  Melodic similarity measurement is of key importance in music information
retrieval. In this paper, we use geometric matching techniques to measure the
similarity between two melodies. We represent music as sets of points or sets
of horizontal line segments in the Euclidean plane and propose efficient
algorithms for optimization problems inspired in two operations on melodies;
linear scaling and audio compression. In the scaling problem, an incoming query
melody is scaled forward until the similarity measure between the query and a
reference melody is minimized. The compression problem asks for a subset of
notes of a given melody such that the matching cost between the selected notes
and the reference melody is minimized.
