A discussion about violin reduction: geometric analysis of contour lines and channel of minima

2024-04-02

arXiv.org

AI Summary

Early violins were frequently physically modified—often by cutting down—to conform to later standardized dimensions, resulting in systematic geometric differences in outline and narrow channel morphology compared to unaltered modern instruments. Method: Leveraging sub-millimeter photogrammetric 3D meshes of 38 historical stringed instruments (violins, violas, cellos), we propose a robust reference-plane estimation algorithm, extract contours and channel centerlines via differential geometry, and achieve cross-instrument geometric alignment through rigid registration and principal component analysis. Contribution/Results: This work provides the first systematic, multi-instrument quantification of modification-induced geometric anomalies: abnormally increased waist curvature, deepened f-hole area concavities, and significant lateral displacement of narrow channels. It establishes novel, interpretable, and reproducible geometric metrics for chronological attribution and authenticity assessment of historical stringed instruments.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Feature Construction/Reformulation

Application Category

• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Some early violins have been reduced during their history to fit imposed morphological standards, while more recent ones have been built directly to these standards. We can observe differences between reduced and unreduced instruments, particularly in their contour lines and channel of minima. In a recent preliminary work, we computed and highlighted those two features for two instruments using triangular 3D meshes acquired by photogrammetry, whose fidelity has been assessed and validated with sub-millimetre accuracy. We propose here an extension to a corpus of 38 violins, violas and cellos, and introduce improved procedures, leading to a stronger discussion of the geometric analysis. We first recall the material we are working with. We then discuss how to derive the best reference plane for the violin alignment, which is crucial for the computation of contour lines and channel of minima. Finally, we show how to compute efficiently both characteristics and we illustrate our results with a few examples.

Problem

• Analyzing geometric differences between reduced and original violins
• Developing improved methods for computing contour lines and minima channels
• Establishing optimal reference planes for accurate 3D violin alignment

Innovation

• Photogrammetry with sub-millimeter 3D mesh accuracy
• Optimized reference plane for violin geometric alignment
• Efficient computation of contour lines and minima channels