Skip to main content
SpringerLink
Log in

Analytical design methods for directional Gaussian 2D FIR filters

  • Published:
Multidimensional Systems and Signal Processing Aims and scope Submit manuscript

Abstract

This paper proposes two analytical design methods in the frequency domain for directional Gaussian 2D FIR filters, with a straight directional or an elliptically-shaped frequency response and with a specified selectivity and orientation in the frequency plane. One method relies on the substitution of a frequency mapping into the factored polynomial approximation of the Gaussian, while the other one is based on decomposing the frequency response into Gaussian components along three properly chosen directions in the frequency plane. The frequency response of the 2D directional filter results directly in a factored form, which is a major advantage in implementation. The filters are accurate, efficient and they eliminate the necessity of interpolation. With the mapping substitution method, they result also adjustable in orientation and aspect ratio. Several design examples are given for various specifications, and simulation results of directional filtering on test images are provided, to prove their applicability in image processing.

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.

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

Similar content being viewed by others

References

  • Charalampidis, D. (2009). Efficient directional Gaussian smoothers. IEEE Geoscience and Remote Sensing Letters, 6(3), 383–387. doi:10.1109/LGRS.2009.2014397.

    Article  Google Scholar 

  • Chen, C. K., & Lee, J. H. (1994). McClellan transform based design techniques for two-dimensional linear-phase FIR filters. IEEE Transactions on Circuits and Systems I, 41(8), 505–517. doi:10.1109/81.311540.

    Article  Google Scholar 

  • Geusebroek, J. M., Smeulders, A. W. M., & van de Weijer, J. (2003). Fast anisotropic Gauss filtering. IEEE Transactions on Image Processing, 12(8), 938–943. doi:10.1109/TIP.2003.812429.

    Article  MathSciNet  MATH  Google Scholar 

  • Harn, L., & Shenoi, B. A. (1986). Design of stable two-dimensional IIR filters using digital spectral transformations. IEEE Transactions on Circuits and Systems, 33(5), 483–490. doi:10.1109/TCS.1986.1085949.

    Article  Google Scholar 

  • Horng, Y. R., Tseng, Y. C. & Chang, T. S. (2010). Stereoscopic images generation with directional Gaussian filter. IEEE International Symposium on Circuits and Systems ISCAS 2010, 30 May–2 June, 2010, Paris (pp. 2650–2653). doi:10.1109/ISCAS.2010.5537052.

  • Hsiao, P. Y. et al. (2006). A parameterizable digital-approximated 2D Gaussian smoothing filter for edge detection in noisy image. IEEE International Symposium on Circuits and Systems ISCAS 2006, 21–24 May 2006, Kos, Greece. doi:10.1109/ISCAS.2006.1693303.

  • Joginipelly, A., Varela, A., Charalampidis, D., Schott, R., Fitzsimmons, R. (2012). Efficient FPGA implementation of steerable Gaussian smoothers. 44th Southeastern Symposium on System Theory, 11–13 March 2012, Jacksonville, Florida (pp. 78–82). doi:10.1109/SSST.2012.6195131.

  • Lakshmanan, V. (2004). A separable filter for directional smoothing. IEEE Geoscience and Remote Sensing Letters, 1(3), 192–195. doi:10.1109/LGRS.2004.828178.

    Article  Google Scholar 

  • Lampert, C. H. & Wirjadi, O. (2006). Anisotropic Gaussian filtering using fixed point arithmetic. IEEE International Conference on Image Processing, 8–11 October 2006, Atlanta (pp.1565–1568). doi:10.1109/ICIP.2006.312606.

  • Lampert, C. H., & Wirjadi, O. (2006). An optimal nonorthogonal separation of the anisotropic Gaussian convolution filter. IEEE Transactions on Image Processing, 15(11), 3501–3513. doi:10.1109/TIP.2006.877501.

    Article  MathSciNet  Google Scholar 

  • Lam, S. Y., & Shi, B. E. (2007). Recursive anisotropic 2-D Gaussian filtering based on a triple-axis decomposition. IEEE Transactions on Image Processing, 16(7), 1925–1930. doi:10.1109/TIP.2007.896673.

    Article  MathSciNet  Google Scholar 

  • Matei, R. & Ungureanu, P. (2009). Image processing using elliptically-shaped filters. IEEE International Symposium on Signals, Circuits and Systems, ISSCS 2009, Iasi, Romania, vol. 2, pp. 337–340. doi:10.1109/ISSCS.2009.5206111.

  • Matei, R. (2013). Design of 2D parametric filters for directional Gaussian smoothing. 21-st European Conference on Circuit Theory and Design, ECCTD 2013, 8-12 September 2013, Dresden, Germany (pp. 1–4). doi:10.1109/ECCTD.2013.6662240.

  • Najim, M. (Ed.). (2006). Digital filters design for signal and image processing. New York: Wiley.

    Google Scholar 

  • Nguyen, D., & Swamy, M. N. S. (1986). Approximation design of 2-D digital filters with elliptical magnitude response of arbitrary orientation. IEEE Transactions on Circuits and Systems, 33(6), 597–603. doi:10.1109/TCS.1986.1085966.

    Article  Google Scholar 

  • Tzeng, S. T. (2004). Design of 2D FIR digital filters with symmetric properties by genetic algorithm approach. IEEE Asia-Pacific Conf. on Circuits and Systems. Tainan, 1, 417–420. doi:10.1109/APCCAS.2004.1412784.

    Google Scholar 

  • Venkatesh, M. & Seelamantula, C. S. (2015). Directional bilateral filters. IEEE International Conference on Acoustics, Speech and Signal Processing, Brisbane, 19–24 April 2015, pp. 1578–1582. doi:10.1109/ICASSP.2015.7178236.

  • Wang, P., Zhang, B. C. & Wang, Y. F. (2006). An anisotropic gaussian filter for noise filtering of InSAR interferogram. International Conference on Radar 2006, 16–19 Oct. 2006, Shanghai (pp.1–4). doi:10.1109/ICR.2006.343226.

  • Yeung, K. S., & Chan, S. C. (2002). Design and implementation of multiplier-less tunable 2-D FIR filters using McClellan transformation. Int. Symposium Circuits and Systems ISCAS 2002. Scottsdale, Arizona, 5, 761–764. doi:10.1109/ISCAS.2002.1010815.

    Google Scholar 

  • Young, I. T., & van Vliet, L. J. (1995). Recursive implementation of the Gaussian filter. Signal Processing, 44(2), 139–151. doi:10.1016/0165-1684(95)00020-E.

    Article  Google Scholar 

  • Zhu, W. P., Ahmad, M. O., & Swamy, M. N. S. (1999). A least-square design approach for 2D FIR filters with arbitrary frequency response. IEEE Transactions on Circuits and Systems II, 46(8), 1027–1034. doi:10.1109/82.782044.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Electronics, Telecommunications and Information Technology, “Gheorghe Asachi” Technical University, Bd. Carol I No. 11, 700506, Iasi, Romania

    Radu Matei

Authors
  1. Radu Matei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Radu Matei.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Matei, R. Analytical design methods for directional Gaussian 2D FIR filters. Multidim Syst Sign Process 29, 185–211 (2018). https://doi.org/10.1007/s11045-016-0458-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11045-016-0458-4

Keywords

Search

Navigation