Correcting 3 sigma in 2D gaussian distribution #445
Conversation
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
* corrected the use of 3 sigma in 2D space. the correct interval is +/- 3.4086, since it is a multivariate gaussian distribution
|
Did you observe any material improvements in terms of quality? |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
2D multivariate distribution has a different probability related to 1-2-3 sigma
The black scatter is a plot of 1000 samples 2D multivariate gaussian distribution. The blue ellipse uses the 3 sigma scaling. 3 sigma scaling works well in 1 dimension, and correspond to 99.7% probability. However, the corresponding probability in 2D is actually lower if 3 sigma scaling is used. To get the equivalent 99.7% red ellipse in 2D, it should be scaled by 3.4086 instead.
This is also described in the table in this link
Thus, I propose to change the scale_factor to 3.4086, to have the same effect of the 99.7% ellipse such that the contribution of the gaussian beyond the ellipse boundary becomes vanishingly small.
Also modified the inside view frustum test to use the AABB of the ellipse directly.