CGAL users discussion list

[Marc Pouget <>]

At first sight i would say you may get better results by adjusting  
the parameters:

1. if you set the degree of the fitting to be 1, then you will  
actually get the PCA result which seems good

2. if you also need curvatures or if the surface seems smooth enough,  
you may want to try to increase the degree to 2. Then it is desirable  
that the point of interest be at the center of the patch of selected  
vertices for the estimation.
On your example, this symmetry can be improved, instead of selecting  
a given number of vertices (i suppose that's what you did ?) select  
instead a given number of rings. This does not completely solve the  
symmetry problem because of the triangulation artifact but it is  
likely to give a better balance.


Hope this will be helpful
Best
Marc


On 13 , Oct , 2009, at 15:40 , Thorben Kröger wrote:

> On Tuesday 13 October 2009 07:24:30 Marc Pouget wrote:
> > Please give us more details about your expectations and experiments
> > if you want some feedback
>
> OK, bear with me then :-)
>
> I want to estimate normals on digital surfaces obtained from a  
> segmentation.
> In our case, the digital surfaces are comprised of the surface- 
> elements of
> voxels, so the surfaces lie in-between the voxels. They are not sub- 
> pixel
> accurate by definition and thus typical stair-like artefacts are  
> obvious.
>
> Initial tests based on the Jet_fitting_3 example code for a  
> polyhedral mesh
> did not result in any good estimates even for large (32 vertices)
> neighborhoods; the normal orientation varied a lot from vertex to  
> neighbouring
> vertex even for quite smooth parts of my surface.
>
> Therefore, I tested everything on a simple testcase, two plots of  
> which are
> attached to this mail:
>
> On the plot "snapshot_plane.png" you see onto the side of a sampled  
> plane,
> which has the typical stair artefacts. A 3D view is in  
> "snapshot_plane_2.png"
>
> I hand crafted code to triangulate this plane to exclude any  
> possible errors
> in wrong triangulations, then fed the vertices and edges to a
> CGAL::Polyhedron_incremental_builder_3 to build the polyhedron.
>
> I based my code on the cgal jet fitting example "Mesh_estimation.cpp".
>
> I randomly chose one vertex and put debug code into the
> Monge_via_jet_fitting.h header to output the list of vertices  
> considered.
> These are drawn as blue '*' symbols around the vertex. This looks  
> all ok.
>
> Next, I examined the ouput of the monge fit for the chosen vertex.  
> The results
> are the colored arrows which originate in the chosen vertex.
>
> - the green arrow represents the TRUE normal of the plane as  
> constructed
> - the deep red arrow is the estimated normal using the vertex plus the
>   surrounding blue '*' points with the complete CGAL jet-fitting  
> method
> - the pink arrows are the maximal and minimal principal direction  
> as given
>   by the monge fit procedure. You can see that they are off.
> - the orange arrows look very much ok, and the orange normal is  
> completely
>   correct (the sign doesn't matter of course):
>   These are just the eigenvectors obtained from the PCA analysis in  
> the
>   code, the polynomial fitting results are _not_ considered
>
> How can it be that I arrived at this result? At the moment I am  
> suspecting a
> bug in CGAL, but of course I cannot exclude a bug or thinking error  
> on my
> part; are there any requirements I might have disregarded? Any  
> definitions of
> angles etc. I might have used in the wrong way?
>
> I'll be happy to send code along and try to reduce it to a more  
> minimal
> testcase if necessary; at the moment I pass data for visualization  
> purposes to
> Matlab, so the code is run as a Matlab Mex file, therefor it's a  
> bit "messy"
> to debug for anyone not using Matlab.
>
> Thanks for your time,
>
> Thorben
>
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> discuss<snapshot_plane.png><snapshot_plane_2.png>