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This paper has introduced Poisson point processes as a model for fundamental frequency estimation in polyphonic music. The principal advantage of such an approach is the simplicity of the resulting likelihood function, allowing many notes to be superimposed in a straightforward manner, and without performing any explicit data association task to link detected peaks with particular note harmonics. Several possible forms for the rate function were considered and example transcription results were given for polyphonic piano music.

We anticipate that performance gains can be achieved by embedding the Poisson model in a hierarchical model that links multiple frames together, thus directly modeling the evolution of pitches with time.¹⁵ A useful starting point is a hidden Markov model for pitch transitions over time, with a Poisson observation model for individual frames.

A further unexplored area is a model for the DFT amplitude process, which could guide the transcription process to better results and also lead to inference of additional quantities such as note timbre, playing volume, or instrument identity. Here one can consider extending the point process to a marked point process,⁸ in which both amplitudes and frequencies of peaks are modeled. Initial investigations have shown that this is a promising approach.