[Registration] PCL-NDT codes calculate gauss_c1, c2 may have problem? equation 6.7

[Kin-Zhang]

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My confusion:

Paper: 2009 Phd Thesis <The Three-Dimensional Normal-Distributions Transform>

Equation here:

Code here:

   // Initializes the gaussian fitting parameters (eq. 6.8) [Magnusson 2009]
   const double gauss_c1 = 10.0 * (1 - outlier_ratio_);
   const double gauss_c2 = outlier_ratio_ / pow(resolution_, 3);

Question: Why the PCL code write the constant c1, c2 as, pcl source code link:

Why the c1, c2 could be formulated as the codes said, and why 10 times on c1 also?

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Other related issues to understand more:

1. https://github.com/PointCloudLibrary/pcl/issues/5056
2. same question in StackOverflow: https://stackoverflow.com/questions/75057084/normal-distributions-transform-pcl-ndt-codes-calculate-c1-c2-may-have-problem

[mvieth]

@Kin-Zhang Am I mistaken or is this the same question as in issue #5056 ? I believe we did not find a complete answer yet, but you will at least find a partial answer there. I will try to look into this problem again over the next few days when I have time. But I would rather close this issue and continue discussion in #5056 if you agree that it is the same question.

[Kin-Zhang]

Sorry, not really #5056 is about the gauss_c2, and it discussed the outlier ratio and c2.

But My question is more related to the c1 and the formulation with codes of both of them.

I also comment on #5056 and gave my opinion on how he/she can have good results in experiments.