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siavashk / pycpd

Pure Numpy Implementation of the Coherent Point Drift Algorithm
MIT License
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"Error" sounds misleading... #17

Closed sandyhsia closed 6 years ago

sandyhsia commented 6 years ago

Hi, In the bunny example, I found "Error" in the visualization is misleading, because it is increasing all the time, and a the last iteration, error suddenly becomes zero. for example, iteration 20: screenshot from 2018-08-10 11-30-56

iteration 39 screenshot from 2018-08-10 11-33-19

when I check the source code and the paper, it sounds like error means the difference between Q (objective function) in current iteration and previous iteration. For example, in rigid_registration.py:

self.q = (xPx - 2 * self.s * trAR + self.s * self.s * self.YPY) / (2 * self.sigma2) + self.D * self.Np/2 * np.log(self.sigma2)
self.err = np.abs(self.q - qprev)

Given the np.abs(), we even can't figure out whether the Q is actually increasing?? or decreasing. Q might converge through EM algorithm, so error (actually the difference) < tolerance might be a metric to see whether it converges. But I hope the name of the variable could be clearer.

Second question is, while optimizing Q, is the sigma2 also decreasing? and thus could be a metric to see whether it converges?

siavashk commented 6 years ago

With regards to the variable name, i.e. error being misleading, you are right. I do not have bandwidth right now to fix it, but if you submit a pull request with the appropriate changes, I would be happy to review and approve it. Just make sure to branch off development.

With regards to sigma2, yes, one could probably use that as an estimate of the GMMs uncertainty for drawing target points. I do not quite remember, but when I was a graduate student I had trouble making a variance based stopping criteria and just comparing q to q-prev seemed to provide better results.