CloudCompare forum

Hi! I am using CloudCompare's "Compute geometric features" tool, and a question has arisen. According to the documentation (paper "Contour detection in unstructured 3D point clouds") the variable "Verticality" is defined as:

1 − |<[0 0 1], e3>|

I'm a bit lost and I don't understand the formula, would it be possible for someone to explain it?

Thanks in advance!

I found a bit more info in the paper "STREAMED VERTICAL RECTANGLE DETECTION IN TERRESTRIAL LASER SCANS
FOR FACADE DATABASE PRODUCTION":
But I still don't understand exactly how to create the tensor, can anyone tell me how to create it from the coordinates of the points that make up the neighbourhood?

Hi,

By 'tensor', they actually refer to the 'cross correlation matrix'. And e1, e2 and e3 are the eigenvectors of the this matrix, while sigma 1, 2 and 3 are the associated eigenvalues. e3 is the eigen vector associated to the smallest eigenvalue.