Rapid and brief communication: Planar rectification by solving the intersection of two circles under 2D homography

Authors:
Horace H. S. Ip;Yisong Chen
Affiliations:
Image Computing Group, Department of Computer Science, AIMtech Center, City University of Hong Kong, Kowloon, Hong Kong;Image Computing Group, Department of Computer Science, AIMtech Center, City University of Hong Kong, Kowloon, Hong Kong
Venue:
Pattern Recognition
Year:
2005

Citing 3
Cited 2

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Abstract

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.