Principal curvatures vs normal curvatures

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Principal curvatures vs normal curvatures

Antoine Rennuit-2

Hello,

Anyone knows the difference between the curvatures computed out of NormalEstimation<>::compute() and the ones computed out of PrincipalCurvaturesEstimation<>::compute()?

The way the NormalEstimation<>::compute() curvatures are computed is explained in this link (click here), and is a rough but meaningful scalar approximation. But I was not able to find anything on how principal curvatures are computed.

Any idea?

Kind regards,

Antoine

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Re: Principal curvatures vs normal curvatures

Sérgio Agostinho

The class documentation seems to provide some feedback.


Perform Principal Components Analysis (PCA) on the point normals of a surface patch in the tangent plane of the given point normal, and return the principal curvature (eigenvector of the max eigenvalue), along with both the max (pc1) and min (pc2) eigenvalues.
Cheers



On 01/03/2018 10:09, Antoine Rennuit wrote:
Hello,

Anyone knows the difference between the curvatures computed out of NormalEstimation<>::compute() and the ones computed out of PrincipalCurvaturesEstimation<>::compute()?

The way the NormalEstimation<>::compute() curvatures are computed is explained in this link (click here), and is a rough but meaningful scalar approximation. But I was not able to find anything on how principal curvatures are computed.

Any idea?

Kind regards,

Antoine


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Re: Principal curvatures vs normal curvatures

Antoine Rennuit-2

Thanks a lot, I had missed this one. But then does this mean that the eigen values are equal to the curvatures? This does not look very obvious, or does it?


Regards,


Antoine.



De : PCL-users <[hidden email]> de la part de Sérgio Agostinho <[hidden email]>
Envoyé : dimanche 4 mars 2018 10:40
À : [hidden email]
Objet : Re: [PCL-users] Principal curvatures vs normal curvatures
 

The class documentation seems to provide some feedback.


Perform Principal Components Analysis (PCA) on the point normals of a surface patch in the tangent plane of the given point normal, and return the principal curvature (eigenvector of the max eigenvalue), along with both the max (pc1) and min (pc2) eigenvalues.
Cheers



On 01/03/2018 10:09, Antoine Rennuit wrote:
Hello,

Anyone knows the difference between the curvatures computed out of NormalEstimation<>::compute() and the ones computed out of PrincipalCurvaturesEstimation<>::compute()?

The way the NormalEstimation<>::compute() curvatures are computed is explained in this link (click here), and is a rough but meaningful scalar approximation. But I was not able to find anything on how principal curvatures are computed.

Any idea?

Kind regards,

Antoine


_______________________________________________
[hidden email] / http://pointclouds.org
http://pointclouds.org/mailman/listinfo/pcl-users


_______________________________________________
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http://pointclouds.org/mailman/listinfo/pcl-users
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Re: Principal curvatures vs normal curvatures

Sérgio Agostinho

The notion of curvature is loosely defined as you can read on the Wikipedia page for the topic. I quote a relevant paragraph for this discussion


Curvature is normally a scalar quantity, but one may also define a curvature vector that takes into account the direction of the bend in addition to its magnitude. The curvature of more complex objects (such as surfaces or even curved n-dimensional spaces) is described by more complex objects from linear algebra, such as the general Riemann curvature tensor.

Based on the description of the method, in this context, curvature is an (Eigen) vector. It has a magnitude associated with it, the Eigen value. PCA is applied on a surface patch of normals to estimate these parameters.



On 04/03/2018 15:31, Antoine Rennuit wrote:

Thanks a lot, I had missed this one. But then does this mean that the eigen values are equal to the curvatures? This does not look very obvious, or does it?


Regards,


Antoine.



De : PCL-users [hidden email] de la part de Sérgio Agostinho [hidden email]
Envoyé : dimanche 4 mars 2018 10:40
À : [hidden email]
Objet : Re: [PCL-users] Principal curvatures vs normal curvatures
 

The class documentation seems to provide some feedback.


Perform Principal Components Analysis (PCA) on the point normals of a surface patch in the tangent plane of the given point normal, and return the principal curvature (eigenvector of the max eigenvalue), along with both the max (pc1) and min (pc2) eigenvalues.
Cheers



On 01/03/2018 10:09, Antoine Rennuit wrote:
Hello,

Anyone knows the difference between the curvatures computed out of NormalEstimation<>::compute() and the ones computed out of PrincipalCurvaturesEstimation<>::compute()?

The way the NormalEstimation<>::compute() curvatures are computed is explained in this link (click here), and is a rough but meaningful scalar approximation. But I was not able to find anything on how principal curvatures are computed.

Any idea?

Kind regards,

Antoine


_______________________________________________
[hidden email] / http://pointclouds.org
http://pointclouds.org/mailman/listinfo/pcl-users



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http://pointclouds.org/mailman/listinfo/pcl-users


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Re: Principal curvatures vs normal curvatures

Antoine Rennuit-2
Thanks Sergio, now I understand the principal curvatures in the PCL is not the riemannian curvature.

Cheers,

Antoine m.


-------- Message d'origine --------
De : Sérgio Agostinho <[hidden email]>
Date : 04/03/2018 15:55 (GMT+01:00)
Objet : Re: [PCL-users] Principal curvatures vs normal curvatures

The notion of curvature is loosely defined as you can read on the Wikipedia page for the topic. I quote a relevant paragraph for this discussion


Curvature is normally a scalar quantity, but one may also define a curvature vector that takes into account the direction of the bend in addition to its magnitude. The curvature of more complex objects (such as surfaces or even curved n-dimensional spaces) is described by more complex objects from linear algebra, such as the general Riemann curvature tensor.

Based on the description of the method, in this context, curvature is an (Eigen) vector. It has a magnitude associated with it, the Eigen value. PCA is applied on a surface patch of normals to estimate these parameters.



On 04/03/2018 15:31, Antoine Rennuit wrote:

Thanks a lot, I had missed this one. But then does this mean that the eigen values are equal to the curvatures? This does not look very obvious, or does it?


Regards,


Antoine.



De : PCL-users [hidden email] de la part de Sérgio Agostinho [hidden email]
Envoyé : dimanche 4 mars 2018 10:40
À : [hidden email]
Objet : Re: [PCL-users] Principal curvatures vs normal curvatures
 

The class documentation seems to provide some feedback.


Perform Principal Components Analysis (PCA) on the point normals of a surface patch in the tangent plane of the given point normal, and return the principal curvature (eigenvector of the max eigenvalue), along with both the max (pc1) and min (pc2) eigenvalues.
Cheers



On 01/03/2018 10:09, Antoine Rennuit wrote:
Hello,

Anyone knows the difference between the curvatures computed out of NormalEstimation<>::compute() and the ones computed out of PrincipalCurvaturesEstimation<>::compute()?

The way the NormalEstimation<>::compute() curvatures are computed is explained in this link (click here), and is a rough but meaningful scalar approximation. But I was not able to find anything on how principal curvatures are computed.

Any idea?

Kind regards,

Antoine


_______________________________________________
[hidden email] / http://pointclouds.org
http://pointclouds.org/mailman/listinfo/pcl-users



_______________________________________________
[hidden email] / http://pointclouds.org
http://pointclouds.org/mailman/listinfo/pcl-users


_______________________________________________
[hidden email] / http://pointclouds.org
http://pointclouds.org/mailman/listinfo/pcl-users