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.

翻译：在绘画杰作的司法鉴定研究中，支撑材料的分析至关重要。对于平纹织物，经线和纬线的密度被用作主要特征，同时经向与纬向的偏角也具有辅助作用。这些特征可通过画布进行局部研究。本研究提出以深度学习为工具开展局部密度与角度分析。我们使用委拉斯开兹、鲁本斯、里贝拉等画家的36幅画作样本训练模型。在流程初始阶段完成数据制备与增强，随后聚焦于纱线交叉点的监督式分割。具有Inception结构的U-Net网络配合Dice损失函数被证明是该任务的优选方案，并基于分割出的交叉点估算密度与角度。我们报告了对若干画布的分析测试结果，并与该问题中广泛使用的频域方法进行对比。研究表明，这种新方法在频域分析工具失效的某些案例中取得成功，同时在其他案例中优化了结果。此外，本方案无需对待处理图像的部分区域进行标注。作为案例研究，我们将该新算法应用于委拉斯开兹和穆里略的两对画布分析，证实所用织物来自同一卷布料。