Iterative closest point

Iterative Closest Point (ICP) [1][2][3] 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 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.[4] The ICP algorithm was first introduced by Chen and Medioni,[2] and Besl and McKay.[1]

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:[4]

  1. 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).
  2. 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 after weighting and rejecting outlier points.
  3. Transform the source points using the obtained transformation.
  4. Iterate (re-associate the points, and so on).

Zhang [3] 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,[5] from which point-to-point and point-to-plane are the most popular. The latter usually performs better in structured environments.[6][7]

Implementations

See also

References

  1. 1 2 Besl, Paul J.; N.D. McKay (1992). "A Method for Registration of 3-D Shapes". IEEE Trans. on Pattern Analysis and Machine Intelligence. Los Alamitos, CA, USA: IEEE Computer Society. 14 (2): 239–256. doi:10.1109/34.121791.
  2. 1 2 Chen, Yang; Gerard Medioni (1991). "Object modelling by registration of multiple range images". Image Vision Comput. Newton, MA, USA: Butterworth-Heinemann: 145–155. doi:10.1016/0262-8856(92)90066-C.
  3. 1 2 Zhang, Zhengyou (1994). "Iterative point matching for registration of free-form curves and surfaces". International Journal of Computer Vision. Springer. 13 (12): 119–152. doi:10.1007/BF01427149.
  4. 1 2 Rusinkiewicz, Szymon; Marc Levoy (2001). Efficient Variants of the ICP Algorithm. Proceedings Third International Conference on 3-D Digital Imaging and Modeling. Quebec City, Quebec, Canada. pp. 145–152. doi:10.1109/IM.2001.924423.
  5. ↑ Pomerleau, François; Colas, Francis; Siegwart, Roland (2015). "A Review of Point Cloud Registration Algorithms for Mobile Robotics". Foundations and Trends in Robotics. 4 (1): 1–104. doi:10.1561/2300000035.
  6. ↑ Kok-Lim Low (February 2004). "Linear Least-Squares Optimization for Point-to-Plane ICP Surface Registration" (PDF). Comp.nys.edu.sg. Technical Report TR04-004, Department of Computer Science, University of North Carolina at Chapel Hill. Retrieved 2017-02-27.
  7. ↑ François Pomerleau, Francis Colas, Roland Siegwart, and Stéphane Magnenat. Comparing ICP Variants on Real-World Data Sets. In Autonomous Robots, 34(3), pages 133–148, DOI: 10.1007/s10514-013-9327-2, April 2013.
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