A Technique for Improving the Performance of Median Smoothers at the Corners Characterized by Low Order Polynomials
Median filters with larger windows offer greater smoothing and are more robust than the median filters of smaller windows. However, the larger median smoothers (the median filters with the larger windows) fail to track low order polynomial trends in the signals. Due to this, constant regions are produced at the signal corners, leading to the loss of fine details. In this paper, an algorithm, which combines the ability of the 3-point median smoother in preserving the low order polynomial trends and the superior noise filtering characteristics of the larger median smoother, is introduced. The proposed algorithm (called the combiner algorithm in this paper) is evaluated for its performance on a test image corrupted with different types of noise and the results obtained are included.
[1] E.Ataman, V.K.Aatre and K.M.Wong, "Some Statistical Properties of Median Filters," IEEE Trans. Acoust., Speech and Signal Processing,
vol.ASSP-29, pp.1073-1075, Oct.1981.
[2] K.Oflazer, "Design and Implementation of a Single-Chip 1-D Median Filter," IEEE Trans. Acoust., Speech and Signal Processing, vol.ASSP-
31, no.5, pp.1164-1168, Oct.1983.
[3] N.Demassieux, F.Jutand, M.Saint-Paul and M.Dana, "VLSI Architecture for a One-Chip Video Median Filter," Proc. Int. Conf. on Acoust., Speech and Signal Processing, pp.1001-1004, 1985.
[4] E.Ataman, V.K.Aatre and K.M.Wong, "A Fast Method for Real Time
Median Filtering," IEEE Trans. Acoust., Speech and Signal Processing, vol.ASSP-28, no.4, pp.415-421, Aug.1980.
[5] D.J.Delman, "Digital Pipelined Median Filter Design for Real-Time
Image Processing," Proc. SPIE, vol.298, pp.184-188, Aug.1981.
[6] L.R.Rabiner, M.R.Sambur and C.E.Schmidt, "Applications of a
Nonlinear Smoothing Algorithm to Speech Processing," IEEE Trans.
Acoust., Speech and Signal Processing, vol.ASSP-23, pp.552-557, Dec.1975.
[7] N.S.Jayant, "Average- and Median-Based Smoothing Techniques for
Improving Digital Speech Quality in the Presence of Transmission
Errors," IEEE Trans. Commun., vol.COM-24, pp.1043-1045,Sept.1976.
[8] I.Pitas and A.N.Venetsanopoulos, Nonlinear Digital Filters: Principles
and Applications. Boston, MA: Kluwer Academic, 1990.
[9] W.K.Pratt, Digital Image Processing. New York: Wiley-Interscience,
1991.
[10] A.C.Bovik, "Streaking in Median Filtered Images," IEEE Trans.
Acoust., Speech and Signal Processing, vol.ASSP-35, no.4, pp.493-503, April 1987.
[11] Y.H.Lee and S.A.Kassam(1985), "Generalized Median Filtering and Related Nonlinear Filtering Techniques," IEEE Trans. Acoust., Speech
and Signal Processing, vol.ASSP-33, pp.672-683, June 1985.
[12] G.R.Arce and M.P.McLoughlin, "Theoretical Analysis of Max/Median
Filters," IEEE Trans. Acoust., Speech and Signal Processing,
vol.ASSP-35, no.1, pp.60-69, Jan. 1987.
[13] A.Nieminen and P.Heinonen and Y.Neuvo, "A New Class of Detail
Preserving Filters for Image Processing," IEEE Trans. Pattern Anal.
and Mach. Intell., vol.PAMI-9, pp.74-90, Jan. 1987.
[14] P.Heinonen and Y.Neuvo, "FIR-Median Hybrid Filters," IEEE Trans.
Acoust., Speech and Signal Processing, vol.ASSP-35, pp.832-838, June
1987.
[15] G.R.Arce and R.E.Foster, "Detail Preserving Ranked-Order Based
Filters for Image Processing," IEEE Trans. Acoust., Speech and Signal
Processing, vol.ASSP-37, pp.83-98, Jan. 1989.
[16] R.Bernstein, "Adaptive Nonlinear Filters for Simultaneous Removal of
Different Kinds of Noise in Images," IEEE Trans. Circuits and
Systems, vol.CAS-34, no.11, pp.1275-1291, Nov. 1987.
[17] H.M.Lin and A.N.Willson,Jr., "Median Filters with Adaptive Length,"
IEEE Trans. Circuits and Systems, vol.CAS-35, no.6, pp.675-690, June
1988.
[18] L.Yin, R.Yang, M.Gabbouj and Y.Neuvo, "Weighted Median Filters: A
Tutorial," IEEE Trans. Circuits and Systems-II: Analog and Digital
Signal Processing, vol.43, no.3, pp.157-192, Mar. 1996.
[19] S.J.Ko and Y.H.Lee, "Center Weighted Median Filters and Their
Applications to Image Enhancement," IEEE Trans. Circuits and
Systems, vol.CAS-38, no.9, pp.984-993, Sept. 1991.
[20] Z.Wang and D.Zhang, "Progressive Switching Median Filter for the
Removal of Impulse Noise from Highly Corrupted Images," IEEE
Trans. Circuits and Systems-II:Analog and Digital Signal Processing,
Vol.46, No.1, pp.78-80, Jan.1999.
[21] T.Chen, K.K.Ma and L.H.Chen, "Tri-State Median Filter for Image
Denoising," IEEE Trans. Image Processing, Vol.8, No.12, pp.1834-
1838, Dec.1999.
[22] H.L.Eng and K.K.Ma, "Noise Adaptive Soft Switching Median Filter,"
IEEE Trans. Image Processing, Vol.10, No.2, pp.242-251, Feb.2001.
[23] S.Zhang and M.A.Karim, "A New Impulse Detector for Switching
Median Filters,"IEEE Signal Processing Letters, Vol.9, no.11, pp.360-
363, Nov.2002.
[24] T.C.Lin and P.T.Yu, "Salt-Pepper Impulse Noise Detection and
Removal Using Multiple Thresholds for Image Restoration," Journal of
Information Science and Engineering 22, 189-198, (2006).
[25] N.C.Gallagher,Jr. and G.L.Wise, "A Theoretical Analysis of the
Properties of Median Filters," IEEE Trans. Acoust., Speech and Signal
Processing, vol.ASSP-29, pp.1136-1141, Dec. 1981.
[1] E.Ataman, V.K.Aatre and K.M.Wong, "Some Statistical Properties of Median Filters," IEEE Trans. Acoust., Speech and Signal Processing,
vol.ASSP-29, pp.1073-1075, Oct.1981.
[2] K.Oflazer, "Design and Implementation of a Single-Chip 1-D Median Filter," IEEE Trans. Acoust., Speech and Signal Processing, vol.ASSP-
31, no.5, pp.1164-1168, Oct.1983.
[3] N.Demassieux, F.Jutand, M.Saint-Paul and M.Dana, "VLSI Architecture for a One-Chip Video Median Filter," Proc. Int. Conf. on Acoust., Speech and Signal Processing, pp.1001-1004, 1985.
[4] E.Ataman, V.K.Aatre and K.M.Wong, "A Fast Method for Real Time
Median Filtering," IEEE Trans. Acoust., Speech and Signal Processing, vol.ASSP-28, no.4, pp.415-421, Aug.1980.
[5] D.J.Delman, "Digital Pipelined Median Filter Design for Real-Time
Image Processing," Proc. SPIE, vol.298, pp.184-188, Aug.1981.
[6] L.R.Rabiner, M.R.Sambur and C.E.Schmidt, "Applications of a
Nonlinear Smoothing Algorithm to Speech Processing," IEEE Trans.
Acoust., Speech and Signal Processing, vol.ASSP-23, pp.552-557, Dec.1975.
[7] N.S.Jayant, "Average- and Median-Based Smoothing Techniques for
Improving Digital Speech Quality in the Presence of Transmission
Errors," IEEE Trans. Commun., vol.COM-24, pp.1043-1045,Sept.1976.
[8] I.Pitas and A.N.Venetsanopoulos, Nonlinear Digital Filters: Principles
and Applications. Boston, MA: Kluwer Academic, 1990.
[9] W.K.Pratt, Digital Image Processing. New York: Wiley-Interscience,
1991.
[10] A.C.Bovik, "Streaking in Median Filtered Images," IEEE Trans.
Acoust., Speech and Signal Processing, vol.ASSP-35, no.4, pp.493-503, April 1987.
[11] Y.H.Lee and S.A.Kassam(1985), "Generalized Median Filtering and Related Nonlinear Filtering Techniques," IEEE Trans. Acoust., Speech
and Signal Processing, vol.ASSP-33, pp.672-683, June 1985.
[12] G.R.Arce and M.P.McLoughlin, "Theoretical Analysis of Max/Median
Filters," IEEE Trans. Acoust., Speech and Signal Processing,
vol.ASSP-35, no.1, pp.60-69, Jan. 1987.
[13] A.Nieminen and P.Heinonen and Y.Neuvo, "A New Class of Detail
Preserving Filters for Image Processing," IEEE Trans. Pattern Anal.
and Mach. Intell., vol.PAMI-9, pp.74-90, Jan. 1987.
[14] P.Heinonen and Y.Neuvo, "FIR-Median Hybrid Filters," IEEE Trans.
Acoust., Speech and Signal Processing, vol.ASSP-35, pp.832-838, June
1987.
[15] G.R.Arce and R.E.Foster, "Detail Preserving Ranked-Order Based
Filters for Image Processing," IEEE Trans. Acoust., Speech and Signal
Processing, vol.ASSP-37, pp.83-98, Jan. 1989.
[16] R.Bernstein, "Adaptive Nonlinear Filters for Simultaneous Removal of
Different Kinds of Noise in Images," IEEE Trans. Circuits and
Systems, vol.CAS-34, no.11, pp.1275-1291, Nov. 1987.
[17] H.M.Lin and A.N.Willson,Jr., "Median Filters with Adaptive Length,"
IEEE Trans. Circuits and Systems, vol.CAS-35, no.6, pp.675-690, June
1988.
[18] L.Yin, R.Yang, M.Gabbouj and Y.Neuvo, "Weighted Median Filters: A
Tutorial," IEEE Trans. Circuits and Systems-II: Analog and Digital
Signal Processing, vol.43, no.3, pp.157-192, Mar. 1996.
[19] S.J.Ko and Y.H.Lee, "Center Weighted Median Filters and Their
Applications to Image Enhancement," IEEE Trans. Circuits and
Systems, vol.CAS-38, no.9, pp.984-993, Sept. 1991.
[20] Z.Wang and D.Zhang, "Progressive Switching Median Filter for the
Removal of Impulse Noise from Highly Corrupted Images," IEEE
Trans. Circuits and Systems-II:Analog and Digital Signal Processing,
Vol.46, No.1, pp.78-80, Jan.1999.
[21] T.Chen, K.K.Ma and L.H.Chen, "Tri-State Median Filter for Image
Denoising," IEEE Trans. Image Processing, Vol.8, No.12, pp.1834-
1838, Dec.1999.
[22] H.L.Eng and K.K.Ma, "Noise Adaptive Soft Switching Median Filter,"
IEEE Trans. Image Processing, Vol.10, No.2, pp.242-251, Feb.2001.
[23] S.Zhang and M.A.Karim, "A New Impulse Detector for Switching
Median Filters,"IEEE Signal Processing Letters, Vol.9, no.11, pp.360-
363, Nov.2002.
[24] T.C.Lin and P.T.Yu, "Salt-Pepper Impulse Noise Detection and
Removal Using Multiple Thresholds for Image Restoration," Journal of
Information Science and Engineering 22, 189-198, (2006).
[25] N.C.Gallagher,Jr. and G.L.Wise, "A Theoretical Analysis of the
Properties of Median Filters," IEEE Trans. Acoust., Speech and Signal
Processing, vol.ASSP-29, pp.1136-1141, Dec. 1981.
@article{"International Journal of Electrical, Electronic and Communication Sciences:53396", author = "E. Srinivasan and D. Ebenezer", title = "A Technique for Improving the Performance of Median Smoothers at the Corners Characterized by Low Order Polynomials", abstract = "Median filters with larger windows offer greater smoothing and are more robust than the median filters of smaller windows. However, the larger median smoothers (the median filters with the larger windows) fail to track low order polynomial trends in the signals. Due to this, constant regions are produced at the signal corners, leading to the loss of fine details. In this paper, an algorithm, which combines the ability of the 3-point median smoother in preserving the low order polynomial trends and the superior noise filtering characteristics of the larger median smoother, is introduced. The proposed algorithm (called the combiner algorithm in this paper) is evaluated for its performance on a test image corrupted with different types of noise and the results obtained are included.
", keywords = "Image filtering, detail preservation, median filters,nonlinear filters, order statistics filtering, Rank order filtering.", volume = "1", number = "9", pages = "1287-8", }
