Scaling, scaling factor

[akselsv]

Hi,

I have two point clouds of two objects with the same geometry but different in scale. The two point coulds have different orientation and position. The geometry is complex.
I would like to rescale one of the pointclouds so that it fits the other with a minimum error ( maybe using the least square error somehow?).
The scale factor is of interest for me.


Does anybody know a way of doing this in cloudcompare?

Thanks

[daniel]

You can either use the 'point-pair based alignment tool' (http://www.cloudcompare.org/doc/wiki/in ... itle=Align) or the 'Fine registration (ICP)' tool (http://www.cloudcompare.org/doc/wiki/in ... ?title=ICP). In the second case you'll have to roughly register the two clouds first (with the Graphical Transformation tool for instance) and maybe apply a rough scaling also if the scales are very different (with Edit > Multiply/scale).

In both tools you have a 'adjust scale' option that will optimize the scale. And in both cases CC will display the applied scale in a small report dialog as well as in the console (when you click on OK).

[akselsv]

Thanks Daniel. Worked like a charm!

I'm very interested in the math behind the 'fine registration tool', both for the alignment and scaling. Do you have any idea to where I might look? :)

Thanks
Aksel

[daniel]

The basis is always Horn's method for registering a set of point pairs:
http://people.csail.mit.edu/bkph/papers ... tation.pdf

In the 'Align' tool, as the user defines the pairs it's quite easy and it can be done in one step. With the ICP registration method one has to guess the pairs automatically (in effect we simply use the closest points) and the process is repeated until the clouds don't move anymore. Here is the article of Besl (ICP): http://www.cs.virginia.edu/~mjh7v/bib/Besl92.pdf

For the scaling, we use the modification of Horn's step proposed by Zinsser et. al in "Point Set Registration with Integrated Scale Estimation":
http://www5.informatik.uni-erlangen.de/ ... 05-PSR.pdf

[akselsv]

Thank you for the very quick response, Daniel. Very usefull!