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On temporal coherency of probabilistic models for audio-to-score alignment

Philippe Cuvillier 1, 2
1 MuTant - Synchronous Realtime Processing and Programming of Music Signals
UPMC - Université Pierre et Marie Curie - Paris 6, IRCAM, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
2 Repmus - Représentations musicales
STMS - Sciences et Technologies de la Musique et du Son
Abstract : This thesis deals with automatic alignment of audio recordings with corresponding music scores. We study algorithmic solutions for this problem in the framework of probabilistic models which represent hidden evolution on the music score as stochastic process. We begin this work by investigating theoretical foundations of the design of such models. To do so, we undertake an axiomatic approach which is based on an application peculiarity: music scores provide nominal duration for each event, which is a hint for the actual and unknown duration. Thus, modeling this specific temporal structure through stochastic processes is our main problematic. We define temporal coherency as compliance with such prior information and refine this abstract notion by stating two criteria of coherency. Focusing on hidden semi-Markov models, we demonstrate that coherency is guaranteed by specific mathematical conditions on the probabilistic design and that fulfilling these prescriptions significantly improves precision of alignment algorithms. Such conditions are derived by combining two fields of mathematics, Lévy processes and total positivity of order 2. This is why the second part of this work is a theoretical investigation which extends existing results in the related literature.
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Philippe Cuvillier. On temporal coherency of probabilistic models for audio-to-score alignment. Signal and Image Processing. UPMC - Paris 6 Sorbonne Universités, 2016. English. ⟨tel-01448687v1⟩

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