Skip to main content
SpringerLink
Log in

Pi-Tag: a fast image-space marker design based on projective invariants

  • Original Paper
  • Published:
Machine Vision and Applications Aims and scope Submit manuscript

Abstract

Visual marker systems have become an ubiquitous tool to supply a reference frame onto otherwise uncontrolled scenes. Throughout the last decades, a wide range of different approaches have emerged, each with different strengths and limitations. Some tags are optimized to reach a high accuracy in the recovered camera pose, others are based on designs that aim to maximizing the detection speed or minimizing the effect of occlusion on the detection process. Most of them, however, employ a two-step procedure where an initial homography estimation is used to translate the marker from the image plane to an orthonormal world, where it is validated and recognized. In this paper, we present a general purpose fiducial marker system that performs both steps directly in image-space. Specifically, by exploiting projective invariants such as collinearity and cross-ratios, we introduce a detection and recognition algorithm that is fast, accurate and moderately robust to occlusion. The overall performance of the system is evaluated in an extensive experimental section, where a comparison with a well-known baseline technique is presented. Additionally, several real-world applications are proposed, ranging from camera calibration to projector-based augmented reality.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

References

  1. Bradski, G., Kaehler, A.: Learning OpenCV: Computer Vision with the OpenCV Library, 1st edn. O’Reilly Media, Inc., Cambridge (2008)

  2. Cameron, J., Lasenby, J.: Estimating human skeleton parameters and configuration in real-time from markered optical motion capture. In: Conference on Articulated Motion and Deformable Objects (2008)

  3. Cho, Y., Lee, J., Neumann, U.: A multi-ring color fiducial system and a rule-based detection method for scalable fiducial-tracking augmented reality. In: Proceedings of International Workshop on Augmented Reality (1998)

  4. Claus, D., Fitzgibbon, A.W.: Reliable automatic calibration of a marker-based position tracking system. In: IEEE Workshop on Applications of Computer Vision (2005)

  5. Davison, A.J., Reid, I.D., Molton, N.D., Stasse, O.: Monoslam: real-time single camera slam. IEEE Trans. Pattern Anal. Mach. Intell. 26(6), 1052–1067 (2007)

    Article  Google Scholar 

  6. Dorfmller, K.: Robust tracking for augmented reality using retroreflective markers. Comput. Graph. 23(6), 795–800 (1999)

    Article  Google Scholar 

  7. Douxchamps, D., Chihara, K.: High-accuracy and robust localization of large control markers for geometric camera calibration. IEEE Trans. Pattern Anal. Mach. Intell. 31, 376–383 (2009)

    Article  Google Scholar 

  8. Fiala, M.: Linear markers for robot navigation with panoramic vision. In: Proceedings of the 1st Canadian Conference on Computer and Robot Vision, CRV ’04, pp. 145–154. IEEE Computer Society, Washington, DC (2004)

  9. Fiala, M.: Designing highly reliable fiducial markers. IEEE Trans. Pattern Anal. Mach. Intell. 32(7), 1317–1324 (2010)

    Google Scholar 

  10. Gatrell, L., Hoff, W., Sklair, C.: Robust image features: concentric contrasting circles and their image extraction. In: Proceedings of Cooperative Intelligent Robotics in Space. SPIE, Washington (1991)

  11. Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  12. Heikkilä, J.: Geometric camera calibration using circular control points. IEEE Trans. Pattern Anal. Mach. Intell. 22, 1066–1077 (October 2000)

  13. Huynh, D.Q.: The cross ratio: a revisit to its probability density function. In: Proceedings of the British Machine Vision Conference BMVC 2000 (2000)

  14. Jiang, G., Quan, L.: Detection of concentric circles for camera calibration. IEEE Int. Conf. Comput. Vis. 1, 333–340 (2005)

    Google Scholar 

  15. Kannala, J., Salo, M.,: Heikkilä, J.: Algorithms for computing a planar homography from conics in correspondence. In: British Machine Vision Conference (2006)

  16. Kato, H., Billinghurst, M.: Marker tracking and hmd calibration for a video-based augmented reality conferencing system. In: Proceedings of the 2nd IEEE and ACM International Workshop on Augmented Reality. IEEE Computer Society, Washington, DC (1999)

  17. Kazhdan, M., Bolitho, M., Hoppe, H.: Poisson surface reconstruction. In: Proceedings of the Fourth Eurographics symposium on Geometry processing, SGP ’06, pp. 61–70. Aire-la-Ville, Switzerland (2006)

  18. Knyaz, V.A. Head Of Group, Sibiryakov, R.V.: The development of new coded targets for automated point identification and non-contact surface measurements. In: 3D Surface Measurements, International Archives of Photogrammetry and Remote Sensing (1998)

  19. Li, Y., Wang, Y.-T., Liu, Y.: Fiducial marker based on projective invariant for augmented reality. J. Comput. Sci. Technol. 22, 890–897 (2007)

    Article  Google Scholar 

  20. Loaiza, M., Raposo, A., Gattass, M.: A novel optical tracking algorithm for point-based projective invariant marker patterns. In: Proceedings of the 3rd International Conference on Advances in Visual Computing, vol. Part I, ISVC’07, pp. 160–169. Springer, Berlin (2007)

  21. Maidi, M., Didier, J.-Y., Ababsa, F., Mallem, M.: A performance study for camera pose estimation using visual marker based tracking. Mach. Vis. Appl. 21 (2010)

  22. Mallon, J., Whelan, P.F.: Which pattern? biasing aspects of planar calibration patterns and detection methods. Pattern Recogn. Lett. 28(8), 921–930 (2007)

    Article  Google Scholar 

  23. Meer, P., Lenz, R., Ramakrishna, S.: Efficient invariant representations. Int. J. Comput. Vis. 26, 137–152 (1998)

    Article  Google Scholar 

  24. Naimark, L., Foxlin, E.: Circular data matrix fiducial system and robust image processing for a wearable vision-inertial self-tracker. In: Proceedings of the 1st International Symposium on Mixed and Augmented Reality, ISMAR ’02. IEEE Computer Society, Washington, DC (2002)

  25. Ouellet, J., Hebert, P.: Precise ellipse estimation without contour point extraction. Mach. Vis. Appl. 21 (2009)

  26. Rusinkiewicz, S., Levoy, M.: Efficient variants of the icp algorithm. In: Proceedings of the Third International Conference on 3D Digital Imaging and Modeling, pp. 145–152 (2001)

  27. Sauvola, J., Pietikainen, M.: Adaptive document image binarization. Pattern Recogn. 33(2), 225–236 (2000)

    Article  Google Scholar 

  28. Teixeira, L., Loaiza, M., Raposo, A., Gattass, M.: Augmented reality using projective invariant patterns. In: Advances in Visual Computing. Lecture Notes in Computer Science, vol. 5358. Springer, Berlin (2008)

  29. Thormählen, T., Broszio, H.: Automatic line-based estimation of radial lens distortion. Integr. Comput. Aided Eng. 12(2), 177–190 (2005)

    Google Scholar 

  30. Tsonisp, V.S., Konstantinos, V.Ch., Trahaniaslj, P.E.: Landmark-based navigation using projective invariants. In: Proceedings of the 1998 IEEE International Conference on Intelligent Robots and Systems. IEEE Computer Society, Victoria, Canada (1998)

  31. Uchiyama, H., Saito, H.: Random dot markers. In: Virtual Reality Conference, IEEE, pp. 271–272 (2011)

  32. van Rhijn, A., Mulder, J.D.: Optical tracking using line pencil fiducials. In: Proceedings of the Eurographics Symposium on Virtual Environments (2004)

  33. Van Liere, R., Mulder, J.D.: Optical tracking using projective invariant marker pattern properties. In: Proceedings of the IEEE Virtual Reality Conference. IEEE Press, New York (2003)

  34. Wagner, D., Langlotz, T., Schmalstieg, D.: Robust and unobtrusive marker tracking on mobile phones. In: Proceedings of the 7th IEEE/ACM International Symposium on Mixed and Augmented Reality, ISMAR ’08, pp. 121–124. IEEE Computer Society, Washington, DC (2008)

  35. Wagner, D., Reitmayr, G., Mulloni, A., Drummond, T., Schmalstieg, D.: Real time detection and tracking for augmented reality on mobile phones. IEEE Trans. Vis. Comput. Graph. 99, 355–368 (2010)

    Google Scholar 

  36. Walthelm, A., Kluthe, R.: Active distance measurement based on robust artificial markers as a building block for a service robot architecture. In: IFAC Symposium on Artificial Intelligence in Real Time Control. Budapest Polytechnic, Budapest (2000)

  37. Yoon, J.-H., Park, J.-S., Kim, C.: Increasing camera pose estimation accuracy using multiple markers. In: Advances in Artificial Reality and Tele-Existence. Lecture Notes in Computer Science, vol. 4282. pp. 239–248. Springer, Berlin (2006)

  38. Yu, Q., Li, Q., Deng, Z.: Online motion capture marker labeling for multiple interacting articulated targets. Comput. Graph. Forum 26(3), 477–483 (2007)

    Article  Google Scholar 

  39. Yu, R., Yang, T., Zheng, J., Zhang, X.: Real-time camera pose estimation based on multiple planar markers. In: Proceedings of the 2009 Fifth International Conference on Image and Graphics ICIG ’09, pp. 640–645. IEEE Computer Society, Washington, DC (2009)

  40. Zhang, X., Fronz, S., Navab, N.: Visual marker detection and decoding in ar systems: a comparative study. In: Proceedings of the 1st International Symposium on Mixed and Augmented Reality, ISMAR ’02, pp. 97. IEEE Computer Society, Washington, DC (2002)

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Scienze Ambientali, Informatica e Statistica, Università Ca’ Foscari Venezia, Venice, Italy

    Filippo Bergamasco, Andrea Albarelli & Andrea Torsello

Authors
  1. Filippo Bergamasco
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrea Albarelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Andrea Torsello
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrea Albarelli.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bergamasco, F., Albarelli, A. & Torsello, A. Pi-Tag: a fast image-space marker design based on projective invariants. Machine Vision and Applications 24, 1295–1310 (2013). https://doi.org/10.1007/s00138-012-0469-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00138-012-0469-6

Keywords

Search

Navigation