  In this work, the authors develop regression approaches based on deep
learning to perform thread density estimation for plain weave canvas analysis.
Previous approaches were based on Fourier analysis, which is quite robust for
some scenarios but fails in some others, in machine learning tools, that
involve pre-labeling of the painting at hand, or the segmentation of thread
crossing points, that provides good estimations in all scenarios with no need
of pre-labeling. The segmentation approach is time-consuming as the estimation
of the densities is performed after locating the crossing points. In this novel
proposal, we avoid this step by computing the density of threads directly from
the image with a regression deep learning model. We also incorporate some
improvements in the initial preprocessing of the input image with an impact on
the final error. Several models are proposed and analyzed to retain the best
one. Furthermore, we further reduce the density estimation error by introducing
a semi-supervised approach. The performance of our novel algorithm is analyzed
with works by Ribera, Vel\'azquez, and Poussin where we compare our results to
the ones of previous approaches. Finally, the method is put into practice to
support the change of authorship or a masterpiece at the Museo del Prado.

Computer Vision and Pattern Recognition;Machine Learning;Image and Video Processing