arxiv: 2604.02446 · v1 · submitted 2026-04-02 · 💻 cs.CV · cs.AI

Recognition: 2 theorem links

· Lean Theorem

From Elevation Maps To Contour Lines: SVM and Decision Trees to Detect Violin Width Reduction

Phil\'emon Beghin , Anne-Emmanuelle Ceulemans , Fran\c{c}ois Glineur

Authors on Pith no claims yet

Pith reviewed 2026-05-13 21:25 UTC · model grok-4.3

classification 💻 cs.CV cs.AI

keywords violinwidth reductionelevation mapscontour linesSVMdecision trees3D meshesphotogrammetry

0 comments

The pith

Contour lines from violin 3D meshes let SVM and decision trees detect width reduction at least as effectively as elevation maps.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests whether machine learning can automatically spot reductions in the width of violins from 3D photogrammetric meshes. It compares two ways of feeding the data into support vector machines and decision trees: raw elevation maps extracted directly from the meshes versus parametric contour lines that are fitted to the same geometry. Elevation maps sometimes produce strong classification results, yet they never exceed the performance of the contour-line inputs. A reader would care because this comparison shows whether targeted feature engineering on contours can replace bulk geometric data for reliable detection of a specific shape change.

Core claim

The central claim is that SVM and decision trees applied to parametric contour lines fitted to 3D photogrammetric violin meshes detect width reduction with performance that is never surpassed by the same models trained on elevation maps derived from the identical meshes, even though the elevation-map approach occasionally yields strong results on its own.

What carries the argument

Parametric contour lines fitted to 3D meshes, serving as compact input features for SVM and decision-tree classifiers that distinguish reduced versus unreduced violin widths.

If this is right

Contour-line inputs supply a more stable or efficient representation than full elevation maps for this geometric classification task.
Feature engineering that isolates contours can match or exceed raw data performance while using fewer input dimensions.
The same SVM and decision-tree pipeline can be applied to contour lines for related violin measurements without needing the complete mesh surface.
Detection of width reduction becomes feasible from standard photogrammetric scans once contour fitting is performed.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same contour-fitting step could be tested on other string instruments such as violas or cellos to check whether the performance gap persists across similar shapes.
If contour lines remain superior, future work might replace the full mesh with a small set of cross-sectional curves for faster scanning and storage in heritage databases.
A direct comparison on synthetic meshes with controlled width reductions would isolate whether the advantage comes from noise rejection or from the parametric form itself.

Load-bearing premise

That the photogrammetric 3D meshes accurately represent the violins' true geometry and that width reductions produce consistent, detectable signals in either elevation maps or contour lines without being overwhelmed by scanning noise or unrelated shape variations.

What would settle it

Measure classification accuracy on a new set of violin meshes where width reduction is independently verified by precise caliper measurements on the physical instruments; if the contour-line models lose their advantage or both methods drop below usable accuracy, the claim is falsified.

Figures

Figures reproduced from arXiv: 2604.02446 by Anne-Emmanuelle Ceulemans, Fran\c{c}ois Glineur, Phil\'emon Beghin.

**Figure 2.** Figure 2: Elevation map sampled every 0.25 mm × 0.25 mm and zone of interest (red rectangle). The two red lines on the scale bar indicate the minimum and maximum elevations of the violin sound board. We test both raw elevations and normalised elevations. For the latter, we perform centering by subtracting their mean and scaling by their standard deviation. Both gobal statistics were computed while excluding undefine… view at source ↗

**Figure 3.** Figure 3: Elevation maps resampled on a 5 × 10 square grid. The top line shows the resampling of a non reduced instrument (inv. no 2833) while the bottom line illustrates the resampling of a reduced instrument (inv. no 2846). The left-hand side highlights relative resampling and the right-hand side absolute resampling. Zones with zero elevation (no intersection between the grid and the mesh) are left in white. The t… view at source ↗

**Figure 4.** Figure 4: Impact of the parameters on the contour lines fitting. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: Fitting of contour lines of the sound board of an instrument (left) and [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 6.** Figure 6: Several 2D representations of violin features. The top-left figure illustrates [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

**Figure 7.** Figure 7: Leave-one-out cross-validation for several regularisation strengths. Input features: resampled β profile (left); 5 × 10 elevation map with relative resampling (right). 3.3 Decision Trees We additionally investigate Decision Tree classifiers as a complementary approach. Given the small size of the dataset, tree depth must remain strongly constrained to prevent overfitting. As for the regularisation hyperp… view at source ↗

read the original abstract

We explore the automatic detection of violin width reduction using 3D photogrammetric meshes. We compare SVM and Decision Trees applied to a geometry-based raw representation built from elevation maps with a more targeted, feature-engineered approach relying on parametric contour lines fitting. Although elevation maps occasionally achieve strong results, their performance does not surpass that of the contour-based inputs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Standard SVM and decision trees applied to violin 3D meshes with contour lines compared to elevation maps, but no dataset size or performance numbers are given so the comparison cannot be judged.

read the letter

The paper applies SVM and decision trees to 3D photogrammetric meshes of violins to detect width reduction. It compares a geometry-based elevation map representation against parametric contour lines, concluding that the contour-based inputs perform at least as well. The new element here is the targeted feature engineering with contour lines for this cultural heritage task. Elevation maps are more raw, while contours extract specific shape parameters that might better isolate width changes. That distinction is sensible for the problem and gives the paper a clear experimental question. The main limitation is the complete absence of quantitative details in the abstract. No mention of how many instruments were scanned, what the accuracy figures are, or what validation was used. This makes it impossible to judge whether the performance difference is real or just noise. The stress-test correctly flags that the comparison needs consistent splits and error metrics to be convincing, and those are not supplied. There are no internal contradictions or circular claims; it is a direct empirical setup. The weakest part is the reliance on the 3D meshes being faithful to the actual violin geometry without discussing potential scanning artifacts. This paper is aimed at researchers in digital cultural heritage or musicology who might use automated analysis for instrument conservation. A reader interested in applied classification on 3D cultural objects could find the comparison useful as a starting point, though they would need to replicate the experiments themselves to trust the numbers. I think it should go to peer review so the authors can provide the missing experimental protocol and results. That would let referees assess if the contour approach really adds value.

Referee Report

2 major / 1 minor

Summary. The paper claims that SVM and Decision Trees can detect violin width reduction from 3D photogrammetric meshes, and that a feature-engineered representation based on parametric contour-line fitting outperforms or at least matches a raw geometry representation built from elevation maps, although elevation maps occasionally yield strong results.

Significance. If the comparative result is substantiated with quantitative metrics and reproducible validation, the work could inform feature design choices for detecting subtle geometric deformations in 3D cultural-heritage models. The direct head-to-head evaluation of raw elevation maps versus targeted contour features on the same meshes is a concrete contribution to the application of classical ML methods in this niche domain.

major comments (2)

[Abstract] Abstract: the central comparative claim is stated without any dataset size, number of labeled meshes, performance numbers (accuracy, precision, recall, or AUC), cross-validation scheme, or statistical significance test, rendering the result impossible to assess or reproduce.
[Methods] Methods/Experiments: no description is provided of how elevation maps are rasterized from the photogrammetric meshes, how parametric contour lines are fitted, the train/test split protocol, or the exact SVM kernel and Decision-Tree hyperparameters; without these details the attribution of any performance gap to feature choice versus data artifacts cannot be verified.

minor comments (1)

[Abstract] Abstract: the sentence 'their performance does not surpass that of the contour-based inputs' is ambiguous; clarify whether contour lines are strictly superior or merely non-inferior.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below and will incorporate the requested details into the revised manuscript.

read point-by-point responses

Referee: [Abstract] Abstract: the central comparative claim is stated without any dataset size, number of labeled meshes, performance numbers (accuracy, precision, recall, or AUC), cross-validation scheme, or statistical significance test, rendering the result impossible to assess or reproduce.

Authors: We agree that the abstract should include quantitative details to allow assessment of the claims. In the revision we will add the number of labeled meshes, key performance metrics (accuracy, AUC), the cross-validation protocol, and any significance testing results. revision: yes
Referee: [Methods] Methods/Experiments: no description is provided of how elevation maps are rasterized from the photogrammetric meshes, how parametric contour lines are fitted, the train/test split protocol, or the exact SVM kernel and Decision-Tree hyperparameters; without these details the attribution of any performance gap to feature choice versus data artifacts cannot be verified.

Authors: We acknowledge that additional implementation details are needed. The revised methods section will explicitly describe the rasterization of elevation maps from the meshes, the parametric contour-line fitting procedure, the train/test split protocol, the SVM kernel, and the hyperparameter settings for both classifiers. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper performs a direct empirical comparison of SVM and decision-tree classifiers on two input representations (elevation maps versus parametric contour lines) for detecting violin width reduction from photogrammetric meshes. No derivations, equations, fitted parameters renamed as predictions, or self-citation chains appear in the provided abstract or described content. The central claim rests on performance metrics obtained from the same labeled data under consistent splits, which is self-contained and externally falsifiable. No load-bearing step reduces to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the unstated premise that 3D meshes faithfully represent physical violins and that width reduction is a separable geometric feature. No free parameters or new entities are introduced in the abstract.

axioms (1)

domain assumption Photogrammetric meshes provide sufficiently accurate geometry for width reduction detection.
Implicit in building elevation maps and contours from the meshes.

pith-pipeline@v0.9.0 · 5359 in / 1070 out tokens · 57611 ms · 2026-05-13T21:25:09.030350+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We compare SVM and Decision Trees applied to a geometry-based raw representation built from elevation maps with a more targeted, feature-engineered approach relying on parametric contour lines fitting.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Each contour line was then fitted with a parabola-like curve described by four parameters α, β, γ, δ

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

7 extracted references · 7 canonical work pages

[1]

Baroque violas with reduced soundboxes: An evaluation method

Anne-Emmanuelle Ceulemans, Phil´ emon Beghin, Paul Fisette, Fran¸ cois Glineur, and Iona Thys. Baroque violas with reduced soundboxes: An evaluation method. The Galpin Society Journal 76 (LXXVI), pages 109–126, 2023

work page 2023
[2]

Revealing lost 16th-century royal emblems on two Andrea Amati’s violins using XRF scanning.Heritage Science, 8(1):1–12, 2020

Marie Radepont, Jean-Philippe ´Echard, Matthias Ockerm¨ uller, Hortense de la Co- dre, and Oulfa Belhadj. Revealing lost 16th-century royal emblems on two Andrea Amati’s violins using XRF scanning.Heritage Science, 8(1):1–12, 2020

work page 2020
[3]

Validation of a photogrammetric approach for the objective study of early bowed instruments.Heritage Science, 11(1):170, 2023

Phil´ emon Beghin, Anne-Emmanuelle Ceulemans, Paul Fisette, and Fran¸ cois Glineur. Validation of a photogrammetric approach for the objective study of early bowed instruments.Heritage Science, 11(1):170, 2023

work page 2023
[4]

A discus- sion about violin reduction: Geometric analysis of contour lines and channel of minima

Phil´ emon Beghin, Anne-Emmanuelle Ceulemans, and Fran¸ cois Glineur. A discus- sion about violin reduction: Geometric analysis of contour lines and channel of minima. In Rocco Furferi, Lapo Governi, Yary Volpe, Francesco Gherardini, and Kate Seymour, editors,The Future of Heritage Science and Technologies II, pages 432–446, Cham, 2026. Springer Nature Sw...

work page 2026
[5]

Identifi- cation of violin reduction via contour lines classification.2025 Digital Heritage International Congress (Digital Heritage - Siena - September 2025) - To appear

Phil´ emon Beghin, Anne-Emmanuelle Ceulemans, and Fran¸ cois Glineur. Identifi- cation of violin reduction via contour lines classification.2025 Digital Heritage International Congress (Digital Heritage - Siena - September 2025) - To appear. arXiv preprint arXiv:2507.07743, 2025

work page arXiv 2025
[6]

Pointnet: Deep learning on point sets for 3d classification and segmentation

Charles R Qi, Hao Su, Kaichun Mo, and Leonidas J Guibas. Pointnet: Deep learning on point sets for 3d classification and segmentation. InProceedings of the IEEE conference on computer vision and pattern recognition, pages 652–660, 2017

work page 2017
[7]

Deep sets.Advances in neural information processing systems, 30, 2017

Manzil Zaheer, Satwik Kottur, Siamak Ravanbakhsh, Barnabas Poczos, Russ R Salakhutdinov, and Alexander J Smola. Deep sets.Advances in neural information processing systems, 30, 2017

work page 2017