How to Do Selection of a Continuous Graph in Digitize? about digitize

[ashander]

This seems like something to avoid if at all possible.

In most cases when a continuous curve is presented, there should be associated equations (or at least reproducible methods to get equations) for the curve.

The question you ask strikes me as a the inverse problem of smoothing which seeks to infer functions that capture important patterns in data. You're asking how to produce data along a curve that captures important aspects of an underlying curve. Perhaps there's a general literature on this question in mathematics or statistics.

[sami10007]

Yes, you are right that it is an inverse problem but I would not call it about smoothing. The inverse problem can be solved by knowing the velocity of the constant piecewise distribution. I think it can be solved in Mathematica. Extra difficulty is with rasterized image. However, I am only interested in relative changes, not to absolute units. I think this difficulty is the main reason why my thread of Mathematica got closed here http://mathematica.stackexchange.com/q/119336/9815 The points are distributed by the constant piecewise velocity. In the thread, you see the actual data that I use.

It would be really great to get more feedback about the formulation of the inverse problem such that I could better understand if the extraction is at all possible in Mathematica.