filters.cpd

The Coherent Point Drift (CPD) filter uses the algorithm of [MS10] algorithm to compute a rigid, nonrigid, or affine transformation between datasets. The rigid and affine are what you’d expect; the nonrigid transformation uses Motion Coherence Theory [YG88] to “bend” the points to find a best alignment.

Note

CPD is computationally intensive and can be slow when working with many points (i.e. > 10,000). Nonrigid is significatly slower than rigid and affine.

The first input to the change filter are considered the “fixed” points, and all subsequent inputs are “moving” points. The output from the change filter are the “moving” points after the calculated transformation has been applied, one point view per input. Any additional information about the cpd registration, e.g. the rigid transformation matrix, will be placed in the stage’s metadata.

When to use CPD vs ICP

Summarized from the Non-rigid point set registration: Coherent Point Drift paper.

  • CPD outperforms the ICP in the presence of noise and outliers by the use of a probabilistic assignment of correspondences between pointsets, which is innately more robust than the binary assignment used in ICP.
  • CPD does not work well for large in-plane rotation, such transformation can be first compensated by other well known global registration techniques before CPD algorithm is carried out
  • CPD is most effective when estimating smooth non-rigid transformations.

Dynamic Plugin

This stage requires a dynamic plugin to operate

Examples

[
    "fixed.las",
    "moving.las",
    {
        "type": "filters.cpd",
        "method": "rigid"
    },
    "output.las"
]

If method is not provided, the cpd filter will default to using the rigid registration method. To get the transform matrix, you’ll need to use the “metadata” option of the pipeline command:

$ pdal pipeline cpd-pipeline.json --metadata cpd-metadata.json

The metadata output might start something like:

{
    "stages":
    {
        "filters.cpd":
        {
            "iterations": 10,
            "method": "rigid",
            "runtime": 0.003839,
            "sigma2": 5.684342128e-16,
            "transform": "           1 -6.21722e-17  1.30104e-18  5.29303e-11-8.99346e-17            1  2.60209e-18 -3.49247e-10 -2.1684e-19  1.73472e-18            1 -1.53477e-12           0            0            0            1"
        },
    },

See also

filters.transformation to apply a transform to other points. filters.icp for deterministic binary point pair assignments.

Options

method
Change detection method to use. Valid values are “rigid”, “affine”, and “nonrigid”. [Default: “rigid”“]

[MS10]Andriy Myronenko and Xubo Song. Point set registration: coherent point drift. IEEE transactions on pattern analysis and machine intelligence, 32(12):2262–75, dec 2010.
[YG88]Alan L. Yuille and Norberto M. Grzywacz. The Motion Coherence Theory. Second International Conference on Computer Vision, 1988.