Geometric Algorithms for Transposition Invariant Content-Based Music Retrieval
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We represent music as sets of points or sets of horizontal line segments in the Euclidean plane. Via this geometric representation we cast transposition invariant content-based music retrieval problems as ones of matching sets of points or sets of horizontal line segments in plane under translations. For finding the exact occurrences of a point set (the query pattern) of size m within another point set (representing the database) of size n, we give an algorithm with running time O(mn), and for finding partial occurrences another algorithm with running time O(mn log m). We also use the total length of the overlap between the line segments of a translated query and a database (i.e., the shared time) as a quality measure of an occurrence and present an O(n log n + mn log m) algorithm for finding translations giving the largest possible overlap. Some experimental results on the performance of the algorithms are reported.