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 significantly 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"
        },
    },

Options

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

where: An expression that limits points passed to a filter. Points that don’t pass the expression skip the stage but are available to subsequent stages in a pipeline. [Default: no filtering]
where_merge: A strategy for merging points skipped by a ‘where’ option when running in standard mode. If true, the skipped points are added to the first point view returned by the skipped filter. If false, skipped points are placed in their own point view. If auto, skipped points are merged into the returned point view provided that only one point view is returned and it has the same point count as it did when the filter was run. [Default: auto]

[GM19]

D. Gatziolis and R. J. McGaughey. Reconstructing aircraft trajectories from multi-return airborne laser-scanning data. Remote Sensing, 2019.

[LLW+19]

Xuechen Li, Yinlong Liu, Yiru Wang, Chen Wang, Manning Wang, and Zhijian Song. Fast and Globally Optimal Rigid Registration of 3D Point Sets by Transformation Decomposition. unknown, 2019. Available at https://arxiv.org/pdf/1812.11307.pdf.

[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.