Planar rectification by solving the intersection of two circles under 2D homography

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)1117-1120
Journal / PublicationPattern Recognition
Issue number7
Publication statusPublished - Jul 2005


In this paper, we show that planar rectification can be achieved by simply solving the intersection of two circles on a plane. The resulting closed form solution gives the images of the 'circular points' on the image plane and eliminates the troublesome step of vanishing line detection that presents in many previous solutions to the planar rectification problem. Specifically, we formulate the problem as solving a set of quadratic equations with two variables and propose an efficient algorithm to convert them into a standard real coefficient quartic equation for which a closed form solution is obtained. The experimental results confirm the advantages of the method. © 2005 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.

Research Area(s)

  • Absolute conic, Circular points, Planar homography, Polynomial equations