON] et al. [2] at Case Western Reserve University (Cleveland, OH, USA). This dataset is available for download at [[https://github.com/hincz-lab/machine-learning-for-art-attribution](https://github.com/hincz-lab/machine-learning-for-art-attribution)]([https://github.com/hincz-lab/machine-learning-for-art-attribution](https://github.com/hincz-lab/machine-learning-for-art-attribution)) (accessed on 1 May 2025). Four students from the Cleveland Institute of Art painted three copies of a photograph of a water lily (see Figure 2). All paintings were created using the same oil colors and paintbrushes on paper. The scanned image of each painting measures 3000 \(\times\) 2400 pixels. We refer to this dataset as the Cleveland dataset throughout this paper.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Original-Replica** & **Ground** & **Paint** & **Brushes** & **Image Size (Pixels)** \\ \hline
1 & Canvas & Oils & Soft and Hard & 6272 \(\times\) 6528 \\
2 & Canvas & Acrylics & Soft and Hard & 6272 \(\times\) 6528 \\
3 & Smooth Board & Oils & Soft and Hard & 6272 \(\times\) 6528 \\
4 & Bare Linen Canvas & Oils & Soft & 3200 \(\times\) 6144 \\
5 & Chalk and Glue & Oils & Soft & 3328 \(\times\) 4608 \\
6 & Canvas & Acrylics & Soft & 3456 \(\times\) 5504 \\
7 & Smooth Board & Oils & Soft & 6400 \(\times\) 6528 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Data of paintings in the Princeton dataset.  
It would be valuable to test our methodology with a dataset including different artistic styles and epochs. However, we were unable to find such a dataset in the public domain. The datasets utilized in this study provide pairs of original-replica paintings that are as similar as possible, as they were created under identical controlled conditions using various canvases, brushes, and paints. Creating such a dataset that also includes significant diversity in artistic styles remains challenging.