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Research Article | Open Access

Fitting quadrics with a Bayesian prior

University of Bath, Claverton Down, Bath, BA2 7AY, UK.
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Abstract

Quadrics are a compact mathematical formulation for a range of primitive surfaces. A problem arises when there are not enough data points to compute the model but knowledge of the shape is available. This paper presents a method for fitting a quadric with a Bayesian prior. We use a matrix normal prior in order to favour ellipsoids when fitting to ambiguous data. The results show the algorithm copes well when there are few points in the point cloud, competing with contemporary techniques in the area.

Keywords

geometrystatisticsgraphicscomputer vision

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Computational Visual Media
Volume 2 Issue 2,
June 2016
Pages 107-117
DOI: 10.1007/s41095-016-0041-9
Cite this article:
Beale D, Yang Y-L, Campbell N, et al. Fitting quadrics with a Bayesian prior. Computational Visual Media, 2016, 2(2): 107-117. https://doi.org/10.1007/s41095-016-0041-9
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10.1007/s41095-016-0041-9.T1Relationship between eigenvalues and shape of the corresponding quadric

ShapePositiveZeroNegative
Ellipsoid300
Cylinder210
Paraboloid210
Plane000
Hyperboloid201
Hyperbolic section111