# Thread Counting in Plain Weave for Old Paintings Using Semi-Supervised Regression Deep Learning Models

arXiv: https://arxiv.org/abs/2303.15999 · HTML: https://mlsanity.com/paper/2303.15999/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 31 references that are in the map.
- First posted on arXiv 28 Mar 2023.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Boosting offline handwritten text recognition in historical documents with few labeled lines](https://mlsanity.com/paper/2012.02544/) (2020)
- [Generalised Image Outpainting with U-Transformer](https://mlsanity.com/paper/2201.11403/) (2022)
- [Crossing Points Detection in Plain Weave for Old Paintings with Deep Learning](https://mlsanity.com/paper/2302.11924/) (2023)
- [On the Power Spectral Density Applied to the Analysis of Old Canvases](https://mlsanity.com/paper/1705.10060/) (2017)

## Built on by (most cited first, 1 of 1)

- [Forensic Study of Paintings Through the Comparison of Fabrics](https://mlsanity.com/paper/2506.20272/) (2025)

## Abstract (arXiv)

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.