Detect Scale

[jmac698]

Hi,
I have two ordered lists of numbers, one of which has scaled along the x axis. How do I find the multiplication factor? It's likely between .5 and 2 on real data.
There must be something better than trying every scale with a correlation.
Ideally should be robust against clipping and noise.
Thanks.

[jmac698]

I did some tests with log (find the log of both histograms before comparing), and that works great for finding scale, which is just the offset between them, but it doesn't work if some addition was done to one of them, as this changes the shape of the graph and they don't look the same anymore.
I need to find a way to detect scale which is invariant to translation first.
A simple type of feature detection would be to scan the graphs horizontally and try to find the same points in each and just divide them to find the scale, but with noise you could get some other points dipping into the row.
The solution I've read about involves taking the FFT of each, because this is translation invariant. Not only is it complicated, but you have to deal with border effects.
They also mentioned SIFT but I haven't read about it yet. I wish there were something simpler.