Spherical Harmonics comparison,
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Posted 23 March 2012 - 03:44 PM
I'd like to know if there is a correct way to compare 2 spherical harmonics: I have a set of SH (3rd order = 9 coefs) and - for a given SH - I'd like to find out which SH in the set are "similar" to the given one.
I did a basic L2 distance on coefs set but it is obviously not correct, and I have no idea of which value my threshold should have.
I guess there's already smart solution for this problem but my friend google doesn't know where to look.
Any suggestions ?
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Posted 23 March 2012 - 07:25 PM
Here, c and d are your coefficients, and the y's are the SH basis functions. So a Monte Carlo integration would be something like
for a set of N points (uniformly distributed) on the unit sphere. Here w(x) is a weight function, which would be equal to 4pi if you use a uniform distribution on the sphere.
You could also replace taking the absolute value with an L2 norm to get the L2 distance. I think I got all that right... hope that helps.