2D Shape Outline Recognition

Question

I am looking to implement shape recognition/matching of similar curves (discreet point arrays) in 2D.

I have found a paper on the subject but Im somewhat lost when it comes to implementing this in code.

I have figured out that this function needs to be minimized:

But where do I start?

1. μ seem to be the measurement of distortion, which I want to minimize allright.
2. ψ seem to be some argument that is restricted to be between 0 and π/2
3. "R is a parameter", which means?
4. κ is the curvature, ?
5. ξ is yet another parameter...
6. gahhh

Can somebody please outline an approach to this in english? And perhaps in some pseudo-code?

Answer 1

I think it's unlikely that you'll be able to get this to work without understanding the math, and the way to understand the math is to work through the paper from the beginning; if you jump to the last equation and try to code it, naturally it won't make sense. Here are the answers to your specific questions, for what they're worth:

1. μ is indeed a "measurement of distortion", or a cost of deforming one curve into the other.
2. ψ is indeed restricted to [0 and π/2]. It is the angle of the (h,h-bar) curve (sorry, I don't know how to enter special characters).
3. "R is a parameter", which means it's arbitrary, a measure of how important orientation is, relative to displacement.
4. κ is the curvature, of C, the first curve.
5. ξ is a parameter describing advancement along both curves. As ξ advances from 0 to L-tilde, h(ξ) goes from 0 to L, and h-bar(ξ) goes from 0 to L-bar.

Answer 2

We start of with some definitions:

• Curvature is how much the curve deviates from being flat.
• A parameter defines what curve you are looking for. Eg f(x) = kx + m, k and m are parameters.

As for the minimisation, you can have a look here: http://en.wikipedia.org/wiki/Calculus_of_variations