The Geometry of Colors in Van Gogh’s Sunflowers

“Paintings fade like flowers”: van Gogh’s prediction on the impact of age on paintings came true for most of his paintings. We have studied the consequences of this aging on the Sunflowers in a vase with a yellow background series, namely its original, F454, currently in London, and two replicates, F457, in Tokyo, and F458, in Amsterdam, which van Gogh painted using the original as a model. The background and flower renditions in those paintings have faded and turned brown, making them less vibrant that van Gogh had most likely intended. We have attempted to restore van Gogh’s intent using a computational approach based on data science. After identifications of regions of interest (ROI) within the three paintings F454, F457, and F458 that capture the flowers, stems of the flowers, and background, respectively, we studied the geometry of the color space (in RGB representation) occupied by those ROIs. By comparing those color spaces with those occupied by similar ROIs in photographs of real sunflowers, we identified shifts in all three color coordinates, R, G, and B, with the positive shift in the blue coordinate being the more salient. We have proposed two algorithms, PCR-1 and PCR-2, for correcting that shift in blue and generate representations of the paintings that aim to restore their original conditions. The reduction of the blue component in the yellow hues has lead to more vibrant and less brownish digital rendition of the three Sunflowers in a vase with a yellow background.