Computing the curvature of a boundary

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Said Rahal
Said Rahal 2012-7-13
In the following figure I computed the area of the object using the function "regioprops". Moreover I was asked to determine the curvature of the boundaries so my plan is the following: 1) Extract the x and y 2) fit the points into a curve (function). 3)Using a mathematical equation found in the literature which include the firt and second derivative, I will compute the curvature of the boundary
Can you please share with me your view concerning this plan, and if you are thinking of a better one, I will be glad to listen. Thanks
Note: I wanted to attach the image but I could not.(may I am not doing it right)
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Image Analyst
Image Analyst 2012-7-14
Post your picture to tinypic.com or similar. The curvature may change value from point to point. Your curvature will be the average curvature over the entire region you used - I assume you already know that though. What is your formula? Something on http://en.wikipedia.org/wiki/Curvature?

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Matt Kindig
Matt Kindig 2012-7-13
Hi Said,
I have done something similar. Here's one approach: If you have the Spline Fitting Toolbox, you can use the periodic spline fitting tools to fit a piecewise cubic function to the x and y coordinates. By enforcing periodicity, you will be able to guarantee continuity of the first and second derivatives at the boundary. You can then easily calculate the curvature of each of the spline segments.
If you don't have the Spline Fitting Toolbox, you can still fit a periodic spline using the 'splinefit' function on the File Exchange.
Does this make sense?
Good luck, Matt
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Said Rahal
Said Rahal 2012-7-16
Thanks Matt for assistance, but the function is complicated. So what I will probably do is use Mathmetica (to fit the points and differentiate the obtained function) with MATLAB. Thank you for your time

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