Finding scaling factor for two signals to have same shape

I have two signals (see figure) with differences mostly in amplitude. I need to find optimal scaling factor so they look the same as much as possible. Do you know any criteria I can use? I dont want any spectral analysis. I tried root mean square error between curves and ratio of maxima. Thank you.

[dpb]

What about the apparent linear-decreasing trend in the baseline of the top figure?

Answer 1

[John D'Errico]

Sigh, what the human eye sees as similar looking signals is not always so clear to a computer. There are issues with...

 - Baselines. It seems that one set of curves takes off from zero, the other does not.

 - Shapes. The curves do have seriously different shapes. While they look similar, the peaks have differing widths. The set on top seems to be considerably wider in each peak than those below.

 - Time shifts. I'll call the x axis time, although I have no reason to conclude it is time. Regardless, the peaks do not seem to be perfectly aligned with those from the other set.

 - Peak to peak variability. Should each of these peaks be adjusted separately? DPB points out what appear to be trends in the peak heights. I'll just call it variability. Regardless, there appears to be a fair amount of variability between peak heights in each set, and that pattern does not seem terribly consistent between the two sets. Any such conclusion based on such a small sample is statistically virtually meaningless of course.

You might deal with some of these issues simply enough, at least in theory. For example, the differing widths of those peaks might be accounted for if there were some blurring activity occurring. Thus convolve the bottom set of peaks with a Gaussian spread function, and the resulting shapes might more accurately mirror the set above.

My point in all this is, in order to model what you see, you need to postulate a model that accounts for these differences. The better the model, the better the convergence between the two sets of curves.