A 2008 study by Johnson and colleagues asked whether quantitative analysis of high-resolution digital scans can identify the hand of Vincent van Gogh, reporting that wavelet- and brushstroke-based features separate authentic van Gogh paintings from works by contemporaries, and observing that copies carry an excess of fine-scale (high-frequency) wavelet coefficients whose origin was not understood. The authors listed the conditions still missing before such analysis could serve routine attribution or forgery detection: representative corpora spanning the artist's periods, modeling of material, conservation, and digitization confounds, richer (color, multispectral) modalities, and an explanation of what the discriminating statistics actually measure. The problem asks for a causally grounded and robust resolution: determine whether the excess fine-scale statistics in copies reflect the copying process or legitimate stylistic, material, or imaging causes, and establish validated criteria that distinguish copies and imitations from authentic works with the confounds explicitly disentangled. Later literature (2012-2026) improved feature families and classifiers but did not resolve the causal question or demonstrate confound-robust authentication on representative corpora, so the problem remains open.

Background

Connoisseurship — attributing a painting to an artist by expert visual judgment — has been supplemented since the early 2000s by visual stylometry, the statistical analysis of high-resolution digital scans of artworks. The landmark precursor was Lyu, Rockmore, and Farid (2004), who showed that statistics of wavelet coefficients distinguish authentic drawings by Pieter Bruegel the Elder from acknowledged imitations. A wavelet transform decomposes an image into details at successive scales; the fine-scale (highest-frequency) coefficients encode the sharpest local variations, such as brushstroke edges, canvas weave, and scanning noise. In that study imitations carried different fine-scale statistics from authentic sheets, and the same program was then extended to oil paintings.

Johnson and colleagues (2008) reported a three-group attack on Vincent van Gogh's brushwork using roughly one hundred high-resolution gray-scale scans of paintings by van Gogh and his contemporaries, provided by the Van Gogh and Kröller-Müller museums: the Penn State group analyzed texture patches with wavelet statistics and stroke-geometry features; the Princeton group used complex wavelet coefficients with a hidden Markov tree model (a probabilistic model of how wavelet coefficients depend on each other across scales) to embed paintings by similarity; and the Maastricht group trained a support vector machine (a standard supervised classifier) on energies of Gabor-filtered patches (Gabor filters are oriented band-pass filters selective for edge direction and scale), finding the total energy larger in non-van-Gogh paintings. Only 23 unquestioned van Gogh paintings — selected by art historians to span periods and techniques — served as the style reference, so every other painting was ranked against a small positive-only model. Encouraging separations appeared, but the authors' own closing assessment listed what remained unresolved: the reference set might not represent the artist's full stylistic range, so limited positive-only training can yield inconsistent rankings and misclassifications; automatic segmentation and tracing of individual brushstrokes from intermingled gray-scale imagery was imperfect, limiting stroke-geometry features; color and multispectral information was unused; conservation and surface effects (canvas-weave imprints, lining — gluing a new canvas to the back of a painting — flattening of impasto, the thick raised paint texture, and underlying compositions showing through) and digitization limits of dynamic range and resolution were unmodeled; and the excess fine-scale wavelet coefficients found in copies and in some authentic works had no accepted explanation — it was not known whether they record the copying process (for instance hesitant as opposed to deliberately diffuse strokes), legitimate fine work, materials, or imaging.

Later work largely replaced the feature family rather than answering these questions: empirical mode decomposition (an adaptive signal decomposition into oscillatory components) by Hughes et al. (2012); wavelet hidden-Markov-tree Fisher information distances with manual background selection by Qi, Taeb, and Hughes (2013); geometric tight-frame coefficient statistics (a redundant, orientation-selective directional filter system) by Liu, Chan, and Yao (2016), reaching 88.61% leave-one-out accuracy (each painting classified by a model trained on all the others) but correctly rejecting only about two-thirds of non-van-Gogh works; scattering transforms (a cascade of wavelet filter banks and modulus operations yielding translation-invariant representations) by Leonarduzzi, Liu, and Wang (2018); and deep convolutional and transformer networks by Schaerf, Postma, and Popovici (2024), reaching about 85% accuracy on an imitations-only contrast set. Robustness tests showed that classification decisions can shift with acquisition conditions such as contrast manipulation (Jacobsen and Nielsen 2011), and the newest studies still build reference models on fewer than ten paintings (Berkmans, Nys, and Bigerelle 2026). What no study supplies is the causal and robustness layer that the 2008 authors identified as the prerequisite for routine use.

Problem Statement

The problem, as posed by the 2008 study's own discussion of unresolved issues, is to turn the observed statistical separations into a robust and understood tool for deciding whether a painting is by van Gogh or is a copy or imitation. Concretely, for high-resolution digital scans of the van Gogh corpus (paintings by van Gogh, works by his contemporaries, and securely identified copies or imitations): (1) determine the nature and causes of the excess fine-scale wavelet coefficients observed in copies and in some authentic works — whether they are produced by the copying process (for example hesitant as opposed to deliberately diffuse stroke dynamics), by legitimate stylistic or material properties of authentic works, by conservation or surface artifacts, or by the digitization process; (2) establish discrimination criteria (features, models, and decision rules) whose reliability is quantified and whose rankings are stable across resampling, explicitly disentangling authorship from stylistic period, materials and conservation state, and imaging conditions; (3) test whether richer modalities — color imagery and multispectral imagery (scans recorded in several spectral bands beyond the visible range) — improve the discrimination and robustness; and (4) validate the result on reference corpora representative of the artist's stylistic range, so that classification of an unseen work reflects authorship rather than corpus artifacts. These components serve one objective, the standard the 2008 authors set: image-based attribution that an art historian can rely on for routine attribution and forgery detection.

All four components are jointly required for a complete resolution; progress on any one of them alone is not by itself a resolution of the problem.

References

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  2. Siwei Lyu, Daniel Rockmore, Hany Farid (2004). A digital technique for art authentication. Proceedings of the National Academy of Sciences 101:17006-17010. DOI 10.1073/pnas.0406398101. https://doi.org/10.1073/pnas.0406398101
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