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Forward projection model of non-central catadioptric cameras with spherical mirrors

Published online by Cambridge University Press:  05 April 2016

Nuno Goncalves Open the ORCID record for Nuno Goncalves [Opens in a new window] ,
Ana Catarina Nogueira  and
Andre Lages Miguel
Nuno Goncalves*
Affiliation:
Institute of Systems and Robotics, University of Coimbra Polo 2, Pinhal de Marrocos, 3030-290 Coimbra, Portugal. E-mails: anacatnog@isr.uc.pt, andrelages@isr.uc.pt
Ana Catarina Nogueira
Affiliation:
Institute of Systems and Robotics, University of Coimbra Polo 2, Pinhal de Marrocos, 3030-290 Coimbra, Portugal. E-mails: anacatnog@isr.uc.pt, andrelages@isr.uc.pt
Andre Lages Miguel
Affiliation:
Institute of Systems and Robotics, University of Coimbra Polo 2, Pinhal de Marrocos, 3030-290 Coimbra, Portugal. E-mails: anacatnog@isr.uc.pt, andrelages@isr.uc.pt
*
*Corresponding author. E-mail: nunogon@isr.uc.pt
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Summary

Non-central catadioptric vision is widely used in robotics and vision but suffers from the lack of an explicit closed-form forward projection model (FPM) that relates a 3D point with its 2D image. The search for the reflection point where the scene ray is projected is extremely slow and unpractical for real-time applications. Almost all methods thus rely on the assumption of a central projection model, even at the cost of an exact projection.

Two recent methods are able to solve this FPM, presenting a quasi-closed form FPM. However, in the special case of spherical mirrors, further enhancements can be made. We compare these two methods for the computation of the FPM and discuss both approaches in terms of practicality and performance. We also derive new expressions for the FPM on spherical mirrors (extremely useful to robotics and graphics) which speed up its computation.

Keywords

non central catadioptric camerasforward projection modelquadric mirrorsreflection point
Type
Articles
Information
Robotica , Volume 35 , Issue 6 , June 2017 , pp. 1378 - 1396
Copyright
Copyright © Cambridge University Press 2016 

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