Abstract
This work proposes an efficient analytical design procedure for elliptical and circular 2D digital filters with an adjustable response. The design relies on a 1D low-pass prototype filter with a specified bandwidth, to which a particular frequency mapping is applied. The prototype can be scaled in frequency, having adjustable selectivity. This analytical procedure yields 2D filters with accurate shape even near the frequency plane margins, very low distortions and steep transition at a relatively low order, thus being very efficient. The elliptical filters can be tuned to a desired orientation angle and can be used as directional filters. Also an uniform circular filter bank with a specified number of bands is designed. The frequency response results directly factored, and the corresponding filter matrices result as a convolution of small size matrices, which simplifies implementation and allows for a sequential filtering, in several steps. The proposed method is based entirely on accurate approximations and frequency mappings, without using any numerical optimization algorithms. Several examples of filtering on various test images are provided, to illustrate the capabilities of this class of filters.
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Data availability
The datasets (images) analysed during the current study are available in the OSF repository, at the following link: https://osf.io/6dg5y/
References
Lu, W. S., & Antoniou, A. (1992). Two-Dimensional Digital Filters. CRC Press.
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: Fundamental Theory and Applications, 41(8), 505–517. https://doi.org/10.1109/81.311540
Shyu, J., Pei, S., & Huang, Y. (2009). Design of variable two-dimensional FIR digital filters by McClellan transformation. IEEE Trans on Circuits and Systems I, 56(3), 574–582. https://doi.org/10.1109/TCSI.2008.2002119
Nguyen, D., & Swamy, M. (1986). Approximation design of 2-D digital filters with elliptical magnitude response of arbitrary orientation, IEEE Trans. Circuits and Systems, 33(6), 597–603. https://doi.org/10.1109/TCS.1986.1085966
Jackson, S. A., & Ahuja, N. (1996). Elliptical Gaussian filters. In Proceedings of 13th International Conference on Pattern Recognition, IEEE. https://doi.org/10.1109/ICPR.1996.546928
Lavu, K. C., & Ramachandran, V. (2004). Study of elliptical symmetry in 2D IIR Butterworth digital filters. In The 2004 47th Midwest Symposium on Circuits and Systems, 2004. MWSCAS'04. (Vol. 2, pp. 77-80). IEEE. https://doi.org/10.1109/MWSCAS.2004.1354095
Chaudhury, K. N., Munoz-Barrutia, A., & Unser, M. (2010). Fast space-variant elliptical filtering using box splines. IEEE Transactions on Image Processing, 19(9), 2290–2306. https://doi.org/10.1109/TIP.2010.2046953
bdul-Jabbar, J. M., & Abdulkader, Z. N. (2012, October). Iris recognition using 2-D elliptical-support wavelet filter bank. In 2012 3rd International Conference on Image Processing Theory, Tools and Applications (IPTA) (pp. 359-363). IEEE. https://doi.org/10.1109/IPTA.2012.6469520
Yuanyuan, Z. (2012). Fingerprint image enhancement based on elliptical shape Gabor filter. In 2012 6th IEEE International Conference Intelligent Systems. IEEE. https://doi.org/10.1109/IS.2012.6335240
Kwan, H. K., & Chan, C. L. (1989). Design of linear phase, circularly symmetric two-dimensional recursive digital filters. IEEE Transactions on Circuits and Systems, 36(7), 1023–1029. https://doi.org/10.1109/31.31341
Reddy, M. S., & Hazra, S. N. (1988). Design of two-dimensional circularly symmetric low-pass IIR filters using transformation. IEEE Transactions on Circuits and Systems, 35(9), 1186–1188. https://doi.org/10.1109/31.7586
Guillemot, C., & Ansari, R. (1994). Two-dimensional filters with wideband circularly symmetric frequency response. IEEE Transactions on Circuits and Systems II, 41(10), 703–707. https://doi.org/10.1109/82.329742
Bindima, T., Manuel, M., & Elias, E. (2016, November). An efficient transformation for two dimensional circularly symmetric wideband FIR filters. In 2016 IEEE Region 10 Conference (TENCON) (pp. 2838-2841). IEEE. https://doi.org/10.1109/TENCON.2016.7848561
Hung, T. Q., Tuan, H. D., & Nguyen, T. Q. (2007). Design of diamond and circular filters by semi-definite programming. In 2007 IEEE International Symposium on Circuits and Systems (pp. 2966-2969). IEEE. https://doi.org/10.1109/ISCAS.2007.377969
Nosratinia, A., & Ahmadi, M. (1991). An accelerated method for the design of 2-D circularly symmetric FIR filters. In IEEE Pacific Rim Conference on Communications, Computers and Signal Processing Conference Proceedings (pp. 510-513). IEEE. https://doi.org/10.1109/PACRIM.1991.160788
Zhang, J., Tan, T., & Ma, L. (2002). Invariant texture segmentation via circular Gabor filters. In 2002 International Conference on Pattern Recognition (Vol. 2, pp. 901-904). IEEE.https://doi.org/10.1109/ICPR.2002.1048450
Matei, R., & Ungureanu, P. (2009). Image processing using elliptically-shaped filters. In 2009 International Symposium on Signals, Circuits and Systems (pp. 337-340). IEEE. https://doi.org/10.1109/ISSCS.2009.5206111
Matei, R. (2018). Analytical design of elliptically-shaped 2D recursive filters. In 2018 IEEE 61st International Midwest Symposium on Circuits and Systems (MWSCAS) (pp. 964-967). IEEE. https://doi.org/10.1109/MWSCAS.2018.8624079
Matei, R. (2018). Analytical design methods for directional Gaussian 2D FIR filters. Multidimensional Systems and Signal Processing, 29(1), 185–211. https://doi.org/10.1007/s11045-016-0458-4
Matei, R., & Matei, D. (2018). Circular IIR filter design and applications in biomedical image analysis. In 2018 10th International Conference on Electronics, Computers and Artificial Intelligence (ECAI). IEEE. https://doi.org/10.1109/ECAI.2018.8679092
Matei, R. (2020). Analytic design of uniform circular filter banks. In 2020 Signal Processing: Algorithms, Architectures, Arrangements, and Applications (SPA) (pp. 58-62). IEEE. https://doi.org/10.23919/SPA50552.2020.9241281
Matei, R. (2021, August). Efficient Design Procedure for Circular Filter Banks. In 2021 IEEE International Midwest Symposium on Circuits and Systems (MWSCAS) (pp. 259-262). IEEE.https://doi.org/10.1109/MWSCAS47672.2021.9531686
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Matei, R. Design and applications of adjustable 2D digital filters with elliptical and circular symmetry. Analog Integr Circ Sig Process 114, 345–358 (2023). https://doi.org/10.1007/s10470-023-02152-0
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DOI: https://doi.org/10.1007/s10470-023-02152-0