Skip to main content
SpringerLink
Log in

Line Localization from Single Catadioptric Images

  • Published:
International Journal of Computer Vision Aims and scope Submit manuscript

Abstract

Indoor environments often contain several line segments. The 3D reconstruction of such environments can thus be reduced to the localization of lines in the 3D space. Multi-view reconstruction requires the solution of the correspondence problem. The use of a single image to localize space lines is attractive, since the correspondence problem can be avoided. However, using a central camera the line localization from single image is an ill-posed problem, because there are infinitely many lines sharing the same image.

In this work we relaxed the constraint on single viewpoint imaging and considered a wide class of non-central catadioptric cameras, constituted by an axial symmetric mirror and a perspective camera placed at a generic relative position. In the paper we report the results of our study on line localization for such cameras, reporting the conditions that allow a line to be localized from a single image. We show how the analysis can be extended to other classes of non-central devices sharing a similar imaging model. We also present a brief overview of the main algorithms for line localization from single image that have been proposed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Avidan, S., & Shashua, A. (2000). Trajectory triangulation: 3D reconstruction of moving points from a monocular image sequence. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(4), 348–357.

    Article  Google Scholar 

  • Baker, S., & Nayar, S. K. (1999). A theory of single-viewpoint catadioptric image formation. International Journal of Computer Vision, 35(2), 175–196.

    Article  Google Scholar 

  • Bakstein, H., & Pajdla, T. (2001). An overview of non-central cameras. In Computer vision winter workshop.

    Google Scholar 

  • Barreto, J., & Araujo, H. (2003). Paracatadioptric camera calibration using lines. In Proceedings of the IEEE international conference on computer vision, ICCV ’03 (Vol. 2, pp. 1359–1365), Los Alamitos, CA, USA, 13–16 Oct. 2003. Los Alamitos: IEEE Comput. Soc.

    Chapter  Google Scholar 

  • Bogner, S. L. (1995). An introduction to panospheric imaging. In Proceedings of IEEE international conference on systems, man and cybernetics intelligent systems for the 21st century (Vol. 4, pp. 3099–3106), 22–25 Oct. 1995.

    Chapter  Google Scholar 

  • Brewster, D. S. (1838). A treatise on optics. London: Longman, Rees, Orme, Brown and Green.

    Google Scholar 

  • Bronnimann, H., Everett, H., Lazard, S., Sottile, F., & Whitesides, S. (2005). Transversals to line segments in three-dimensional space. Discrete Compututational Geometry, 34(3), 381–390.

    Article  MathSciNet  Google Scholar 

  • Caglioti, V., & Gasparini, S. (2005). Localization of 3D lines from single images using off-axis catadioptric cameras. In Proceedings of the 6th workshop on omnidirectional vision, OMNIVIS 2005.

    Google Scholar 

  • Caglioti, V., & Gasparini, S. (2005). On the localization of straight lines in 3D space from single 2D images. In Proceedings of the IEEE international conference on computer vision and pattern recognition, CVPR ’05 (Vol. 1, pp. 1129–1134), Los Alamitos, CA, USA, 20–25 June 2005. Los Alamitos: IEEE Comput. Soc.

    Google Scholar 

  • Caglioti, V., & Gasparini, S. (2006). How many planar viewing surfaces are there in noncentral catadioptric cameras? Towards singe-image localization of space lines. In Proceedings of the IEEE international conference on computer vision and pattern recognition, CVPR ’06 (Vol. 1, pp. 1266–1273), Los Alamitos, CA, USA, 17–22 June 2006. Los Alamitos: IEEE Comput. Soc.

    Google Scholar 

  • Caglioti, V., Gasparini, S., & Taddei, P. (2007). Methods for space line localization from single catadioptric images: new proposals and comparisons. In Proceedings of the 7th workshop on omnidirectional vision, OMNIVIS 2007.

    Google Scholar 

  • Caglioti, V., Taddei, P., Boracchi, G., Gasparini, S., & Giusti, A. (2007). Single-image calibration of off-axis catadioptric cameras using lines. In Proceedings of the 7th workshop on omnidirectional vision, OMNIVIS 2007.

    Google Scholar 

  • Cauchois, C., Brassart, E., Drocourt, C., & Vasseur, P. (1999). Calibration of the omnidirectional vision sensor: SYCLOP. In Proceedings of the IEEE international conference on robotics and automation (Vol. 2, pp. 1287–1292), Los Alamitos, CA, USA, 10–15 May 1999. Los Alamitos: IEEE Comput. Soc.

    Google Scholar 

  • Chahl, J. S., & Srinivasan, M. V. (1997). Reflective surfaces for panoramic imaging. Applied Optics, 36(31), 8275–8285.

    Article  Google Scholar 

  • Croteau, A., Pelletier, J.-G., & Dubuc, Y. (2000). Panocam a digital high-resolution panoramic camera for underground installations survey. In Proceedings of the IEEE 9th international conference on transmission and distribution construction, operation and live-line maintenance (pp. 83–86), 8–12 Oct. 2000.

    Google Scholar 

  • Feldman, D., Pajdla, T., & Weinshall, D. (2003). On the epipolar geometry of the crossed-slits projection. In Proceedings of the IEEE international conference on computer vision, ICCV ’03 (Vol. 2, pp. 988–995), Washington, DC, USA, Oct. 2003. Los Alamitos: IEEE Comput. Soc.

    Chapter  Google Scholar 

  • Fermuller, C., Aloimonos, Y., Baker, P., Pless, R., Neumann, J., & Stuart, B. (2000). Multi-camera networks: eyes from eyes. In Proceedings of the 1st workshop on omnidirectional vision, OMNIVIS 2000 (pp. 11–18), 12 June 2000.

    Chapter  Google Scholar 

  • Firoozfam, P., & Negahdaripour, S. (2002). Multi-camera conical imaging; calibration and robust 3D motion estimation for ROV based mapping and positioning. In Proceedings of OCEANS MTS/IEEE conference and exhibition (Vol. 3, pp. 1595–1602), 29–31 Oct. 2002.

    Google Scholar 

  • Fischler, M. A., & Bolles, R. C. (1981). Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM, 24(6), 381–395.

    Article  MathSciNet  Google Scholar 

  • Fitzgibbon, A., Pilu, M., & Fisher, R. B. (1999). Direct least square fitting of ellipses. IEEE Transactions on Pattern Analysis and Machine Intelligence, 21(5), 476–480.

    Article  Google Scholar 

  • Furukawa, Y., Curless, B., Seitz, S., & Szeliski, R. (2009). Manhattan-world stereo. In Proceedings of the IEEE international conference on computer vision and pattern recognition, CVPR ’09 (pp. 1422–1429), Los Alamitos, CA, USA, June 2009. Los Alamitos: IEEE Comput. Soc.

    Google Scholar 

  • Gasparini, S. (2007). 3D Reconstruction from single catadioptric images. PhD thesis, Politecnico di Milano.

  • Gasparini, S., & Sturm, P. (2009). Advances in pattern recognition (APR). Multi-view matching tensors from lines for general camera models (pp. 198–214). Berlin: Springer.

    Google Scholar 

  • Geyer, C., & Daniilidis, K. (2002). Paracatadioptric camera calibration. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(5), 687–695.

    Article  Google Scholar 

  • Gregory, R. (1966). Eye and brain: the psychology of seeing (1st ed.). London: Weidenfeld and Nicolson.

    Google Scholar 

  • Grossberg, M., & Nayar, S. (2001). A general imaging model and a method for finding its parameters. In Proceedings of the IEEE international conference on computer vision, ICCV ’01 (pp. 108–115), Los Alamitos, CA, USA, 2001. Los Alamitos: IEEE Comput. Soc.

    Chapter  Google Scholar 

  • Hartley, R. I., & Zisserman, A. (2004). Multiple view geometry in computer vision (2nd ed.). Cambridge: Cambridge University Press.

    MATH  Google Scholar 

  • Hassner, T., & Basri, R. (2006). Example based 3d reconstruction from single 2d images. In Proceedings of the 2006 conference on computer vision and pattern recognition workshop, CVPRW06 (p. 15), June 2006. Los Alamitos: IEEE Comput. Soc.

    Chapter  Google Scholar 

  • Hicks, R., & Bajcsy, R. (2000). Catadioptric sensors that approximate wide-angle perspective projections. In Proceedings of the IEEE international conference on computer vision and pattern recognition, CVPR ’00 (Vol. 1, pp. 545–551), Los Alamitos CA, USA, 13–15 June 2000. Los Alamitos: IEEE Comput. Soc.

    Chapter  Google Scholar 

  • Hicks, R. A., & Bajcsy, R. (2001). Reflective surfaces as computational sensors. Image and Vision Computing, 19(11), 773–777.

    Article  Google Scholar 

  • Hilbert, D., & Cohn-Vossen, S. (1932). Geometry and the imagination. New York: Chelsea.

    Google Scholar 

  • Hong, J., Tan, X., Pinette, B., Weiss, R., & Riseman, E. (1991). Image-based homing. In Proceedings of the IEEE international conference on robotics and automation (pp. 620–625), Los Alamitos, CA, USA, 9–11 April 1991. Los Alamitos: IEEE Comput. Soc.

    Chapter  Google Scholar 

  • Ishiguro, H., Yamamoto, M., & Tsuji, S. (1992). Omni-directional stereo. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(2), 257–262.

    Article  Google Scholar 

  • Kanbara, M., Ukita, N., Kidode, M., & Yokoya, N. (2006). 3d scene reconstruction from reflection images in a spherical mirror. In Proceedings of the international conference on pattern recognition, ICPR ’06 (Vol. 4, pp. 874–879), 20–24 Aug. 2006.

    Google Scholar 

  • Lanman, D., Wachs, M., Taubin, G., & Cukierman, F. (2006). Reconstructing a 3d line from a single catadioptric image. In Proceedings of the international symposium on 3D data processing, visualization and transmission (pp. 89–96).

    Chapter  Google Scholar 

  • Marchese, F. M., & Sorrenti, D. G. (2001). Omni-directional vision with a multi-part mirror. In Lecture notes computer science. RoboCup 2000: robot soccer world cup IV (pp. 179–188), London, UK, 2001. London: Springer.

    Chapter  Google Scholar 

  • Micusik, B., & Pajdla, T. (2004). Autocalibration & 3D reconstruction with non-central catadioptric cameras. In Proceedings of the IEEE international conference on computer vision and pattern recognition, CVPR ’04 (Vol. 1, pp. 58–65), Los Alamitos, CA, USA, 27–2 July 2004. Los Alamitos: IEEE Comput. Soc.

    Chapter  Google Scholar 

  • Pajdla, T. (2002). Stereo with oblique cameras. International Journal of Computer Vision, 47(1–3), 161–170.

    Article  MATH  Google Scholar 

  • Peleg, S., & Ben-Ezra, M. (1999). Stereo panorama with a single camera. In Proceedings of the IEEE international conference on computer vision and pattern recognition, CVPR ’99 (Vol. 1), Los Alamitos, CA, USA, 23–25 June 1999. Los Alamitos: IEEE Comput. Soc.

    Google Scholar 

  • Pless, R. (2003). Using many cameras as one. In Proceedings of the IEEE international conference on computer vision and pattern recognition, CVPR’03 (Vol. 2, pp. 587–93), 18–20 June, 2003.

    Google Scholar 

  • Ponce, J. (2009). What is a camera? In Proceedings of the IEEE international conference on computer vision and pattern recognition (pp. 1526–1533).

    Google Scholar 

  • Rees, D. (1970). Panoramic television viewing system. United States Patent n. 3505465.

  • Semple, J. G., & Kneebone, G. T. (1998). Oxford Classic Texts. Algebraic projective geometry.

    MATH  Google Scholar 

  • Shum, H.-Y., Kalai, A., & Seitz, S. (1999). Omnivergent stereo. In Proceedings of the IEEE international conference on computer vision, ICCV ’99 (Vol. 1, pp. 22–29), Los Alamitos, CA, USA, 20–27 Sept. 1999. Los Alamitos: IEEE Comput. Soc.

    Google Scholar 

  • Sturm, P. (2000). A method for 3D reconstruction of piecewise planar objects from single panoramic images. In Proceedings of the 1st workshop on omnidirectional vision, OMNIVIS 2000 (pp. 119–126), Los Alamitos, CA, USA, June 2000. Los Alamitos: IEEE Comput. Soc.

    Chapter  Google Scholar 

  • Sturm, P. (2005). Multi-view geometry for general camera models. In Proceedings of the IEEE international conference on computer vision and pattern recognition, CVPR ’05 (Vol. 1, pp. 206–212), Los Alamitos, CA, USA, 20–25 June, 2005. Los Alamitos: IEEE Comput. Soc.

    Google Scholar 

  • Swaminathan, R., & Nayar, S. (2000). Nonmetric calibration of wide-angle lenses and polycameras. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(10), 1172–1178.

    Article  Google Scholar 

  • Swaminathan, R., Grossberg, M. D., & Nayar, S. K. (2006). Non-single viewpoint catadioptric cameras: geometry and analysis. International Journal of Computer Vision, 66(3), 211–229.

    Article  Google Scholar 

  • Swaminathan, R., Wu, A., & Dong, H. (2008). Depth from distortions. In Proceedings of the 8th workshop on omnidirectional vision, OMNIVIS (p. 2008).

    Google Scholar 

  • Teller, S., & Hohmeyer, M. (1999). Determining the lines through four lines. Journal of Graphics Tools, 4(3), 11–22.

    Google Scholar 

  • Thrun, S. (2002). Robotic mapping: a survey. In G. Lakemeyer & B. Nebel (Eds.), Exploring artificial intelligence in the new millenium (pp. 1–35). San Mateo: Morgan Kaufmann.

    Google Scholar 

  • Wilczkowiak, M., Boyer, E., & Sturm, P. (2001). Camera calibration and 3d reconstruction from single images using parallelepipeds. In Proceedings of the IEEE international conference on computer vision, ICCV ’01 (Vol. 1, pp. 142–148), 7–14 July, 2001.

    Chapter  Google Scholar 

  • Yagi, Y., & Kawato, S. (1990). Panorama scene analysis with conic projection. In Proceedings of the IEEE/RSJ international conference on intelligent robots and systems (pp. 181–187), Los Alamitos, CA, USA, July 1990. Los Alamitos: IEEE Comput. Soc.

    Google Scholar 

  • Yu, J., & McMillan, L. (2004). General linear cameras. In Proceedings of the European conference on computer vision, ECCV ’04 (pp. 14–27).

    Google Scholar 

  • Zheng, J. Y., & Tsuji, S. (1990). Panoramic representation of scenes for route understanding. In Proceedings of the international conference on pattern recognition, ICPR ’90 (Vol. i, pp. 161–167), 6–21 June 1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. INRIA Grenoble–Rhône-Alpes, 655 Avenue de l’Europe, 38334, Montbonnot St. Martin, France

    Simone Gasparini

  2. Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133, Milano, Italy

    Vincenzo Caglioti

Authors
  1. Simone Gasparini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vincenzo Caglioti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Simone Gasparini.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gasparini, S., Caglioti, V. Line Localization from Single Catadioptric Images. Int J Comput Vis 94, 361–374 (2011). https://doi.org/10.1007/s11263-011-0435-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11263-011-0435-1

Keywords

Search

Navigation