Surface Normals Approximation Not Consistent as PCL approach.

[dagata-mining]

Hi,

I've been playing a long time with Libpointmatcher, one thing we recently found out when running tests and different implementations with point cloud, is that the current PCA approach for normal calculation is not as robust and as precise as the pcl::computePointNormal() normal_3d.h approach. Something to do with the solver maybe when creating the eigen matrix from covariance matrix. I think having better normals would definetly help the ICP-Plane precision and this would be a good improvement

Here's the typical use case when we benched mark the normals approaches.

Create a point cloud from a cylinder (~5m diameter, +/- 1cm resolution), apply a gaussian error of +/- 2.0cm (usual blurr for lidars typically used in robotic). From the x-y value of the points you can easily extrapolate the theorical normal of that point with basic math geomtery.

Now calculate both the normals using your surface normals calculation approach and the one from pcl (using the same knn and radius of course). You'll see that the error between the pcl approach is less than the one with your appoach. While this might not have a huge impact, it is still intersting to consider to improve libpoint matcher performance.

[boxanm]

Hey @dagata-mining! This is indeed an interesting observation! Do you have any example code that we could reuse for comparing the two libraries?