Crossing Points Detection in Plain Weave for Old Paintings with Deep Learning

In the forensic studies of painting masterpieces, the analysis of the support is of major importance. For plain weave fabrics, the densities of vertical and horizontal threads are used as main features, while angle deviations from the vertical and horizontal axis are also of help. These features can be studied locally through the canvas. In this work, deep learning is proposed as a tool to perform these local densities and angle studies. We trained the model with samples from 36 paintings by Vel\'azquez, Rubens or Ribera, among others. The data preparation and augmentation are dealt with at a first stage of the pipeline. We then focus on the supervised segmentation of crossing points between threads. The U-Net with inception and Dice loss are presented as good choices for this task. Densities and angles are then estimated based on the segmented crossing points. We report test results of the analysis of a few canvases and a comparison with methods in the frequency domain, widely used in this problem. We concluded that this new approach succeeds in some cases where the frequency analysis tools fail, while improving the results in others. Besides, our proposal does not need the labeling of part of the to-be-processed image. As case studies, we apply this novel algorithm to the analysis of two pairs of canvases by Vel\'azquez and Murillo, to conclude that the fabrics used came from the same roll.