filters.icp

The ICP filter uses the Iterative Closest Point (ICP) algorithm to calculate a rigid (rotation and translation) transformation that best aligns two datasets. The first input to the ICP filter is considered the “fixed” points, and all subsequent points are “moving” points. The output from the filter are the “moving” points after the calculated transformation has been applied, one point view per input. The transformation matrix is inserted into the stage’s metadata.

Note

ICP requires the initial pose of the two point sets to be adequately close, which is not always possible, especially when the transformation is non-rigid. ICP can handle limited non-rigid transformations but be aware ICP may be unable to escape a local minimum. Consider using CPD instead.

From [LLW+19]:

ICP starts with an initial guess of the transformation between the two point sets and then iterates between finding the correspondence under the current transformation and updating the transformation with the newly found correspondence. ICP is widely used because it is rather straightforward and easy to implement in practice; however, its biggest problem is that it does not guarantee finding the globally optimal transformation. In fact, ICP converges within a very small basin in the parameter space, and it easily becomes trapped in local minima. Therefore, the results of ICP are very sensitive to the initialization, especially when high levels of noise and large proportions of outliers exist.

Examples

[
    "fixed.las",
    "moving.las",
    {
        "type": "filters.icp"
    },
    "output.las"
]

To get the transform matrix, you’ll need to use the --metadata option from the pipeline command:

$ pdal pipeline icp-pipeline.json --metadata icp-metadata.json

The metadata output might start something like:

{
    "stages":
    {
        "filters.icp":
        {
            "centroid": "    583394  5.2831e+06   498.152",
            "composed": "           1  2.60209e-18 -1.97906e-09       -0.374999  8.9407e-08            1  5.58794e-09      -0.614662 6.98492e-10 -5.58794e-09            1   0.033234           0            0            0            1",
            "converged": true,
            "fitness": 0.01953125097,
            "transform": "           1  2.60209e-18 -1.97906e-09       -0.375  8.9407e-08            1  5.58794e-09      -0.5625 6.98492e-10 -5.58794e-09            1   0.00411987           0            0            0            1"
        }

To apply this transformation to other points, the centroid and transform metadata items can by used with filters.transformation in another pipeline. First, move the centroid of the points to (0,0,0), then apply the transform, then move the points back to the original location. For the above metadata, the pipeline would be similar to:

[
    {
        "type": "readers.las",
        "filename": "in.las"
    },
    {
        "type": "filters.transformation",
        "matrix": "1 0 0 -583394   0 1 0 -5.2831e+06   0 0 1 -498.152   0 0 0 1"
    },
    {
        "type": "filters.transformation",
        "matrix": "1  2.60209e-18 -1.97906e-09       -0.375  8.9407e-08            1  5.58794e-09      -0.5625 6.98492e-10 -5.58794e-09            1   0.00411987           0            0            0            1"
    },
    {
        "type": "filters.transformation",
        "matrix": "1 0 0 583394   0 1 0 5.2831e+06  0 0 1 498.152  0 0 0 1"
    },
    {
        "type": "writers.las",
        "filename": "out.las"
    }
]

Note

The composed metadata matrix is a composition of the three transformation steps outlined above, and can be used in a single call to filters.transformation as opposed to the three separate calls.

Options

max_iter: Maximum number of iterations. [Default: 100]
max_similar: Max number of similar transforms to consider converged. [Default: 0]
mse_abs: Absolute threshold for MSE. [Default: 1e-12]
rt: Rotation threshold. [Default: 0.99999]
tt: Translation threshold. [Default: 9e-8]

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]