Implementation of Koehl's method for calculating geometric moments

[brianthelion]

The current method for calculating Zernike moments depends on first calculating the geometric moments for the mesh. This is the slowest step in the algorithm, by far.

The current implementation depends on a method due to Pozo that is O(N^6). Koehl proposes a recursive method that is O(N^3).

[brianthelion]

I now have the method working and will focus on optimization.

[brianthelion]

Optimization is almost finished. I have reduced per-face computational time at N=20 from 0.20s (Pozo's method) to 0.01s (Koehl's method). Things are coming along nicely.

[brianthelion]

Here are the latest benchmarks for Koehl's method on a standard Mindboggle mesh (~300k faces):

• ~90 seconds at N=5 (vs. 360 seconds for Pozo)
• ~3 minutes at N=10 (vs. 32 minutes for Pozo)
• ~12 minutes at N=20 (vs. forever for Pozo)

Looking to push tomorrow.