Nonlinear Image Processing

CHAPTER 4: SD-ROM FILTER 131

Figure 4.12" The Lena image (a) corrupted by general streaks and (b) restored using the

SD-ROM-based approach.

Table 4.8: Restoration of Lena Image Corrupted by General Streaks.

Algorithm MAE MSE PSNR

Median filter (3x3) 3.28 38.8 32.3 dB

Median filter (5x5) 4.71 70.0 29.7 dB

SD-ROM-based approach 0.32 11.3 37.6 dB

Remarks:

1. In some cases, especially for images corrupted with thick streaks, improved

results are obtained if Step 1, Step 2, or both are performed twice.

2. For general streaks the performance of the algorithm becomes more depen-

dent on the threshold values selected in Step 1. Lower values (T1 = 4, T2 = 15,

T3 = 30, and T4 = 40) are suitable for smooth or highly corrupted images. If

excessive blurring is observed in the restored image, the thresholds can be

increased up to about T1 = 15, T2 = 30, T3 = 50, and T4 = 80.

Figure 4.12 and Table 4.8 illustrate the performance of this algorithm as applied

to the restoration of the Lena image corrupted by general streaks.

4.8 Concluding Remarks

In this chapter the SD-ROM method for the removal of impulse noise from image

data has been presented, in which the filtering operation is conditioned on the

132 EDUARDO ABREU

rank-ordered differences, defined as the differences between the input pixel and

the remaining rank-ordered pixels in a sliding window. Two algorithms have been

described, one based on a simple detection-estimation strategy involving thresh-

olds and another incorporating fuzzy rules. In the latter case, strategies for the

design of the weighting coefficients have been presented for recursive and nonre-

cursive implementation, including a least-squares derivation for the nonrecursive

case, which leads to a close form expression for the optimal weighting coefficients.

Computer simulation examples have been included to illustrate the effectiveness of

the SD-ROM method using several distinct noise types, including impulsive, Gaus-

sian, and mixed impulsive and Gaussian. Finally, a simple algorithm for restora-

tion of images corrupted by streaks, based on the SD-ROM approach, has been

described.

References

[Arc86] G. R. Arce, N. C. Gallagher, and T. Nodes. Median filters: theory and ap-

plications. In

Advances in Computer Vision and Image Processing,

(T. Huang,

ed.), JAI Press, Greenwich, CT (1986).

[Abr96b] E. Abreu, M. Lightstone, S. K. Mitra, and K. Arakawa. A new efficient

approach for the removal of impulse noise from highly corrupted images.

IEEE Trans. Image Process.,

Special Issue on Nonlinear Image Processing, 5(6),

1012-1025 (June 1996).

[Abr95] E. Abreu and S. K. Mitra. A signal-dependent rank ordered mean (SD-

ROM) filter--a new approach for removal of impulses from highly corrupted

images. In

Proc. Intl. Conf. on Acoustics, Speech, and Signal Processing,

Vol. 4,

pp. 2371-2374 (Detroit, MI, May 1995).

[Abr96a] E. Abreu and S. K. Mitra. A simple algorithm for restoration of images

corrupted by streaks. In

Proc. IEEE Intl. Symp. on Circuits and Systems,

pp.

730-733 (Atlanta, GA, May 1996).

[Ara95] K. Arakawa. A median filter based on fuzzy rules.

IEICE Trans.,

J78-A(2),

123-131 (February 1995) In Japanese.

[Ban93] G.J.F. Banon and A. L. B. Candeias. Restoration of NOAA images by mathe-

matical morphology. In

Proc. SIBGRAPI

V/, pp. 139-145 (1993). In Portuguese.

[Bov83] A. C. Bovik, T. Huang, and D. C. Munson. A generalization of median filter-

ing using linear combinations of order statistics.

IEEE Trans. Acoust. Speech

Signal Process.

31, 1342-1350 (December 1983).

[Cha98] C. Chandra, M. S. Moore, and S. K. Mitra. An efficient method for the

removal of impulse noise from speech and audio signals. In

Proc. IEEE Intl.

Symp. on Circuits and Systems,

Vol. 4, pp. 206-209 (Monterey, CA, June 1998).