Renotation of Optical Music Recognition Data

We present the problem of music renotation, in which the results of optical music recognition are rendered in image format, while changing various parameters of the notation, such as the size of the display rectangle or transposition. We cast the problem as one of quadratic programming. We construct parameterizations of each composite symbol expressing the degrees of freedom in its rendering, and relate all the symbols through a connected graph. Some of the edges in this graph become terms in the quadratic cost function expressing a desire for spacing similar to that in the original document. Some of the edges express hard linear constraints between symbols expressing relations, such as alignments, that must be preserved in the renotated version. The remaining edges represent linear inequality constraints, used to resolve overlapping symbols. The optimization is solved through generic techniques. We demonstrate renotation on several examples of piano music.