Principal Component Analysis in CGAL

Abstract : Principal component analysis is a basic component of many geometric computing and processing algorithms. It is most commonly used on point sets, although applicable as well to sets of arbitrary primitives through the computation of covariance matrices. In this paper we provide closed form formulas of covariance matrices for sets of 2D and 3D geometric primitives such as segments, circles, triangles, iso rectangles, spheres, tetrahedra and iso cuboids. We also describe the method of deriving covariance matrices for their dimensional variants such as disks, balls etc. We finally discuss the flexibility and added value of the present approach by discussing its potential use in applications. Our implementation will be available through the next release of the CGAL library.
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https://hal.inria.fr/inria-00327027
Contributor : Pierre Alliez <>
Submitted on : Tuesday, October 7, 2008 - 10:24:53 AM
Last modification on : Saturday, July 21, 2018 - 2:12:01 PM
Long-term archiving on : Friday, June 4, 2010 - 12:16:58 PM

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Ankit Gupta, Pierre Alliez, Sylvain Pion. Principal Component Analysis in CGAL. [Research Report] RR-6642, INRIA. 2008, pp.13. ⟨inria-00327027⟩

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