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, that are quite robust for some scenarios but fail in some other, 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 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：本文作者发展了基于深度学习的回归方法，以执行普通纱线计数来分析画布密度。以前的方法是基于傅里叶分析的，对于某些场景非常稳健，但在一些其他场景中失败，基于机器学习的工具涉及要先对所要处理的绘画进行预标记，或基于线路交点的分割，提供了好的估计解决方案，对于所有无需预标记的场景都可以提供良好的估计。分割方法繁琐且耗时，因为要一步步确定交点位置，并在之后估计密度。在这个创新性的提议中，我们通过回归深度学习模型直接从图像中计算出纱线的密度来避免这一步骤。我们还在初始预处理的输入图像中引入了一些改进，对最终的误差产生了影响。我们提出了几种模型并进行了分析，以保留最佳的模型。此外，我们通过引入半监督方法进一步减少了密度估计误差。我们将我们的新算法的性能与Ribera、Velázquez和Poussin的作品进行了比较，并将结果与以前的方法进行了比较。最后，该方法被用于支持马德里普拉多博物馆一件杰作的作者更改。