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Message-ID: <4a4d03b4$0$95556$742ec2ed@news.sonic.net>
From: Stan Bischof <stan@newserve.worldbadminton.com>
Subject: Re: An Interesting Real-World Problem...
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Geoffrey Akien <geoff.akien@gmail.com> wrote:
> I have some real-world data that I'd like to pick out 
> the dramatic change in gradient of:
> 
> http://www.flickr.com/photos/40058045@N07/3681613485/
> (wish I could include this in the post but never mind)
> 

If you are looking for the "edge" and your data is always about the same shape
as the picture that you have then I would suggest that your best answer
would be the same as you would get from pencil-and-paper:

I would draw three lines to model this data on paper, and the intersections
of those three lines would bound the regions. The three lines would be the
best fits in the three regions so in this case a upward sloped line,
then a downward sloped line and then a flat line.

Do exactly the same on your computer by modeling it with a
piece-wise linear curve fit. You could chunk out the least-squares
analytic solution but there's likely a piecewise linear
function in Matlab curve-fitting toolbox.

A linear spline fit would be about the same thing and then your control
points would be the corners.

Stan