Calculation of verticality

[juacarri]

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!

[juacarri]

I found a bit more info in the paper "STREAMED VERTICAL RECTANGLE DETECTION IN TERRESTRIAL LASER SCANS
FOR FACADE DATABASE PRODUCTION":

Captura.PNG (62.16 KiB) Viewed 1872 times

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?

[daniel]

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.