C2C Distance - Histogramm

[ClaudiaS]

Hi all,
I want to compare a sparse pointcloud (it also contains some holes) with a dense one. I used height funkction (kNN=6) to get "best" results....mean of result is fine, but how to understand peaks of histogramm next to the legend of scalar field? If I adjust higher value for Points(kNN), results will get worser. Which value should you recommend? Is it better to use a value for radius?
Screenshot is attached
Regards,
Claudia

[daniel]

In fact using a fixed number of points only works for cloud with a constant density. Moreover 6 seems very low (this is the theoretical minimum).

You should use a radius-based neighborhood. And for the choice of the local modelization to use, it's not always evident. Triangular meshes are best suited for very clean clouds with sharp edges. Height function is best for smooth/curvy shapes. But both are very sensitive to noise. The least square plane is more robust but also less accurate (it mainly works for planar shapes).

Anyway, even in the best case, there will always be some "wrong" distances locally. The local modeling scheme provides more robust results only in a global point of view.

[ClaudiaS]

Thanks for your answer.
So I ill use radius-based neighbourhood. For this I´ve got some other questions...
What about the initial value of the radius, is it also a theoretical minimum? Probably, I have no idea about the mathemetical backround...is it better to use a higher value than the initial one? How will it affects the computation?

Regards

[daniel]

The initial value is just a random guess (a percentage of the cloud bounding-box) that should work in most cases however. But it must be fine tuned based on the cloud density and shape (especially if it is very much extended in a particular direction, etc.):

• With the best fitting plane, the radius size has a very important influence: the bigger it is the more points will be 'averaged'. It works like a low-pass filter in signal processing. The bigger it is the less influence will have the local surface roughness on the plane position and orientation (so it's very good to remove the noise).
• For the 2D1/2 triangulation the radius has much less influence (especially if the two clouds you compare are already quite close to each other). But the bigger it is the longer it will take to compute. This model is clearly sensible to noise. However it's the only one that can represent shapes with sharp edges.
• Eventually the height function is in-between. It's main interest is to smooth the local roughness while keeping a good attach to the local curvature.

In every case the first requirement is too catch around each point enough neighbors to compute a local model (I would say at least 6 for the plane, and 12 for the others). So the lower limit mainly depends on the cloud density. And for the upper limit, it's mainly a matter of how much you want to take the local roughness (or noise!) into account.