Identification of Violin Reduction via Contour Lines Classification

The first violins appeared in late 16th-century Italy. Over the next 200 years, they spread across Europe and luthiers of various royal courts, eager to experiment with new techniques, created a highly diverse family of instruments. Around 1750, size standards were introduced to unify violin making for orchestras and conservatories. Instruments that fell between two standards were then reduced to a smaller size by luthiers. These reductions have an impact on several characteristics of violins, in particular on the contour lines, i.e. lines of constant altitude, which look more like a U for non reduced instruments and a V for reduced ones. While such differences are observed by experts, they have not been studied quantitatively. This paper presents a method for classifying violins as reduced or non-reduced based on their contour lines. We study a corpus of 25 instruments whose 3D geometric meshes were acquired via photogrammetry. For each instrument, we extract 10-20 contour lines regularly spaced every millimetre. Each line is fitted with a parabola-like curve (with an equation of the type y = alpha*abs(x)**beta) depending on two parameters, describing how open (beta) and how vertically stretched (alpha) the curve is. We compute additional features from those parameters, using regressions and counting how many values fall under some threshold. We also deal with outliers and non equal numbers of levels, and eventually obtain a numerical profile for each instrument. We then apply classification methods to assess whether geometry alone can predict size reduction. We find that distinguishing between reduced and non reduced instruments is feasible to some degree, taking into account that a whole spectrum of more or less transformed violins exists, for which it is more difficult to quantify the reduction. We also find the opening parameter beta to be the most predictive.