Calculation of verticality

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juacarri
Posts: 11
Joined: Tue Oct 08, 2019 7:55 am

Calculation of verticality

Post by 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
Posts: 11
Joined: Tue Oct 08, 2019 7:55 am

Re: Calculation of verticality

Post by juacarri »

I found a bit more info in the paper "STREAMED VERTICAL RECTANGLE DETECTION IN TERRESTRIAL LASER SCANS
FOR FACADE DATABASE PRODUCTION":
Captura.PNG
Captura.PNG (62.16 KiB) Viewed 963 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
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Re: Calculation of verticality

Post by 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.
Daniel, CloudCompare admin
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