Chi2 Distance results

[wilma010206]

Hello everyone!
I am using CloudCompare to compare 2 point clouds via C2M. Using the 'Compute Statistical Parameters' tool I fit a Normal/Gaussian distribution statistical distribution to my scalar field, as in the graphics below:

console.png (5.74 KiB) Viewed 1746 times

The console shows the results of Chi2 Distance

The attachment console.png is no longer available

CloudCompare Wiki describes this parameter as follows:
“The Chi2 distance gives an indication on the local concordance between the scalar values (of each point and its neighbors) and the tested distribution. The greater the less likely is the local distribution likely to follow the tested one”
Which value of Chi2 Distance shows that my scalar field follows a Gaussian distribution?
Does Chi2 Distance represent the test statistic of chi-squared test?
If this is the case, what data should I use to compute the critical value of chi-squared? E.g., could I consider [classes-1] as degrees of freedom, and what significance level do you recommend?

[daniel]

Hi,

Indeed, the Chi2 distance is the one used in the Chi2 test.

The exact way to choose the right number of classes is a bit tricky (see https://github.com/CloudCompare/CloudCo ... ls.cpp#L54).

And for the significance level... I really don't know!

Clearly, without entering into that level of precision, you can generally tell just by looking at how the distribution curve fits the histogram ;)

[wilma010206]

Hi Daniel,

thank you for your answer.

I was wondering if you could also offer some hints as regards the Chi2 distance values providing the best fit of scalar data to a normal distribution.

Gabriella

[daniel]

Well, I don't remember the theory exactly (I used that during my PhD ... 15 years ago!). You can define the maximum Chi2 distance based on a tolerance value. If you look at this file (https://github.com/CloudCompare/CloudCo ... i2Helper.h) it might help you retrieve the right theory behind it (basically it's how to compute the 'fractile').