Skip to main content

The Use of Bilinear Rectangular Elements in Reconstruction of Panoramic Images

  • Chapter
Conjugate Gradient Algorithms and Finite Element Methods

Part of the book series: Scientific Computation ((SCIENTCOMP))

  • 638 Accesses

Abstract

The aim of this paper is to develop an algorithm for mosaicing a sequence of panoramic images of the pipeline inner surface obtained by an inspection robot that is equipped by an omnidirectional camera. This camera is a combination of a regular camera and an axially symmetric hyperbolic mirror. The construction of the robot (see Fig. 1) enabled us to take and store a sequence of images of the inner pipeline surface under the viewing angle 25°–106° from the camera optical axis and 360° around this axis. Since the axes of pipeline and camera were not identical, each picture was considerably deformed.

Photo and the associated schematic illustration of the inspection robot; a — glass tube, b — panoramic hyperbolic mirror, c — camera, d — light bulb, e — additional hyperbolic mirror, f — prospecting tractor of the British Company Pearpoint, g — chassis.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. R. Hestenes, E. Stiefel, Methods of conjudate gradients for solving linear systems. J. Res. Nat. Bur. Standards 49 (1952), 409–436.

    Article  MathSciNet  MATH  Google Scholar 

  2. M. Křížek, P. Neittaanmäki, Finite Element Approximation of Variational Problems and Applications, Longman Scientific & Technical, Harlow, 1990.

    MATH  Google Scholar 

  3. P. Křížek, Mosaicing of panoramic images, Master Thesis, Faculty of Electrical Engineering, Prague, 2003, 1–62.

    Google Scholar 

  4. P. Křížek, V. Smutný, Mosaicing unwarped panoramic images into an infinite bitmap, Research Report CTU-CMP-2002-21, Centre for Machine Perception, Czech Technical University, Prague (2002), 1–29.

    Google Scholar 

  5. K. Rektorys, Survey of Applicable Mathematics, Kluwer, Amsterdam, 1994.

    Google Scholar 

  6. M. Šonka, V. Hlaváč, R. Boyle, Image Processing Analysis and Machine Vision, 2nd ed., PWS, Boston, 1998.

    Google Scholar 

  7. http://cmp.felk.cvut.cz/~krizekp1/

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Křížek, P. (2004). The Use of Bilinear Rectangular Elements in Reconstruction of Panoramic Images. In: Křížek, M., Neittaanmäki, P., Korotov, S., Glowinski, R. (eds) Conjugate Gradient Algorithms and Finite Element Methods. Scientific Computation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18560-1_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-18560-1_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-62159-8

  • Online ISBN: 978-3-642-18560-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics