Skip to main content

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 212))

Abstract

Geometric invariants have wide applications in computer vision. In most of existing methods, 3D invariants have been obtained from reconstruction, where fundamental matrices between image pairs should be firstly established. Consequently, additional computation errors are introduced during invariants construction. Moreover, it is very time consuming. In this paper, a novel method is proposed to calculate 3D projective invariants from images, without reconstruction. Furthermore, the represented framework is valid even when prior information about corresponding features is not enough for reconstruction. It has been verified in experiments that the proposed method is considerably accurate compared with ground truth, and more efficient compared with reconstruction based methods.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Weiss I (1993) Geometric invariants and object recognition. Int J Comput Vision 10:207–231

    Article  Google Scholar 

  2. Wu YH, Hu ZY (2003) The invariant representations of a quadric cone and a twisted cubic. IEEE Trans Pattern Anal Mach Intell 25:1329–1332

    Article  Google Scholar 

  3. Begelfor E, Werman M (2006) Affine invariance revisited. IEEE comput soc conf comp vision pattern recognit 2:2087–2094

    Google Scholar 

  4. Bayro-Corrochano E, Banarer V (2002) A geometric approach for the theory and applications of 3D projective invariants. J Math Imag Vision 16:131–154

    Article  MathSciNet  MATH  Google Scholar 

  5. Lasenby J, Bayro-Corrochano E, Lasenby AN, Sommer G (1996) A new framework for the formation of invariants and multiple-view constraints in computer vision. International conference on image processing 1:313–316

    Google Scholar 

  6. Maybank SJ (1998) Relation between 3D invariants and 2D invariants. Image Vis Comput 16:13–20

    Article  Google Scholar 

  7. Sung-Woo L, Bum-Jae Y, Hager GD (1999) Model-based 3D object tracking using projective invariance. IEEE international conference on robotics and automation 2:1589–1594

    Google Scholar 

  8. Tico M, Rusu C, Kuosmanen P (1999) A geometric invariant representation for the identification of corresponding points. International conference on image processing 4: 462–466

    Google Scholar 

  9. Tsui HT, Zhang ZY, Kong SH (1997) Feature tracking from an image sequence using geometric invariants. IEEE computer society conference on computer vision and pattern recognition 1:244–249

    Google Scholar 

  10. Forsyth D, Mundy JL, Zisserman A, Coelho C, Heller A, Rothwell C (1991) Invariant descriptors for 3D object recognition and pose. IEEE Trans Pattern Anal Mach Intell 13:971–991

    Article  Google Scholar 

  11. Moses Y, Ullman S (1998) Generalization to novel views: universal, class-based, and model-based processing. Int J Comput Vision 29:233–253

    Article  Google Scholar 

  12. Kyoung Sig R, Bume Jae Y, In So K (1998) 3D object recognition using projective invariant relationship by single-view. IEEE international conference on robotics and automation 4:3394–3399

    Google Scholar 

  13. Zhu Y, Seneviratne LD, Earles SWE (1995) A new structure of invariant for 3D point sets from a single view. IEEE international conference on robotics and automation 2:1726–1731

    Google Scholar 

  14. Weiss I, Ray M (2001) Model-based recognition of 3D objects from single images. IEEE Trans Pattern Anal Mach Intell 23:116–128

    Article  Google Scholar 

  15. Basri R, Moses Y (1999) When is it possible to identify 3D objects from single images using class constraints. Int J Comput Vision 33:95–116

    Article  Google Scholar 

  16. Csurka G, Faugeras O (1999) Algebraic and geometric tools to compute projective and permutation invariants. IEEE Trans Pattern Anal Mach Intell 21:58–64

    Article  Google Scholar 

  17. Long Q (1995) Invariants of six points and projective reconstruction from three uncalibrated images. IEEE Trans Pattern Anal Mach Intell 17:34–46

    Article  Google Scholar 

  18. Schaffalitzky I, Zisserman A, Hartley R, Torr P (2000) A six point solution for structure and motion. Lect Notes Comput Sci 1842:632–648

    Google Scholar 

  19. Yan X, Jia-Xiong P, Ming-Yue D, Dong-Hui X (1997) The unique solution of projective invariants of six points from four uncalibrated images. Pattern Recogn 30:513–517

    Article  Google Scholar 

  20. Long Q, Kanade T (1997) Affine structure from line correspondences with uncalibrated affine cameras. IEEE Trans Pattern Anal Mach Intell 19:834–845

    Article  Google Scholar 

  21. Weng J, Huang TS, Ahuja N (1992) Motion and structure from line correspondences; closed-form solution, uniqueness, and optimization. IEEE Trans Pattern Anal Mach Intell 14:318–336

    Article  Google Scholar 

  22. Song BS, Lee KM, Lee SU (2001) Model-based object recognition using geometric invariants of points and lines. Comput Vis Image Underst 84:361–383

    Article  MATH  Google Scholar 

  23. Lasenby J, Bayro-Corrochano E (1997) Computing 3D projective invariants from points and lines. Lect Notes Comput Sci 1296:82–89

    Article  Google Scholar 

  24. Lowe DG (2004) Distinctive image features from scale-invariant keypoints. Int J Comput Vision 60:91–110

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xiao Chen .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wang, X., Chen, X., Qu, S. (2013). Three-Dimensional Geometric Invariant Construction from Images. In: Lu, W., Cai, G., Liu, W., Xing, W. (eds) Proceedings of the 2012 International Conference on Information Technology and Software Engineering. Lecture Notes in Electrical Engineering, vol 212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34531-9_35

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-34531-9_35

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34530-2

  • Online ISBN: 978-3-642-34531-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics