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Concept
Iterative closest point
Summary
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.
The Iterative Closest Point algorithm keeps one point cloud, the reference or target, fixed, while transforming the other, the source, to best match the reference. The transformation (combination of translation and rotation) is iteratively estimated in order to minimize an error metric, typically 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:
For each point (from the whole set of vertices usually referred to as dense or a selection of pairs of vertices from each model) in the source point cloud, match the closest point in the reference point cloud (or a selected set).
Estimate the combination of rotation and translation using a root mean square point to point distance metric minimization technique which will best align each source point to its match found in the previous step. This step may also involve weighting points and rejecting outliers prior to alignment.
Transform the source points using the obtained transformation.
Official source
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