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From my knowledge if you fit geometrical objects into point clouds you want in general minimize the squared distances of the point cloud to your fitted objects. I do so with the downhill simplex method by minimizing the average squared distance. I fit cylinders. In rare input scenarios I end up having not good fitted cylinders - detected by visual validation. Those cylinders have one thing in common. Their axis is not perpendicular to the points's normals. I can modify my error term by multiplying the squared distance of a point to a cylinder with the cosinus of the angle between the point's normal and the cylinder axis. This cosinus is 1 in the worst case and 0 in the best case.

I am looking for a name of this technique and/or publications. I think the most generic formualtion of what I am doing would be:

Modify the squared euclidean distance between input and output accounting to a change in curvature.

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  • $\begingroup$ Do you mean that in your data the points have specified normals ? In that case, you may add to your objective function the deviation between the datapoint's normal and the cylinder's nearest point normal (probably times a scaling factor that you need to make independent on the object's size). $\endgroup$ – BrunoLevy Sep 20 '16 at 15:24
  • $\begingroup$ @brunoLevy I compute for my 3D cloud before the optimization the normals with standard technique. Range search to retrieve a local neighborhood cluster, perform PCA and take the eigenvector with the smallest eigenvalue. I also have the axis and can compute the described cosinus/angle. My question is more about how this technique is called (I just assume I reinvented the wheel today) to be able to find some references to a) improve the technique and b) give a proper citation. $\endgroup$ – Jan Hackenberg Sep 20 '16 at 15:44
  • $\begingroup$ There are two papers that could be interesting: the first one (variational shape approximation), with what you need (maybe L1,2 norm) geometry.caltech.edu/pubs/CAD04.pdf The second one combines positions and normals for reconstructing shapes: gfx.cs.princeton.edu/pubs/Nehab_2005_ECP $\endgroup$ – BrunoLevy Sep 20 '16 at 16:32
  • $\begingroup$ Do you mean the "Nelder-Mead" Simplex method? That horrendous algorithm should have been put out of its misery several decades ago. $\endgroup$ – Mark L. Stone Sep 20 '16 at 23:42
  • $\begingroup$ Are you refering to Iterative Closest Point by Besl and McKay (1992), "A Method for Registration of 3-D Shapes" ? $\endgroup$ – André Sep 21 '16 at 11:15
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I think what your looking for is a good parameterization of cylinder, as well as a fast scheme for performing gradient descent minimization, similar to iterative closest point.

While many papers are available, I would redirect you to this particular one:

Drost, Bertram, and Slobodan Ilic. "Local Hough Transform for 3D Primitive Detection." 3D Vision (3DV), 2015 International Conference on. IEEE, 2015.

There, authors devise a scheme for detection, as well as refinement of the cylinders, with a new parameterization. The approach doesn't use the point normals, however I believe that such a treat would be appropriate. Yet, it is found to be effective enough, when one uses a point-to-primitive distance.

I'm sure you'll find it useful.

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