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.
Overview.
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 a distance from the source to the reference point cloud, such as the sum of squared differences between the coordinates of the matched pairs. ICP is one of the widely used algorithms in aligning three dimensional models given an initial guess of the rigid transformation required.
The ICP algorithm was first introduced by Chen and Medioni, and Besl and McKay.
The Iterative Closest Point algorithm contrasts with the Kabsch algorithm and other solutions to the orthogonal Procrustes problem in that the Kabsch algorithm requires correspondence between point sets as an input, whereas Iterative Closest Point treats correspondence as a variable to be estimated.
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.