  Attribution of paintings is a critical problem in art history. This study
extends machine learning analysis to surface topography of painted works. A
controlled study of positive attribution was designed with paintings produced
by a class of art students. The paintings were scanned using a confocal optical
profilometer to produce surface data. The surface data were divided into
virtual patches and used to train an ensemble of convolutional neural networks
(CNNs) for attribution. Over a range of patch sizes from 0.5 to 60 mm, the
resulting attribution was found to be 60 to 96% accurate, and, when comparing
regions of different color, was nearly twice as accurate as CNNs using color
images of the paintings. Remarkably, short length scales, as small as twice a
bristle diameter, were the key to reliably distinguishing among artists. These
results show promise for real-world attribution, particularly in the case of
workshop practice.
