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Error measurement between given perfect 2D shape and freeform shape drawn by user

I am programming (with vectors) an application which requires a user to draw line according to certain data. Then the user will click a check button which will grade the users drawing to the actual data line. So I am wondering how would I go about grading the accuracy of the two lines?

So far what I have been able to do is interpolate the entire line of both the user line and the actual line. So that the user lines data can match with the actual line data.

What is my next step in finding the accuracy of the user line to the actual line?

I can't use area because the line the user draws is not linear, its freeform.

Heres an image of what i mean:

enter image description here

Community
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John Riselvato
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Lets say user line is $g(x)$ and line drawn by you is $f(x)$

Then grade can be made be inversely proportional to

$$\displaystyle \sum_{x=a}^{b} (g(x)-f(x))^2$$

This is commonly used function.

Pratik Deoghare
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  • I will see how this works out for me. – John Riselvato Dec 05 '11 at 20:42
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    @John, this is RMS applied in a slightly different manner. – picakhu Dec 05 '11 at 20:44
  • I rather like the RMSE better nyways. @picakhu post it as your answer as an answer, so i can give you credit. – John Riselvato Dec 05 '11 at 20:46
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    @John, I would have to elaborate on how you should use it, and I am not sure which approach is best. I think it is better that I do not get credit for it, I do not deserve it. – picakhu Dec 05 '11 at 20:49
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    This just avoids taking the root and average. So it saves computation. We are using this in stanford ml-class online. :) @picakhu is right its just RMS squared times number of points! – Pratik Deoghare Dec 05 '11 at 20:51