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Validation of a photogrammetric approach for the objective study of ancient bowed instruments

Philémon Beghin, Anne-Emmanuelle Ceulemans, Paul Fisette, François Glineur

TL;DR

It is shown how quantitative and qualitative features such as contour lines, channel of minima and a measure of asymmetry between the upper and lower surfaces of a violin can be automatically extracted from the validated photogrammetric meshes, allowing to successfully highlight differences between instruments.

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 propose an objective photogrammetric approach to differentiate between a reduced and an unreduced instrument, whereby a three-dimensional mesh is studied geometrically by examining 2D slices. Our contribution is twofold. First, we validate the quality of the photogrammetric mesh through a comparison with reference images obtained by medical imaging, and conclude that a sub-millimetre accuracy is achieved. Then, we show how quantitative and qualitative features such as contour lines, channel of minima and a measure of asymmetry between the upper and lower surfaces of a violin can be automatically extracted from the validated photogrammetric meshes, allowing to successfully highlight differences between instruments.

Validation of a photogrammetric approach for the objective study of ancient bowed instruments

TL;DR

It is shown how quantitative and qualitative features such as contour lines, channel of minima and a measure of asymmetry between the upper and lower surfaces of a violin can be automatically extracted from the validated photogrammetric meshes, allowing to successfully highlight differences between instruments.

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 propose an objective photogrammetric approach to differentiate between a reduced and an unreduced instrument, whereby a three-dimensional mesh is studied geometrically by examining 2D slices. Our contribution is twofold. First, we validate the quality of the photogrammetric mesh through a comparison with reference images obtained by medical imaging, and conclude that a sub-millimetre accuracy is achieved. Then, we show how quantitative and qualitative features such as contour lines, channel of minima and a measure of asymmetry between the upper and lower surfaces of a violin can be automatically extracted from the validated photogrammetric meshes, allowing to successfully highlight differences between instruments.
Paper Structure (17 sections, 10 equations, 17 figures, 6 tables)

This paper contains 17 sections, 10 equations, 17 figures, 6 tables.

Table of Contents

  1. Historical context and motivation
  2. Mesh acquisition
  3. Photogrammetric mesh
  4. CT scan mesh
  5. Contour isolation
  6. Mesh validation
  7. Registration between photogrammetric and CT representations
  8. Alternative registrations
  9. Error assessment and validation
  10. Simplification
  11. Geometric analysis of the sound boards
  12. Symmetry plane between the sound board and back
  13. Contour lines
  14. Asymmetry between sound board and back
  15. Channel of minima
  16. ...and 2 more sections

Figures (17)

  • Figure 1: Reduced violin vs. its estimated original dimensions (left) moens2015voix Reduction of the height of the sound box vs. reduction of the width (right).
  • Figure 2: Setup and photographed violin (left: light tent, centre: laid down, right: upright).
  • Figure 3: Top: isolated sound board contour (blue) and manually delineated mesh extending over the ribs of the violin (purple). Bottom: zoom on the contour at the level of the ribs.
  • Figure 4: Contour isolation process. Left: Extreme points computed on a wide grid (Step 1). Right: points and shortest path on the mesh (red: extreme points (Step 1), filled blue: nearest neighbours (Step 2), empty blue: added intermediate vertices (Step 3), dashed gray: shortest paths between two consecutive nearest neighbours (Step 3)).
  • Figure 5: Matching problem (left) and average distance $D$ when varying a single angle $\theta_2$ before optimisation (right).
  • ...and 12 more figures