Advances in Applied Clifford Algebras

, Volume 27, Issue 3, pp 1961–1976 | Cite as

Object Detection in Point Clouds Using Conformal Geometric Algebra

  • Aksel SveierEmail author
  • Adam Leon Kleppe
  • Lars Tingelstad
  • Olav Egeland
Open Access


This paper presents an approach for detecting primitive geometric objects in point clouds captured from 3D cameras. Primitive objects are objects that are well defined with parameters and mathematical relations, such as lines, spheres and ellipsoids. RANSAC, a robust parameter estimator that classifies and neglects outliers, is used for object detection. The primitives considered are modeled, filtered and fitted using the conformal model of geometric algebra. Methods for detecting planes, spheres and cylinders are suggested. Least squares fitting of spheres and planes to point data are done analytically with conformal geometric algebra, while a cylinder is fitted by defining a nonlinear cost function which is optimized using a nonlinear least squares solver. Furthermore, the suggested object detection scheme is combined with an octree sampling strategy that results in fast detection of multiple primitive objects in point clouds.


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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Mechanical and Industrial Engineering, Faculty of EngineeringNTNU, Norwegian University of Science and TechnologyTrondheimNorway

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