Skip to main content

Non-Linear Polynomial Filters: Overview, Evolution and Proposed Mathematical Formulation

  • Chapter
  • First Online:
Non-Linear Filters for Mammogram Enhancement

Part of the book series: Studies in Computational Intelligence ((SCI,volume 861))

  • 219 Accesses

Abstract

Last few decades have marked growing interest towards developments in signal processing techniques on account of the diverse spread in multimedia applications (which includes image and video processing).

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 EPUB and 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

References

  • H.H. Chang, C.L. Nikias, A.N. Venetsanopoulos, Efficient implementations of quadratic filters. IEEE Trans. Acoust. Speech Signal Process. 34, 1511–1528 (1986)

    Google Scholar 

  • T. Koh, E. Powers, Second-order Volterra filtering and its application to nonlinear system identification. IEEE Trans. Acoust. Speech Signal Process. 33(6), 1445–1455 (1985)

    Google Scholar 

  • Y. Lou, C.L. Nikias, A.N. Venetsanopoulos, Efficient VLSI array processing structures for adaptive quadratic digital filters. Circuits Syst. Signal Process. 7(2), 253–273 (1988)

    Article  Google Scholar 

  • V.J. Mathews, Adaptive polynomial filters. IEEE Signal Process. Mag. 8(3), 10–26 (1991)

    Article  Google Scholar 

  • V.J. Mathews, G.L. Sicuranza, Polynomial Signal Processing, vol. 27 (Wiley, New York, 2000)

    Google Scholar 

  • B.G. Mertzios, G.L. Sicuranza, A.N. Venetsanopoulos, Efficient realizations of two-dimensional quadratic digital filters. IEEE Trans. Acoust. Speech Signal Process. 37(5), 765–768 (1989)

    Article  Google Scholar 

  • S.K. Mitra, H. Li, I. Li, T.-H. Yu, A new class of non-linear filters for image enhancement, in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP-1991), Toronto, Canada, April 1991, pp. 2525–2528

    Google Scholar 

  • A.V. Oppenheim, R.W. Schafer, Discrete Time Signal Processing, 5th edn. (Prentice Hall of India, New Delhi, 1998)

    Google Scholar 

  • I. Pitas, A.N. Venetsanopoulos, Morphological shape decomposition. IEEE Trans. Pattern Anal. Mach. Intell. 12(1), 38–45 (1990)

    Article  Google Scholar 

  • I. Pitas, A.N. Venetsanopoulos, Order statistics in digital image processing. Proc. IEEE 80(12), 1893–1921 (1992)

    Article  Google Scholar 

  • G. Ramponi, Bi-impulse response design of isotropic quadratic filters. Proc. IEEE 78(4), 665–667 (1990)

    Article  Google Scholar 

  • G. Ramponi, G.L. Sicuranza, Quadratic digital filters for image processing. IEEE Trans. Acoust. Speech Signal Process. 36(6), 937–939 (1988)

    Article  Google Scholar 

  • G.L. Sicuranza, Quadratic filters for signal processing. Proc. IEEE 80(8), 1263–1285 (1992)

    Article  Google Scholar 

  • D.J. Struik, A Source Book in Mathematics 1200–1800 (Princeton University Press, 2014)

    Google Scholar 

  • S. Thurnhofer, S.K. Mitra, A general framework for quadratic Volterra filters for edge enhancement. IEEE Trans. Image Process. 5(6), 950–963 (1996)

    Article  Google Scholar 

  • J.H. Yoon, Y.M. Ro, Enhancement of the contrast in mammographic images using the homomorphic filter method. IEICE Trans. Inf. Syst. 85(1), 298–303 (2002)

    Google Scholar 

  • Y. Zhou, K.A. Panetta, S.S. Agaian, Mammogram enhancement using alpha weighted quadratic filter, in Proceedings of Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Minneapolis, Minnesota, September 2009, pp. 3681–3684

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vikrant Bhateja .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Bhateja, V., Misra, M., Urooj, S. (2020). Non-Linear Polynomial Filters: Overview, Evolution and Proposed Mathematical Formulation. In: Non-Linear Filters for Mammogram Enhancement. Studies in Computational Intelligence, vol 861. Springer, Singapore. https://doi.org/10.1007/978-981-15-0442-6_13

Download citation

Publish with us

Policies and ethics