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

Philémon Beghin; Anne-Emmanuelle Ceulemans; François Glineur

cs.CVApr 2, 2026

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

Authors: Philémon Beghin, Anne-Emmanuelle Ceulemans, François Glineur

Organizations: UCLouvain - ICTEAM - Louvain-la-Neuve, Belgium · UCLouvain - INCAL - Louvain-la-Neuve, Belgium · Musical Instruments Museum (MIM) - Brussels, Belgium

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.

Figures & tables

Panel of Figure 1 — Figure 1: Impact of the reduction of the width of the sound box on the contour lines.

Figure 2: Elevation map sampled every $0.25\text{\,}\mathrm{mm}$ $\times$ $0.25\text{\,}\mathrm{mm}$ 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.

Panel of Figure 3 — Figure 3: Elevation maps resampled on a $5\times 10$ 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 two red lines on each scale bar indicate the minimum and maximum elevations of the violin sound boards.

Figure 4: Impact of the parameters on the contour lines fitting.

Figure 5: Fitting of contour lines of the sound board of an instrument (left) and profile of the parameters

\alpha

\beta

\gamma

and

\delta

for each level (right).

Panel of Figure 6 — Figure 6: Several 2D representations of violin features. The top-left figure illustrates the first two principal components of a $5\times 10$ relative resampled grid (first line of Tables 2 and 3 ) and the other three highlight features derived from the $\boldsymbol{\beta}$ profiles (first three lines of the third box of Tables 1 and 4 ).

Panel of Figure 7 — Figure 7: Leave-one-out cross-validation for several regularisation strengths. Input features: resampled $\boldsymbol{\beta}$ profile (left); $5\times 10$ elevation map with relative resampling (right).

Panel of Figure 8 — Algorithm 1 Robust regularisation choice with per-instrument cross-validation

	Balanced accuracy (in $\%$ )
Number and type of features	Max $C$		Min $C$		Max $C$		Min $C$
	No norm.		No norm.		Norm.		Norm.
	RBF	Lin.	RBF	Lin.	RBF	Lin.	RBF	Lin.
50 ( $5\times 10$ relative grid resampling)	20	57.5	70	57.5	20	90	70	90
250 ( $10\times 25$ relative grid resampling)	30	60	80	60	20	80	70	80
1000 ( $20\times 50$ relative grid resampling)	40	45	90	42.5	20	67.5	70	67.5

Table 1: Balanced accuracies of SVM models with an RBF or a linear kernel trained on different sets of features. First box shows results for elevations with relative resampling, second box with absolute resampling. Third box shows contour parameters, from Beghin et al. (2025) . Balanced accuracies

\geq 90\%

in bold.

	Balanced accuracy (in $\%$ )
Number and type of features	Max $C$ (weak reg.)	Min $C$ (strong reg.)
2 (PCA on all relative grid resampling)	40	90
3 (PCA on all relative grid resampling)	20	70
5 (PCA on all relative grid resampling)	20	70
8 (PCA on all relative grid resampling)	20	70
10 (PCA on all relative grid resampling)	20	70

Table 2: Balanced accuracies of SVM models with an RBF kernel trained on different PCA projections of the relative resampled grids. Balanced accuracies

\geq 90\%

in bold.

	Balanced accuracy (in $\%$ )
Number and type of features	Max $C$ (weak reg.)	Min $C$ (strong reg.)
2 (PCA on $5\times 10$ relative grid resampling)	72.5	72.5
3 (PCA on $5\times 10$ relative grid resampling)	72.5	72.5
10 (PCA on $5\times 10$ relative grid resampling)	72.5	72.5

Table 3: Balanced accuracies of SVM models with a linear kernel trained on different PCA projections of the relative resampled grids. Balanced accuracies

\geq 90\%

in bold.

	Balanced accuracy (in $\%$ )
Number and type of features	min Depth		max Depth
	Gini	Entropy	Gini	Entropy
50 ( $5\times 10$ relative grid resampling)	35	40	42.5	40
250 ( $10\times 25$ relative grid resampling)	40	37.5	45	37.5
1000 ( $20\times 50$ relative grid resampling)	45	37.5	45	35
1625 ( $25\times 65$ relative grid resampling)	40	32.5	40	40

Table 4: Balanced accuracies of Decision Trees models with a gini or entropy criterion trained on different sets of features. First box shows results for elevations with relative resampling, second box with absolute resampling. Third box shows contour parameters, from Beghin et al. (2025) . Balanced accuracies

\geq 90\%

in bold

	Balanced accuracy (in $\%$ )
Number and type of features	min Depth		max Depth
	Gini	Entropy	Gini	Entropy
2 (PCA on 5 x 10 relative grid resampling)	67.5	67.5	67.5	67.5
2 (PCA on 10 x 25 relative grid resampling)	55	65	52.5	62.5
2 (PCA on 20 x 50 relative grid resampling)	55	65	55	65
2 (PCA on 25 x 65 relative grid resampling)	55	65	55	65

Table 5: Balanced accuracies of Decision Trees models with a gini or entropy criterion trained on different PCA projection of the relative resampled grids.

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We introduce Varifold Moments Invariants (VMI) as a unifying framework for many previously introduced Moment Invariants. These invariants are deeply related to other contour features that are invariant under translations and rotations, like Extended Gaussian Image, Elliptic Fourier Descriptors or Shape Distributions. The advantage of the varifold approach to moments consists in being able to combine the geometry of the region, its boundary, and the family of lines tangent to it, in order to create a substantial number of invariant features with high discriminating power and clear geometric meaning. By coupling our VMI feature extraction with the light feature classifiers Random Forest or Multi-Layer-Perceptron, we outperform state-of-the-art approaches based on contours, while decreasing drastically the computational cost to the point of allowing our algorithm to run on light devices. We tested our approach on classification tasks on a large number of widely-used datasets of various types (leaves, objects, cells) and achieved high accuracy with a low number of geometrically interpretable features.

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