interpolation – Rescaling data to make a “continuous” function

I have acquired many sets of data, which all represent a single function, but which are randomly rescaled by a constant (due to the measurement specifics). I’m looking to effectively stitch them together as a continuous sort of function by rescaling each data set, however this has proven difficult since their ranges don’t always overlap. Ideally something like:

Rescaling to continuous data

Where the resulting absolute scale doesn’t matter, but the structural features are important.

The obvious solution is to interpolate/extrapolate nearby curves, and minimize the differences between neighbors. However, I haven’t been able to make this work very well, as I’m not sure if there’s a good way to select which curves should be paired/minimized together. Any suggestions?

Example={{{2.04,3.94},{2.46,3.81},{2.89,3.56},{3.1,3.18},{3.44,2.81},{3.75,2.42},{3.91,2.03},{4.12,1.75},{4.59,1.44},{5.,1.28},{5.14,1.17}},{{0.23,5.26},{0.4,6.02},{0.65,6.81},{0.96,7.47},{1.3,7.86},{1.68,7.96},{1.82,8.08},{2.15,7.84},{2.47,7.39},{2.78,6.78},{3.1,6.11},{3.43,5.33},{3.86,4.61},{4.1,3.81}},{{3.21,7.62},{3.43,6.8},{3.72,5.7},{4.04,4.81},{4.32,3.99},{4.67,3.39},{4.94,2.97},{5.29,2.85},{5.51,2.77},{5.95,3.16},{6.05,3.36}},{{6.79,2.11},{6.98,2.32},{7.2,2.6},{7.66,2.62},{7.83,2.71},{8.21,2.63},{8.5,2.55},{8.62,2.34},{8.97,2.04}},{{7.63,4.03},{7.93,4.18},{8.2,4.02},{8.49,3.87},{8.77,3.46},{9.22,3.13},{9.35,2.51},{9.61,2.21},{9.95, 1.86}}};

Rescaling – How can I limit the size to a maximum rectangle (and not just a square) when exporting to DXO OpticsPro?

The DxO Optics Pro manual has the following to say:

If you enable the Resize Image option, you must select from the following parameters:

  • The maximum size of the output image (whether height or width) in pixels, centimeters, or inches. A single dimension is sufficient for the program to maintain the aspect ratio (proportions) of the image.

If you want to keep the aspect ratio of your exported images, make the adjustment here. If you want to change the aspect ratio instead, you must crop the images to taste before exporting. With AFAIK the Optics Pro, you can not automatically do this for all images in a specific folder.