pcl::PCA eigenvectors/eigenvalues are computed with incorrect Cov matrix? (1.8)

[SergioRAgostinho]

Dug this one out of the dev/user list. Original post here with a rebound here.

Hello,

Line 85-88 of: https://github.com/PointCloudLibrary/pcl/blob/pcl-1.8.0/common/include/pcl/common/impl/pca.hpp
/../
Eigen::Matrix3f alpha = static_castEigen::Matrix3f (cloud_demean.topRows<3> () * cloud_demean.topRows<3> ().transpose ());

// Compute eigen vectors and values
Eigen::SelfAdjointEigenSolverEigen::Matrix3f evd (alpha);
/../

alpha is presumably the covariance matrix as it is passed to SelfAdjonitEigenSolver. But shouldn't that be:

alpha = 1/(N-1) * cloud_demean * cloud_demean.transpose()?

Not putting the 1/(N-1) makes the eigenvalues dependent on the number of points you have in the cloud. Double the number of data points you have in the exact same [x,y,z] interval you will get eigenvalues that are twice as big. The eigenvectors may still be fine as they are also normalized. But it still looks incorrect to me.

Was there a reason to write it like this that I'm missing?

Engin