Machine-learning analysis of microscale surface topography can partition a historical painting into regions of distinct artistic practice without any training labels: the PATCH method (pairwise assignment training for classifying heterogeneity) trains a convolutional neural network to decide, for pairs of small height-map patches, whether they were produced under the same practice, then groups regions into communities that are interpreted as distinct hands or working regimes. Applied to two El Greco paintings, it produced community structures that both track and challenge traditional workshop attributions. The unresolved scientific problem is that the physical causes of this heterogeneity signal are not established. The PATCH authors state their central future-research focus as teasing apart the influences of materials and artists on the measured heterogeneity of artistic practice (HAP): controlled experiments have never separated the contribution of the artist from that of materials and tools. The paper separately raises, as further future directions, the effect of an artist's technique changing over time (including health-driven change), conservation interventions and damage that can generate spurious communities, and the extension of patch comparisons across paintings differing in support, ground, pigments, aging, and scanning conditions. Determining what the signal encodes is the prerequisite for using topographic heterogeneity as valid evidence about who painted what in workshop paintings.

Background

Renaissance and Early Modern paintings were often produced not by a single master but by a workshop: a master directing apprentices and assistants whose contributions are rarely documented. Deciding who executed which parts of such a work is a central problem in technical art history, the discipline that studies artworks with scientific imaging and measurement instruments. One recent line of attack analyzes the three-dimensional microstructure of the paint surface itself. The painting is scanned with an optical profilometer, an instrument that measures surface height at micron-scale resolution, producing a height map (a digital array of elevation values) instead of an ordinary photograph. Because a brush mechanically deposits paint, the height map records the physics of each stroke, and prior work (Ji et al. 2021, 'Discerning the painter's hand: machine learning on surface topography') showed that a convolutional neural network (CNN, a standard deep image classifier) reading small height-map patches can attribute patches to the correct art student with 60-96% accuracy, with the most informative length scales as small as a single brush-bristle diameter (0.2-0.4 mm).

That result, however, relied on ground-truth labels: the student paintings were made by known individuals. Historical workshop paintings have no such labels. The PATCH method (pairwise assignment training for classifying heterogeneity; Van Horn et al., Science Advances 2026) removes this obstacle. In its first phase, pairwise assignment training, a CNN is repeatedly trained to sort the patches of two regions against each other; if its test accuracy is statistically indistinguishable from the random assignment distribution (RAD, the accuracy distribution expected if patches were labeled at random), the two regions are judged to come from the same practice, and if it is significantly higher, from different practices. In its second phase, community finding, regions judged 'same' are linked in a network and a community-detection algorithm (a graph-partitioning method that finds groups with many internal and few external links, scored by modularity Q) partitions the painting. Each resulting community is interpreted as one artistic practice regime. The method was validated on paintings by nine art students and then applied to two paintings by El Greco (Domenikos Theotokopoulos): Christ on the Cross with Landscape, generally credited to El Greco alone, and The Baptism of Christ, whose regions have been attributed to various workshop members. PATCH's community structure for The Baptism roughly follows those attributions but, through the network of connections between communities, calls them into question — for example, the partition contains four communities, yet three of them are so densely interconnected (nearly a third of all network edges run between them) that they cannot represent three cleanly separate hands, suggesting instead one artist working with different brushes or with a technique that changed over time.

This interpretive step exposes the open problem. The measured heterogeneity of artistic practice (HAP) is a topographic signal whose causes were never isolated. The student-painting validation supplied every painter with the same tools, materials, and subject, so it cannot tell the artist's contribution apart from that of materials or tools: Renaissance brushes were made from the bristles or hair of different mammal species with different coarseness, and substitution could alter paint deposition in ways a CNN might read as a change of hand. An artist's technique also changes over time — the paper invokes evidence (Bianucci et al. 2017) that El Greco suffered ischemic events (strokes caused by interrupted blood supply) late in life, so communities in a late painting could reflect fluctuating motor condition rather than collaboration. Conservation confounds the signal from the other side: inpainting (retouching applied by conservators to losses) and canvas damage create regions whose topography differs from the original execution, and indeed one community in Christ on the Cross overlaps an area documented as inpainted. Finally, although PATCH's pairwise phase can compare patches between paintings and its validation did so across the student paintings, all of those comparisons were made under matched materials, support, and scanning conditions; extending patch-level comparison to paintings differing in support, ground, pigments, aging, and scanning conditions — what corpus-scale studies of workshop practice would need — remains future work.

Problem Statement

The problem is to establish what the microscale topographic heterogeneity signal measured by PATCH-style analysis actually encodes — the heterogeneity of artistic practice (HAP) — so that community structure in a painting's patch-comparison network can be validly read as evidence about artistic practice rather than about confounding factors. At its core is the PATCH authors' stated future-research focus: teasing apart the influences of materials and artists on the HAP. The paper separately states three further future-research directions — investigation of changes in style and technique, further mapping of damage and past conservation efforts, and expansion to interpainting comparisons — which are related open directions, not conjunctive acceptance conditions. Item 1 below is the sole required sub-question; items 2-4 may be pursued in addition but are not needed for completion:

  1. Materials and tools versus artist (the authors' central direction). Determine how material or tool substitutions (for example brush type, bristle or hair species and coarseness, and other implement or material substitutions) manifest in the PATCH outputs — pairwise same/different decisions and the resulting community structure — and whether material or tool variation alone can produce heterogeneity signals comparable to those attributed to different artists. Since the nine-student validation already showed that artists sharing the same set of brushes remain separable (nine disjoint communities, modularity Q = 0.875), what remains open is the comparative judgment posed in the opening sentence of this item — whether material or tool variation alone can produce heterogeneity signals comparable to those attributed to different artists, and so be disentangled from the artist's hand — with the manifestation of substitutions in the PATCH outputs supplying the evidence for it. Either answer to that judgment (material or tool variation alone does, or does not, produce comparable heterogeneity) resolves this item; a quantitative apportionment of the signal between the artist and the materials, while welcome, is not required for completion.

  2. Technique change over time (separately stated direction). Determine whether intra-artist temporal variation in technique — including variation driven by age or health, as hypothesized for the late El Greco on the basis of documented ischemic events (Bianucci et al. 2017) — produces PATCH heterogeneity that can be distinguished from genuine multi-hand execution.

  3. Conservation and damage (separately stated direction). Establish how conservation interventions, inpainting, and surface damage manifest in the PATCH outputs, so that post-production regions can be recognized as such against independent evidence rather than being attributed to distinct creative practices in the PATCH network.

  4. Generalization across paintings (separately stated direction). Establish how patch-level comparisons can be extended between different paintings — differing in support, ground, pigments, aging, and scanning conditions — so the heterogeneity measure can support atelier-wide (workshop-wide) and corpus-level studies of workshop practice rather than single-painting analyses.

What unites these directions is the goal of a validated causal account of the microscale topographic signal: for the central confound of materials and tools versus the artist, whether it does or does not move the PATCH outputs. Consistent with the source's interpretive stance — communities found within a dataset 'represent different artists, materials, or both' — an answer that resolves this confound negatively (for example, showing materials dominate the signal) is as valid a result as one that confirms the artistic interpretation, provided it is grounded in controlled evidence.

References

  1. Andrew Van Horn, Lauryn Smith, Mahamad Salah Mahmoud, Michael McMaster, Clara G. Pinchbeck, Ina T. Martin, Andrew Lininger, Anthony Ingrisano, Adam Lowe, Carlos Bayod, Elizabeth S. Bolman, Kenneth Singer, Michael Hinczewski. PATCH: A deep learning method to assess heterogeneity of artistic practice in historical paintings. Science Advances 12(16), eaea0485, 2026. DOI: 10.1126/sciadv.aea0485. https://doi.org/10.1126/sciadv.aea0485 (open-access full text at PubMed Central, PMC13089327)
  2. Andrew Van Horn, Lauryn Smith, Mahamad Mahmoud, Michael McMaster, Clara Pinchbeck, Ina Martin, Andrew Lininger, Anthony Ingrisano, Adam Lowe, Carlos Bayod, Elizabeth Bolman, Kenneth Singer, Michael Hinczewski. PATCH: a deep learning method to assess heterogeneity of artistic practice in historical paintings. arXiv:2502.01912 (v1 2025-02-04, v3 2025-07-16). https://arxiv.org/abs/2502.01912
  3. F. Ji, M. S. McMaster, S. Schwab, G. Singh, L. N. Smith, S. Adhikari, M. O'Dwyer, F. Sayed, A. Ingrisano, D. Yoder, E. S. Bolman, I. T. Martin, M. Hinczewski, K. D. Singer. Discerning the painter's hand: machine learning on surface topography. Heritage Science 9, article 152, 2021. DOI: 10.1186/s40494-021-00618-w. https://doi.org/10.1186/s40494-021-00618-w
  4. R. Bianucci, F. Marías Franco, O. Appenzeller. Historical evidence supports El Greco's depiction of a neurological condition in his attributed self-portrait. Journal of the Neurological Sciences 372, 316-317, 2017. DOI: 10.1016/j.jns.2016.11.077. https://doi.org/10.1016/j.jns.2016.11.077
  5. Eric Chen, Patricia Alves-Oliveira. Patch-Based Spatial Authorship Attribution in Human-Robot Collaborative Paintings. arXiv:2602.17030, 2026. https://arxiv.org/abs/2602.17030
  6. Maxence Bigerelle, Robin Guibert, Anna Mironova, Frederic Robache, Raphael Deltombe, Ludovic Nys, Christopher A. Brown. Fractal and statistical characterization of brushstroke on paintings. Surface Topography: Metrology and Properties 11(1), 015019, 2023. DOI: 10.1088/2051-672x/acbe53. https://doi.org/10.1088/2051-672x/acbe53
  7. Juan Ruiz de Miras, Ana López-Montes, José Luis Vílchez, Rosario Blanc, Domingo Martín. Fractal characterization of restored paintings. Multimedia Tools and Applications 85, article 366, 2026. DOI: 10.1007/s11042-026-21529-7. https://doi.org/10.1007/s11042-026-21529-7
  8. Clarissa Loures, Caio Hosken, Luan Oliveira, Gianlucca Zuin, Adriano Veloso. Enhancing Authorship Attribution with Synthetic Paintings. Proceedings of the 2025 International Conference on Machine Learning and Applications (ICMLA), pp. 283-288, 2025. DOI: 10.1109/ICMLA66185.2025.00044. https://doi.org/10.1109/ICMLA66185.2025.00044 (preprint: arXiv:2603.04343, https://arxiv.org/abs/2603.04343)
  9. Kaustubh Kumar, Ashutosh Ranjan, Vivek Srivastava, Blessin Varkey, Shirish Karande. ArtMine: Discovering and Formalizing Artistic Processes. arXiv:2607.08331, 2026. https://arxiv.org/abs/2607.08331