Abstract
Discovering and extracting new image features pertaining to scene geometry is important to 3D reconstruction and scene understanding. Examples include the classical vanishing points observed in a centric camera and the recent coplanar common points (CCPs) in a crossed-slit camera [21,17]. A CCP is a point in the image plane corresponding to the intersection of the projections of all lines lying on a common 3D plane. In this paper, we address the problem of determining CCP existence in general non-centric cameras. We first conduct a ray-space analysis to show that finding the CCP of a 3D plane is equivalent to solving an array of ray constraint equations. We then derive the necessary and sufficient conditions for CCP to exist in an arbitrary non-centric camera such as non-centric catadioptric mirrors. Finally, we present robust algorithms for extracting the CCPs from a single image and validate our theories and algorithms through experiments.
Chapter PDF
References
Baker, S., Nayar, S.K.: A theory of single-viewpoint catadioptric image formation. IJCV 35(2) (1999)
Caglioti, V., Gasparini, S.: “How many planar viewing surfaces are there in noncentral catadioptric cameras?” towards singe-image localization of space lines. In: 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 1, pp. 1266–1273 (June 2006)
Delage, E., Lee, H., Ng, A.Y.: Automatic single-image 3D reconstructions of indoor manhattan world scenes. In: ISRR (2005)
Gupta, R., Hartley, R.I.: Linear pushbroom cameras. IEEE TPAMI, 963–975 (1997)
Hoiem, D., Efros, A.A., Hebert, M.: Geometric context from a single image. In: ICCV (2005)
Hoiem, D., Efros, A.A., Hebert, M.: Automatic photo pop-up. In: ACM SIGGRAPH (2005)
Levoy, M., Hanrahan, P.: Light field rendering. In: ACM SIGGRAPH, pp. 31–42 (1996)
Meingast, M., Geyer, C., Sastry, S.: Geometric models of rolling-shutter cameras. CoRR (2005)
Pajdla, T.: Stereo with oblique cameras. In: IEEE Workshop on Stereo and Multi-Baseline Vision, pp. 85–91 (2001)
Pajdla, T.: Geometry of two-slit camera. Rapport Technique CTU-CMP-2002-02, Center for Machine Perception, Czech Technical University, Prague (2002)
Ponce, J.: What is a camera? In: The IEEE Conference on Computer Vision and Pattern Recognition (2009)
Shum, H.Y., He, L.W.: Rendering with concentric mosaics. In: Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, pp. 299–306. ACM Press/Addison-Wesley Publishing Co. (1999)
Sturm, P., Ramalingam, S., Tardif, J.P., Gasparini, S., Barreto, J.: Camera models and fundamental concepts used in geometric computer vision. Foundations and Trends in Computer Graphics and Vision 6(1-2), 1–183 (2011)
Swaminathan, R., Grossberg, M., Nayar, S.: Caustics of Catadioptric Cameras. In: IEEE International Conference on Computer Vision (ICCV), vol. 2, pp. 2–9 (July 2001)
Swaminathan, R., Grossberg, M.D., Nayar, S.K.: Non-single viewpoint catadioptric cameras: Geometry and analysis. Int. J. Comput. Vision 66(3), 211–229 (2006)
Tom, H.B.: Rendering novel views from a set of omnidirectional mosaic images. In: Proceedings of Omnivis 2003: Workshop on Omnidirectional Vision and Camera Networks. IEEE Press (2003)
Ye, J., Ji, Y., Yu, J.: Manhattan scene understanding via xslit imaging. In: CVPR (June 2013)
Yu, J., McMillan, L.: Modelling reflections via multiperspective imaging. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005, vol. 1, pp. 117–124 (June 2005)
Yu, J., McMillan, L.: General linear cameras. In: Pajdla, T., Matas, J. (eds.) ECCV 2004. LNCS, vol. 3022, pp. 14–27. Springer, Heidelberg (2004)
Yu, J., McMillan, L., Sturm, P.: Multiperspective modeling, rendering, and imaging. In: ACM SIGGRAPH ASIA 2008 Courses, pp. 14:1–14:36 (2008)
Zomet, A., Feldman, D., Peleg, S., Weinshall, D.: Mosaicing new views: the crossed-slits projection. IEEE TPAMI 25(6), 741–754 (2003)
Zomet, A., Feldman, D., Peleg, S., Weinshall, D.: Non-perspective imaging and rendering with the crossed-slits projection. Tech. rep., Leibnitz Center, Hebrew University of Jerusalem (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
1 Electronic Supplementary Material
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Yang, W., Ji, Y., Ye, J., Young, S.S., Yu, J. (2014). Coplanar Common Points in Non-centric Cameras. In: Fleet, D., Pajdla, T., Schiele, B., Tuytelaars, T. (eds) Computer Vision – ECCV 2014. ECCV 2014. Lecture Notes in Computer Science, vol 8689. Springer, Cham. https://doi.org/10.1007/978-3-319-10590-1_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-10590-1_15
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-10589-5
Online ISBN: 978-3-319-10590-1
eBook Packages: Computer ScienceComputer Science (R0)