41 lines
2.2 KiB
C
41 lines
2.2 KiB
C
/*
|
|
* curvefit.h
|
|
* scorealign
|
|
*
|
|
* Created by Roger B. Dannenberg on 10/20/07.
|
|
* Copyright 2007 by Roger B. Dannenberg. All rights reserved.
|
|
*
|
|
* Dynamic programming does a good job of getting a rough alignment
|
|
* that is very good in a global sense, but there are often short-term
|
|
* "digressions" where the optimal path wanders off the "true" path.
|
|
* These digressions are hard to correct with simple smoothing. This
|
|
* module is intended to assert a "steady tempo" constraint to improve
|
|
* the path. It starts with the dynamic programming path, which is likely
|
|
* to be close to the correct path. The DP path (in pathx[] and pathy[])
|
|
* is divided evenly into segments of approximately line_time seconds
|
|
* along the x axis. For a segment from x1 to x2, linear regression is
|
|
* performed on the DP path from x1 to x2. This specifies an initial
|
|
* line segment. Next, the end-points are joined by averaging: if
|
|
* the segment from x1 to x2 ends at y-end and the segment from x2 to x3
|
|
* starts at y-start, then the end of line x1--x2 and the beginning of
|
|
* line x2--x3 are adjusted to (y-end + y-start)/2. Now the fun starts:
|
|
* the endpoints of all the lines are adjusted up and down in order to
|
|
* minimize a distance function. The distance function estimates the
|
|
* integral of the distance matrix value along the line. Since the line
|
|
* falls between discrete points in the matrix, interpolation is used.
|
|
* The end result is converted back into a discrete path. (Maybe in the
|
|
* future, the pathx[]/pathy[] representation should be generalized to
|
|
* allow for non-integer path coordinates.) The resulting path will
|
|
* have steady tempo at least within each segment. What I hope will
|
|
* happen is that when there are chord changes or melody changes, there
|
|
* will be "narrow" pathways in the distance matrix. Getting the
|
|
* alignment wrong at these transitions will cost a lot. Other places
|
|
* are not so critical, which is why I think DP wanders off the true
|
|
* path. The straight-line path will ensure that for the most part, the
|
|
* score alignment is determined by the transitions, and where alignment
|
|
* is not critical, the alignment will avoid any rubato or over-fitting.
|
|
*/
|
|
|
|
void curve_fitting(Scorealign *sa, bool verbose);
|
|
|