Improved curvature-based inpainting applied to fine art: Recovering van Gogh's partially hidden brush strokes

Underdrawings and pentimenti-typically revealed through x-ray imaging and infrared reflectography-comprise important evidence about the intermediate states of an artwork and thus the working methods of its creator.(1) To this end, Shahram, Stork and Donoho introduced the De-pict algorithm, which recovers layers of brush strokes in paintings with open brush work where several layers are partially visible, such as in van Gogh's Self portrait with a grey felt hat.(2) While that preliminary work served as a proof of concept that computer image analytic methods could recover some occluded brush strokes, the work needed further refinement before it could be a tool for art scholars. Our current work makes several steps to improve that algorithm. Specifically, we refine the inpainting step through the inclusion of curvature-based constraints, in which a mathematical curvature penalty biases the reconstruction toward matching the artist's smooth hand motion. We refine and test our methods using "ground truth" image data: passages of four layers of brush strokes in which the intermediate layers were recorded photographically. At each successive top layer (currently identified by the user), we used k-means clustering combined with graph cuts to obtain chromatically and spatially coherent segmentation of brush strokes. We then reconstructed strokes at the deeper layer with our new curvature-based inpainting algorithm based on chromatic level lines. Our methods are clearly superior to previous versions of the De-pict algorithm on van Gogh's works giving smoother, natural strokes that more closely match the shapes of unoccluded strokes. Our improved method might be applied to the classic drip paintings of Jackson Pollock, where the drip work is more open and the physics of splashing paint ensures that the curvature more uniform than in the brush strokes of van Gogh.