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.

翻译：本文中，作者开发了基于深度学习的回归方法，以进行纯平纹画作的纱线密度估计，通过无需事先标记画作或定位交叉点即可提供良好估计的分割方法，取代了以傅里叶分析为基础的先前方法，该方法在某些情况下非常稳健但在其他情况下失败，也取代了早期的机器学习工具，该工具需要对画作进行事先标记。本文提出的模型可以直接从图像中计算出对纱线数量的估计，而不需要交叉点的定位。我们还通过一些改进的预处理方法提高了输入图像的精度。我们提出并分析了几种模型，以保留最佳模型。此外，我们通过引入半监督算法来进一步降低密度估计误差。我们将新算法的性能与 Ribera、Vel\'azquez 和 Poussin 的作品进行了比较。最后，我们将该方法用于支持普拉多博物馆名作的作者更改。