An improved 2-D median filter employing multishell concept to suppress impulse noise, is presented

Ghani, Farid

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___________________________________________ 0-7803-8560-8/04/$20.00©2004IEEE Improved 2-D Median Filter for On-Line Impulse Noise Suppression  Farid Ghani  School of Electrical and Electronic Engineering, Univesiti Sains Malaysia, 14300 Nibong Tebal, Penang, Malaysia Tel: +60-4-593-7788 x 6064, Fax: +60-4-594-1023, E-mail: fghani@eng.usm.my   Abstract—An improved 2-D median filter employing multishell concept to suppress impulse noise, is presented. The performance of proposed filter is evaluated over image ‘LENA’. The impulsive noise is added using MATLAB utility. The modified strategy reduces the number of replacement and results in better performance and simple hardware realization that is suitable for on-line implementation.  Index Terms—Median Filter, Multi-shell  Median Filter, Impulse Noise  I.  INTRODUCTION  In TV and other imaging systems, impulse noise is a common impairment. The standard T. V. broadcast signal is often contaminated with impulsive noise arising from various sources such as household electrical appliances and atmospheric disturbances. Broad banding of the signal further increases the level of impulsive noise. Various filters are proposed to suppress such impairments [1]. The median filter (MF) [1-2] is widely used for impulse noise suppression and the multishell median filter (MMF) [3] introduces the concept of missing line recovery. Although these filters have satisfactory performance, MMF fails to filter two impulse noises in the same processing window. Moreover, these filters tend to blur the images due to too many replacements. C. J. Juan proposed a modified multishell median filter (MMMF) [4], which removes most of the shortcomings associated with the MF and the MMF. However, it is observed that under certain conditions, to be discussed in the following sections, MMMF fails to perform the desired filtering operation. Moreover, the number of calculations/replacements involved on the basis of MIN/MAX conditions is still too large and makes the filter difficult to realize, particularly for real time applications.  In this paper, the threshold strategy of MMMF is modified so that:  (a) effective noise filtering operations are performed under all conditions, and         (b) number of calculations / replacements is reduced and simplified. This results in a simple hardware realization of the filter.  II. PROPOSED MODIFICATION  Consider a 3x3-processing window, with P5 as the central pixel, as shown in Figure 1.   P1 P2 P3P4 P5 P6P7 P8 P9 Fig. 1.  A 3 x 3 processing window  The output of MMMF as proposed in [4] is ⎪⎩⎪⎨⎧<<<>=[S]Min   P if )P,(PMin [S]Max   P  [S]Min  if P[S]Max   P if )P,(PMax   y)(x,Output 58255582              (1) Where S is the set of samples surrounding central pixels except (P4, P6) i.e.  S = {P1, P2, P3, P7, P8, P9}                 (2) The principle involved in the replacement strategy of Equation (1) is that if P5 is corrupted by noise, it is better to replace its gray level by P2 or P8 than by using Min[S] or Max[S]. Also, due to missing lines error, since P4 and P6 may be lost, they are not considered in Equation (2).  The limitation of Equation (1) is that when Min[S] or Max[S] are also corrupted by impulse noise, i.e. either Min[S] or Max[S] is equal to P5, Equation (1) fails to perform the desired filtering operation. To overcome this limitation following modifications in the replacement strategy of Equation (1), are proposed.  591     ⎪⎩⎪⎨⎧≤<<≥=[S]Min   P if )P,(PMin [S]Max   P  [S]Min  if P[S]Max   P if )P,(PMax   y)(x,Output   58255582   (3) It has been observed that for more than 70-80% points in an image, the gray level distances of P5 from (P2 or P8) and from Max[S] are below 16. This is shown in Fig. 2 for the image ‘LENA’. This fact is used to further reduce unnecessary replacements, thereby reducing the blurring of the images. Thus taking into consideration the gray level distribution of Figure 2, the proposed replacement strategy of Equation (3) can be further modified as   ⎪⎩⎪⎨⎧≥≥−=otherwise  P16  P - [S]Min  if )P,(PMin 16  [S]Max   P if )P,(PMax    y)(x,Output 5582582 (4)  Equation 4 indicates that replacing action takes place only when the distance between P5 and Max[S] or Min[S] is no smaller than 16. This strategy thus  avoids the unnecessary replacements and reduces blurring of the images. Moreover it can be implemented using simple comparators and subtractors.                 Fig. 2.  Gray level distances between central point and its neighboring points for the image ‘LENNA’  III. RESULTS  Figure  3   shows   the    original    image ‘LENNNA’  and  Figure 4 shows the same image when corrupted with impulse noise. Results of median filter and the proposed filter are given in Figures 5 and 6, respectively. Comparing Figures 5 and 6, it is observed that the result of the proposed filter is much better than those obtained using the median filter. Although, the median filter removes the impulsive noise effectively, however, the image gets blurred. The proposed filter removes the impulsive noise and also preserves the details of the image.                   Fig. 3. Image LENNA scanned at 100 dpi and 8 bits/pixel                   Fig. 4. Image LENNA corrupted with impulse noise                   Fig. 5. Output of the Median Filter      ∃ ∃∃ ∃ ∃ ∃ ∃ ∃ ∃ ∃ ∃ ∃ ∃ ∃ ∃ ∃∋ ∋∋ ∋ ∋ ∋ ∋ ∋ ∋ ∋ ∋ ∋ ∋ ∋ ∋ ∋0 2 4 6 8 10 12 14 16Gray Level Distances 0 2000 4000 6000 8000 10000 N 0. o f P I X E L sl  I   P5-Max(P2, P8)  I I P5 - Max(s)  I 592                   Fig. 6. Output of the proposed filter  IV. CONCLUSIONS  A multishell filter employing the modified replacement strategy  is  presented  in   this  paper. The  modified  filter  effectively suppresses the impulse noise. It uses threshold conditions that require fewer comparisons and replacements and is faster as compared to the other multishell median filters. Moreover, it can be realized using simple comparators and subtractors and hence can be effectively used in real time applications.  V.  REFERENCES  [1]. GONZALEZ, RAFAEL C AND WINTZ, P. : 1987 ‘DIGITAL IMGAE PROCESSING’ MA: ADDISION WESLEY.    [2] Pertman, S. S. , Eisenhandler, S., Lyons, P. W.  and Shumila, M. J. 1987 ‘Adaptive median filtering for impulse noise elimination in real time TV signals’, IEEE Trans. Communication, , COM-35, pp. 646-652. [3] Siu, Jim, Li, Jimmy, and Luthi, Stefan: ‘A real time 2-D median based filter for vedio signals’, May 1993, IEEE Trans. on Consumer Electronics, , Vol. 39, no.2, pp. 115-121. [4] Juan, C. J. Feb. 1995, ‘Modified 2-D median filter for impulse noise suppression in a real time   system’, IEEE Trans. on Consumer Electronics, , Vol. 41, no. 1, pp. 73-81.           593JACOBI MOMENTS AS IMAGE FEATURESPew-Thian Yap Raveendran ParamesranDepartment of Electrical EngineeringUniversity of Malaya, Malaysiaemail: ptyap@time.net.my, ravee@um.edu.myABSTRACTIn this paper, we introduce a set of moments which isbased on Jacobi polynomials. The set of Jacobi poly-nomials are orthogonal and this ensures minimal infor-mation redundancy between the moments. By chang-ing the parameters α and β, it is shown that the mo-ments are able to extract both global and local fea-tures. This is unseen in moments such as geometric,Legendre and Zernike moments as they are all globalmoments. This means that, by using Jacobi moments,local information at a particular position of the im-age can be extracted. Experimental results are givento support these claims.1. INTRODUCTIONBack in 1962, Hu [1] started using geometric momentsfor image pattern recognition. Hu’s moments are in-variant to rotation, scale change and translation andthis is especially important for the recognition task forpatterns under different orientations. One importantdevelopment in moments in the field of image process-ing is done by Teague [2]. Teague introduced the no-tion of orthogonal moments. In particular, Legendreand Zernike moments are proposed by Teague as im-age features. Recent development in image momentsincludes [3]–[8]. Mukundan et al. [3] set of discreteTchebichef moments which are well-suited for digitialimages since no approximation is needed in the pro-cess of computing the moments. The set of Krawt-chouk moments was proposed by Yap et al. [6]. Aninteresting of property of Krawtchouk moments is thatthe moments are local moments, that is, informationextracted by Krawtchouk moments is from only a por-tion of the image.In this paper, we introduce a set of moments which isbased on the set of Jacobi polynomials, {Pn(x;α, β)}.Depending on the values of α and β, Jacobi poly-nomials have many well-known special cases. Whenα = β = λ − 12 , λ 6= 0, we have the Gegenbaueror Ultraspherical polynomials. When α = β = − 12and α = β = − 12 , we have the Chebyshev polyno-mials of the first and second kind, respectively. Whenα = β = 0, we have the Legendre or Spherical poly-nomials. Our intention here is not to limit ourselvesto these special cases; arbitrary values for α and β areconsidered instead.0-7803-8560-8/04/$20.00 c©2004IEEEThe set of Jacobi polynomials are orthogonal andthis ensures minimal information redundancy betweenthe moments. By changing the parameters α and β,it is shown that the moments are able to extract bothglobal and local features. Hence, Jacobi moments en-compass the properties of both the global moments(e.g. geometric, Legendre, Zernike and Tchebichefmoments) and local moments (e.g. Krawtchouk mo-ments). Experimental results are given to support theseclaims.2. JACOBI POLYNOMIALSThe kernel of the Jacobi moments consists of the set ofJacobi polynomials. The Jacobi polynomial of the n-thorder, with parameters α and β, is defined as [9]:Pn(x;α, β) =(α+ 1)nn!×2F1( −n, n+ α+ β + 1α+ 1∣∣∣∣1− x2)(1)where x ∈ [−1, 1]. The generalized hypergeometricfunction, rFs, is defined as:rFs(a1, . . . , arb1, . . . , br∣∣∣∣ z ) = ∞∑k=0(a1, . . . , ar)k(b1, . . . , br)kzkk!(2)where (a1, . . . , ar)k = (a1)k, . . . , (ar)k and thePochhammer-symbol:(a)k = a(a+ 1)(a+ 2) . . . (a+ k − 1) (3)with k = 1, 2, 3, . . . and (a)0 = 1. The Jacobi poly-nomials can be written in teh Rodrigues-type formulaas:(1− x)α(1 + x)βPn(x;α, β) =(−1)n2nn!(ddx)n [(1− x)n+α(1 + x)n+β] . (4)For α > −1, β > −1, the set of Jacobi polyno-mials satisfy the orthogonality condition:∫ −1−1w(x;α, β)Pm(x;α, β)Pn(x;α, β)dx =ρ(n;α, β)δmn, (5)594

Improved 2-D Median Filter For On-Line Impulse Noise Suppression.

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Improved 2-D Median Filter For On-Line Impulse Noise Suppression.

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