Feature-based Representation for Violin Bridge Admittances

Frequency Response Functions (FRFs) are one of the cornerstones of musical acoustic experimental research. They describe the way in which musical instruments vibrate in a wide range of frequencies and are used to predict and understand the acoustic differences between them. In the specific case of stringed musical instruments such as violins, FRFs evaluated at the bridge are known to capture the overall body vibration. These indicators, also called bridge admittances, are widely used in the literature for comparative analyses. However, due to their complex structure they are rather difficult to quantitatively compare and study. In this manuscript we present a way to quantify differences between FRFs, in particular violin bridge admittances, that separates the effects in frequency, amplitude and quality factor of the first resonance peaks characterizing the responses. This approach allows us to define a distance between FRFs and clusterise measurements according to this distance. We use two case studies, one based on Finite Element Analysis and another exploiting measurements on real violins, to prove the effectiveness of such representation. In particular, for simulated bridge admittances the proposed distance is able to highlight the different impact of consecutive simulation `steps' on specific vibrational properties and, for real violins, gives a first insight on similar styles of making, as well as opposite ones.

A sub-Riemannian model of the visual cortex with frequency and phase

In this paper we present a novel model of the primary visual cortex (V1) based on orientation, frequency and phase selective behavior of the V1 simple cells. We start from the first level mechanisms of visual perception: receptive profiles. The model interprets V1 as a fiber bundle over the 2-dimensional retinal plane by introducing orientation, frequency and phase as intrinsic variables. Each receptive profile on the fiber is mathematically interpreted as a rotated, frequency modulated and phase shifted Gabor function. We start from the Gabor function and show that it induces in a natural way the model geometry and the associated horizontal connectivity modeling the neural connectivity patterns in V1. We provide an image enhancement algorithm employing the model framework. The algorithm is capable of exploiting not only orientation but also frequency and phase information existing intrinsically in a 2-dimensional input image. We provide the experimental results corresponding to the enhancement algorithm.

A neuro-mathematical model for geometrical optical illusions

Geometrical optical illusions have been object of many studies due to the possibility they offer to understand the behaviour of low-level visual processing. They consist in situations in which the perceived geometrical properties of an object differ from those of the object in the visual stimulus. Starting from the geometrical model introduced by Citti and Sarti in [3], we provide a mathematical model and a computational algorithm which allows to interpret these phenomena and to qualitatively reproduce the perceived misperception.