Questions about Task 4.5

[55mmm]

Hello,

I have a few questions about task 4.5:

(1) We saw in the lecture that PCA normal estimation for a given point can be done by searching for its k nearest neighbors, or by search within a radius r. Section 2.1 of the referenced paper seems to rely on the former, while the spatial index of task 1.2 only supports the latter. Is it fine to use search within a certain radius here, or do we need to extend the feature set of the spatial index?

(2) Either way, what would be some reasonable values for k or r? Can we reuse the Wendland radius here? Do we need to add extra parameters to the GUI?

(3) Last year's Visual Computing class pointed out that PCA is usually computed using SVD rather than by eigendecomposition of the covariance matrix, for numerical stability. In my opinion, this is also much easier to implement, but does not strictly reflect what is being done in Section 2.1 of the paper. Are we free to choose here or do we need to exactly stick with what the paper describes?

Best regards, Michael

[segaviv]

Hi,

For (1) + (2) - both are valid options. You should try to experiment with the parameters and find ones that produce reasonable results (you can also add them to the GUI to make it easier to experiment).

(3) Both are ok, I don't think that numerical stability will be an issue when computing the PCA normals.