Iterative closest point

Iterative Closest Point (ICP) is an algorithm employed to minimize the difference between two clouds of points. ICP is often used to reconstruct 2D or 3D surfaces from different scans, to localize robots and achieve optimal path planning (especially when wheel odometry is unreliable due to slippery terrain), to co-register bone models, etc.

In the Iterative Closest Point or, in some sources, the Iterative Corresponding Point, one point cloud (vertex cloud), the reference, or target, is kept fixed, while the other one, the source, is transformed to best match the reference. The algorithm iteratively revises the transformation (combination of translation and rotation) needed to minimize an error metric, usually the distance from the source to the reference point cloud. ICP is one of the widely used algorithms in aligning three dimensional models given an initial guess of the rigid body transformation required. The ICP algorithm was first introduced by Chen and Medioni, and Besl and McKay.

Inputs: reference and source point clouds, initial estimation of the transformation to align the source to the reference (optional), criteria for stopping the iterations.

Output: refined transformation.

Essentially, the algorithm steps are:

Zhang proposes a modified K-D tree algorithm for efficient closest point computation. In this work a statistical method based on the distance distribution is used to deal with outliers, occlusion, appearance, and disappearance, which enables subset-subset matching.

There exist many ICP variants, from which point-to-point and point-to-plane are the most popular. The latter usually performs better in structured environments.

...
Wikipedia