10.95. Iterative Closest Point

Group (Subgroup)

Reconstruction (Alignment)

Description

This Filter estimates the rigid body transformation (i.e., rotation and translation) between two sets of points represented by Vertex Geometries using the iterative closest point (ICP) algorithm. The two Vertex Geometries are not required to have the same number of points.

The Iterative Closest Point (ICP) algorithm is a method used to minimize the difference between two clouds of points, which we can describe in terms of “moving geometry” and “target geometry.” The basic flow of the algorithm is:

  1. Initial State: We start with two sets of points or geometries. The “moving geometry” is the one we aim to align with the “target geometry.” Initially, the moving geometry may be in any orientation or position relative to the target geometry.

  2. Identify Correspondences: For each point in the moving geometry, we find the closest point in the target geometry. These pairs of points are considered correspondences, based on the assumption that they represent the same point in space after the moving geometry is properly aligned.

  3. Estimate Transformation: With the correspondences identified, the algorithm calculates the optimal rigid body transformation (which includes translation and rotation) that best aligns the moving geometry to the target geometry. This step often involves minimizing a metric, such as the sum of squared distances between corresponding points, to find the best fit.

  4. Apply Transformation: The calculated transformation is applied to the moving geometry, aligning it closer to the target geometry.

  5. Iterate: Steps 2 through 4 are repeated iteratively. With each iteration, the moving geometry is brought into closer alignment with the target geometry. The iterations continue until a stopping criterion is met, which could be a predefined number of iterations, a minimum improvement threshold between iterations, or when the change in the error metric falls below a certain threshold.

  6. Final Alignment: Once the iterations stop, the algorithm concludes with the moving geometry optimally aligned to the target geometry, based on the criteria set for minimizing the differences between them.

ICP has a number of advantages, such as robustness to noise and no requirement that the two sets of points to be the same size. However, performance may suffer if the two sets of points are of significantly different size.

Saving the Output Transformation Matrix

The filter always reports the computed rigid body transformation as an output DataArray. By default the moving geometry itself is left unchanged. If the Apply Transformation to Moving Geometry parameter is enabled, the filter also applies the transformation to the moving geometry’s vertices in place, so that it is aligned to the target geometry.

The output DataArray is a flattened array 16 elements in size that represents a 4x4 transformation matrix. The elements are encoded in ROW MAJOR order, i.e.,

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

represents the following 4x4 matrix

1   2   3   4
5   6   7   8
9   10  11  12
13  14  15  16

The upper-left 3x3 block holds the rotation, and the first three entries of the rightmost column (elements 4, 8, 12) hold the translation, expressed in the coordinate units of the input geometries.

The reported matrix can be supplied to Apply Transformation to Geometry to transform this or another geometry as a separate step.

Required Input Sources

  • Moving Vertex Geometry – the Vertex Geometry to be aligned to the target.

  • Target Vertex Geometry – the fixed reference Vertex Geometry. The two geometries need not have the same number of points.

Input Parameter(s)

Parameter Name

Parameter Type

Parameter Notes

Description

Number of Iterations

Scalar Value

UInt64

The number of times to run the algorithm [more increases accuracy]

Apply Transformation to Moving Geometry

Bool

If checked, geometry will be updated implicitly

Input Data Objects

Parameter Name

Parameter Type

Parameter Notes

Description

Moving Vertex Geometry

Geometry Selection

Vertex

The geometry to align [mutable]

Target Vertex Geometry

Geometry Selection

Vertex

The geometry to be matched against [immutable]

Output Data Object(s)

Parameter Name

Parameter Type

Parameter Notes

Description

Output Transform Array

ArrayCreation

This is the array to store the transform matrix in

Example Pipelines

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