Skip to main content
SpringerLink
Log in

Image and 2D Signal Processing

  • Chapter
  • First Online:
Digital Signal Processing with Matlab Examples, Volume 2

Part of the book series: Signals and Communication Technology ((SCT))

  • 6279 Accesses

Abstract

While many animals depend on audition, olfaction, or pressure sensing, for their lives, in the case of humans vision is of utmost importance. One of the characteristic advances ofmodern times is the digitalization and processing of images. This chapter is precisely an introduction to image processing. In its first sections, the interest is centred on image filtering, improvement, certain modifications, and the emphasizing of edges and borders. This is followed by a concise description of color processing. Then, the chapter deals with important techniques of medical diagnosis related to computational tomography, like the Hough transform and the Radon transform. Section nine introduces filter banks for bi-dimensional processing. Finally, the chapter includes some experiments on using a webcam, and about the backprojection steps related to tomography.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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. R. Ansari, Efficient IIR and FIR fan filters. IEEE Trans. Circuits Syst. 34(8), 941–945 (1987)

    Article  Google Scholar 

  2. A. Averbuch, R.R. Coifman, D.L. Donoho, M. Elad, M. Israeli, Fast and accurate polar Fourier transform. Appl. Comput. Harmonic Anal. 21, 145–167 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. A. Averbuch, R.R. Coifman, D.L. Donoho, M. Israeli, J. Walden, Fast slant stack: a notion of radon transform for data in a cartesian grid which is rapidly computible, algebraically exact, geometrically faithful and invertible. Technical Report 11, Dept. Statistics, Stanford University, USA, 2001

    Google Scholar 

  4. N. Chou, J.A. Izatt, S. Farsiu, Generalized pseudo-polar Fourier grids and applications in registering ophthalmic optical coherence tomography images, in Proceedings 43rd ASILOMAR Conference Signal, Systems and Computers, pp. 807–811 (2009)

    Google Scholar 

  5. B.E. Coggins, P. Zhou, Polar Fourier transforms of radially sampled NMR data. J. Magn. Reson. 182, 84–95 (2006)

    Google Scholar 

  6. A.L. Cunha, M.N. Do, Filter design for directional multiresolution decomposition, in Proceedings SPIE, vol. 5014 (2005)

    Google Scholar 

  7. H. Dammertz, A. Keller, S. Dammertz, Simulation of rank-1 lattices, in Monte Carlo and Quasi-Monte Carlo Methods, pp. 205–216 (Springer, 2008)

    Google Scholar 

  8. M.N. Do, Directional multiresolution image representation. Ph.D. thesis, Department of Communication Systems, Swiss Federal Institute of Technology Lausanne, 2001

    Google Scholar 

  9. M.N. Do, Y.M. Lu, Multidimensional filter banks and multiscale geometric representations. Found. Trends Sign. Process. 5(3), 157–264 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. J.R. Driscoll, D. Healy, Computing Fourier transforms and convolutions on the 2-sphere. Adv. Appl. Math. 15, 202–250 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  11. A. Faridani, E. Grinberg, E.T. Quinto, Radon Transform and Tomograpy (Amer. Mathematical Society, 2001)

    Google Scholar 

  12. M. Fenn, Fast Fourier transform at nonequispaced nodes and applications. Ph.D. thesis, Universität Manheim, Germany, 2005

    Google Scholar 

  13. J. Fessler, Fessler Book Chapter on Tomography (Course 516, University of Michigan, 2012). http://web.eecs.umich.edu/~fessler/course/516/l/c-tomo.pdf

  14. K. Fourmont, Non-equispaced fast Fourier transforms with applicatios to tomography. J. Fourier Anal. Appl. 9(5), 431–450 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  15. Q. Gu, M.N.S. Swamy, On the design of a broad class of 2-D recusive digital filters with fan, diamong and elliptically-symmetric responses. IEEE Trans. Circuits Syst.-II 41(9), 603–614 (1994)

    Article  Google Scholar 

  16. B. Gustafsson, Mathematics for computer tomography. Phys. Scr. T61, 38–43 (1996)

    Article  Google Scholar 

  17. O. Harari, A new nearly polar fft and analysis of Fourier-Radon relations in discrete spaces. Master’s thesis, Ben-Gurion University of the Negev, Beersheba, 2007

    Google Scholar 

  18. AS. Hassanein, S. Mohammad, M. Sameer, M.E. Ragab, A survey on hough transform, theory, techniques and applications (2015). arXiv preprint arXiv:1502.02160

  19. E.S. Karlsen, Multidimensional multirate sampling and seismic migration. Master’s thesis, Dep. Earth Science, University of Bergen, Norway, 2010

    Google Scholar 

  20. J. Keiner, S. Kunis, D. Potts, Using nfft3—a software library for various nonequispaced fast Fourier transforms. ACM Trans. Math. Softw. 36(4) (2009). art.no. 19

    Google Scholar 

  21. J. Kovaèeviæ, M. Vetterli, Design of multidimensional non-separable regular filter banks and wavelets, in Proceedings IEEE International Conference Acoustics, Speech, and Signal Processing, ICASSP-92, vol. 4, pp. 389–392 (1992)

    Google Scholar 

  22. T. Kratochvil, J. Melo. Utilization of MATLAB for TV colorimetry and color spaces analysis, in Proceedings 14th Annual Conference Technical Computing, pp. 53–60 (2006)

    Google Scholar 

  23. S. Kunis, Nonequispaced FFT- generalization and inversion. Ph.D. thesis, Institut für Mathematik, Universität zu Lübeck, Germany, 2006

    Google Scholar 

  24. E. Kupce, R. Freeman, Fast multidimensional NMR: radial sampling of evolution space. J. Magn. Reson. 173, 317–321 (2005)

    Article  Google Scholar 

  25. O. Marques, Practical Image and Video Processing Using MATLAB (J. Wiley, 2011)

    Google Scholar 

  26. R. Matei, Multi-directional filters designed from 1D prototypes, in Proceedings IEEE 55th International Midwest Symposium on Circuits and Systems, (MWSCAS), pp. 864–867 (2012)

    Google Scholar 

  27. F. Nicolls, A. Wilkinson, Multidimensional Digital Signal Processing (Lecture of the EEE4001F course, University of Cape Town, South Africa, 2012). http://www.dip.ee.uct.ac.za/~nicolls/lectures/eee401f/01_mdsp_slides.pdf

  28. J.P. Nilchian, M. Ward, C. Vonesch, M. Unser, Optimized Kaiser-Bessel window functions for computed tomography. IEEE Trans. Image Process. 24(11), 3826–3833 (2015)

    Article  MathSciNet  Google Scholar 

  29. S.C. Pei, S.B. Jaw, Two-dimensional general fan-type FIR digital filter design. Sign. Process. 37, 265–274 (1994)

    Article  MATH  Google Scholar 

  30. Y. Pellin, P.P. Vaidyanathan, Theory and design of two-dimensional filter banks: a review. Multidimension. Syst. Signal Process. 7, 263–330 (1996)

    Article  MATH  Google Scholar 

  31. N.A. Pendergrass, S.K. Mitra, E.I. Jury, Spectral transformations for two-dimensional digital filters. IEEE Trans. Circuits Syst. 23(1), 26–35 (1976)

    Article  MathSciNet  Google Scholar 

  32. D. Potts, G. Steidl, M. Tasche, Fast Fourier transforms for nonequispaced data: a tutorial, in Modern Sampling Theory: Mathematics and Applications, pp. 247–270 (Birkhauser, 2001)

    Google Scholar 

  33. E.Z. Psarakis, V.G. Mertzios, GPh Alexiou, Design of two-dimensional zero phase FIR fan filters via the McClelland transform. IEEE Trans. Circuits Syst. 37(1), 10–16 (1990)

    Article  Google Scholar 

  34. O. Regev, Lattices in Computer Science: Introduction (Lecture of the 0368.4282 course, Tel Aviv University, Israel, 2004). https://www.cims.nyu.edu/~regev/teaching/lattices_fall_2009/

  35. M. Smereka, I. Dulêba, Circular object detection using a modified Hough transform. Int. J. Appl. Math. Comput. Sci. 18(1), 85–91 (2008)

    Article  MathSciNet  Google Scholar 

  36. Y.S. Song, Y.H. Lee, Formulas for McClelland transform parameters in designing 2-D zero-phase FIR fan filters. IEEE Sign. Process. Lett. 3(11), 291–293 (1996)

    Article  Google Scholar 

  37. G. Steidl, A note on fast Fourier transforms for nonequispaced grids. Adv. Comput. Math. 9, 337–353 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  38. M. Tkalcic, J.F. Tasic, Colour spaces—perceptual, historical and applicational background, in Proceedings IEEE Region 8 EUROCON, Computer as a Tool, pp. 304–308 (2003)

    Google Scholar 

  39. P. Toft, The radon transform. Ph.D. thesis, Dept. Mathematical Modelling, Technical University of Denmark, 1996

    Google Scholar 

  40. M. Vetterli, E. Kovacevic, D.J. Legall, Perfect reconstruction filter banks for HDTV representation and coding. Sign. Process.: Image Commun. 2, 349–363 (1990)

    Google Scholar 

  41. M. Vetterli, J. Kovacevic, Wavelets and Subband Coding (Prentice Hall, 1995)

    Google Scholar 

  42. A.F. Ware, Fast approximate Fourier transforms for irregulary spaced data. SIAM Rev. 40, 838–856 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  43. W.P. Zhu, S. Nakamura, An efficient approach for the synthesis of 2-D recursive fan filters using 1-D prototypes. IEEE Trans. Sign. Process. 44(4), 979–983 (1996)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Systems Engineering and Automatic Control, Universidad Complutense de Madrid, Madrid, Spain

    Jose Maria Giron-Sierra

Authors
  1. Jose Maria Giron-Sierra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jose Maria Giron-Sierra .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer Science+Business Media Singapore

About this chapter

Cite this chapter

Giron-Sierra, J.M. (2017). Image and 2D Signal Processing. In: Digital Signal Processing with Matlab Examples, Volume 2. Signals and Communication Technology. Springer, Singapore. https://doi.org/10.1007/978-981-10-2537-2_3

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-2537-2_3

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-2536-5

  • Online ISBN: 978-981-10-2537-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation