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There exists a set of points in a 3D euklidean space. A camera views that point set and that camera is aligned with the world coordinate system.

The center of gravity of the point cloud is in the origin of the world coordinate system, however the point cloud is not aligned properly, so the camera views the point cloud (displayed as 3D model) at an angle that needs to be corrected.

To do so a 3D rotation needs to be applied to the point cloud. How well the point cloud is aligned with the world coordinate system (and therefore the camera) is defined via a loss function that is not relevant here. It analyzes certain qualities of the point cloud, then determines some quality index value for the current alignment, meaning any transformation of the point cloud is associated with some qualitative measurement.

Now I want to sample rotational transformations to determine a good (the best?) candidate, i.e. a rotation of the point cloud which delivers the smallest loss function value. Can this be achieved using particle filters? In my case there is no time component, what I mainly want is to do a basic sampling, recognize good transformation candidates, then resample so that transformations close to the good candidates are preferred, then resample again and so on. So I am asking myself if I could use Sequential Monte Carlo (SMC) to obtain the transformations I am looking for.

Thoughts?

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