ARTICLE IN PRESS

0165-1684/$ - se

doi:10.1016/j.si

�CorrespondE-mail addr

wluo@stmarytx

Signal Processing 87 (2007) 2017–2025

www.elsevier.com/locate/sigpro

Impulse noise removal utilizing second-order difference analysis

Dung Dang, Wenbin Luo�

Engineering Department, St. Mary’s University, San Antonio, TX 78228-8534, USA

Received 3 November 2006; received in revised form 16 December 2006; accepted 20 January 2007

Available online 16 February 2007

Abstract

The pending problem that research in random-valued impulse noise filtering has been facing is the inability to distinguish

noisy values that do not occur as extreme outliers in comparison with other surrounding pixels. In this paper, we propose a

new detection and filtering algorithm that consists of (1) a two-stage detection scheme that employs second-order

difference between pixels to determine the integrity of the image pixels and (2) a noise filtering process that estimates the

original value of each noisy pixel utilizing the information gathered from (1). Due to its unbiased detection criteria, this

method treats both fixed-valued and random-valued noise with extremely high detection rate.

r 2007 Elsevier B.V. All rights reserved.

Keywords: Image restoration; Impulse noise; Median filters; Noise detection

1. Introduction

Mechanical errors and environmental interfer-ence in noise-susceptible electronic equipments orcommunication channels lead to signal impurity [1].In the case of capturing or transmitting imagesignal, this impurity can be classified into severaltypes of image noise. Random occurrences ofenergy spikes of random amplitude generate im-pulse noise. Impulse noise can have fixed-value andrandom-value characteristics that both can bemodeled as follows:

Iði; jÞ ¼Oði; jÞ with probability 1� r;

xði; jÞ with probability r;

((1)

e front matter r 2007 Elsevier B.V. All rights reserved

gpro.2007.01.032

ing author.

esses: ddang@stmarytx.edu (D. Dang),

.edu (W. Luo).

where Oði; jÞ and Iði; jÞ denote the pixel values atlocation ði; jÞ of the original image and the noisyimage, respectively, and r represents the noise ratioof the image. The term xði; jÞ denotes a noise valueindependent from Oði; jÞ having equal probabilityr=2 of being either 0 or 255 in the case of fixed-valued impulse noise and having uniform distribu-tion between 0 and 255 in the case of random-valued noise [2]. It should be mentioned thatrandom bit errors also produce impulsive noise-likeeffects. The model of bit errors and other impulsivenoise models are discussed in [3]. Both color imagesand gray-scale images can be contaminated byimpulse noise. Several methods were proposed torestore the corrupted color images by using variousvector filtering techniques in the literature [31–37].In this paper, we will focus on gray-scale images anduse the model described in Eq. (1), as practiced in[4–30]. Recent works [4–30] have used the fact thatnoisy values usually occur as extreme outliers when

.

ARTICLE IN PRESSD. Dang, W. Luo / Signal Processing 87 (2007) 2017–20252018

compared with other pixels. Upon the constructionof a certain set of criteria or thresholds, separationof noise and original content could take place.However, the scenario becomes significantly morecomplex with random-valued noise. The differencebetween noise and image diminishes and sometimesbecomes extremely difficult to detect.

Our proposed method aims directly at combatingthis issue. It does not only take into account extremeoutliers but also evaluates the rate at which thedifferences between pixel values increase in order todetect sudden changes, one of the features thatdifferentiate noise from the uncorrupted pixels. Theproposed solution consists of two impulse detectionstages and one noise filtering stage. The secondimpulse detection stage refines the findings from thefirst stage while the noise filtering process utilizesthe refined detection results. The proposed algo-rithm exhibits better impulse noise removal abilitythan many other well-known methods, and requiresno previous training. In particular, it can removeimpulse noise from corrupted images very efficientlywhile preserving image details. The experimentalresults presented in this paper indicate that theproposed method performs significantly better thanmany other existing techniques.

The rest of the paper will lay out as follows.Section 2 briefly discusses difference analysis.Section 3 discovers the fundamental feature behinddiscriminating noise and discusses different noisedetection methods implementing the discoveredfeature. Section 4 displays some of the extensiveexperimental results and finally Section 5 concludesthe paper.

2. Difference analysis

Let us, first of all, define a few notations that willappear frequently in the paper. Let I denote thecorrupted, noisy image of size l1 � l2, and I i;j is itspixel value at position ði; jÞ, i.e., I ¼ fI i;j : 1pipl1; 1pjpl2g. Let W ði; jÞ also denote a local windowwith the size of ð2K þ 1Þ � ð2K þ 1Þ such as:

W ði; jÞ ¼ fIði � s; j � tÞj � KpspK ;�KptpKg.

(2)

Let X consist of the pixels from W ði; jÞ arranged inascending order such that:

X ð1ÞpX ð2ÞpX ð3Þ � � �pXðð2Kþ1Þ2Þ

where X ðkÞ 2W ði; jÞ. ð3Þ

During the noise detection process, the evaluationof the integrity of each pixel often utilizes the localwindow surrounding that pixel. One can observethat, statistically, the values of the local windowpixels from the original image would form a certainrange, ½Rmin;Rmax�, with Rmin being the minimumvalue and Rmax being the maximum value of thelocal window. While homogeneous regions intro-duce a small range of ½Rmin;Rmax� and edge-likeregions provide a larger range, this variation stillstays remotely smaller than ½0; 255�. Subsequently,the corruption process induces noise values thatbelong to three ranges: ½0;RminÞ, ½Rmin;Rmax�, andðRmax; 255�. Since the noise pixels in the middlegroup only slightly differ from the original pixels invalues and have minimum effect on the overallquality of the image, noise detection pays greaterattention to the other two groups of pixels, low-intensity and high-intensity noise. Among thesepixel groups, the ownership of the currentlyexamined pixel would reveal its integrity. Therefore,locating the boundaries that separate these twogroups from the center group, ½Rmin;Rmax�, enablessuch noise detection. These two groups requireseparate identification of each boundary due to thelack of correlation between them.

This incentive leads to the idea of dividing X atthe median position as follows:

X 1 ¼ X ðaÞ where 1pap½ð2K þ 1Þ2 þ 1�=2;

X 2 ¼ Xðbþ½ð2Kþ1Þ2�1�=2Þ where 1pbp½ð2K þ 1Þ2 þ 1�=2:

(4)

It is well known that a noisy pixel takes a gray valuesubstantially larger than or smaller than those of itsneighbors [11]. Therefore, the difference betweennoisy and noise-free pixels should significantlydeviate from the differences between surroundingadjacent pixels. This would mark the location of thesought boundary between noisy and noise-freepixels. Hence, in each subset, let us calculate thedifference between each pair of adjacent pixels andarrange the results in ascending order while map-ping which difference belongs to which pair ofadjacent pixels as follows:

L ¼ sort fX 1ðaÞ � X 1ða� 1Þ,

2pap½ð2K þ 1Þ2 þ 1�=2g,

U ¼ sort fX 2ðbÞ � X 2ðb� 1Þ,

2pbp½ð2K þ 1Þ2 þ 1�=2g. ð5Þ

ARTICLE IN PRESS

Fig. 1. An example of 3� 3 local window from image Lena

corrupted by random-valued impulse noise.

D. Dang, W. Luo / Signal Processing 87 (2007) 2017–2025 2019

One of the recent works, boundary discriminative noise

detection (BDND) [22], although presented in adifferent fashion, proposes to select the maximumdifference in each subset, L or U as the boundaryvalue. Subsequently, the corresponding pixel valuefrom the corresponding subset, X 1 or X 2, wouldbecome the lower or upper boundary, Bl or Bu,respectively. One might notice that while ½Rmin;Rmax�

denotes the range of original pixels, Bl signifies thelargest noise value smaller than Rmin and Bu signifiesthe smallest noise value greater than Rmax. Therefore,hypothetically if the mentioned detection methodperforms correctly, ½Rmin;Rmax� and ðBl;BuÞ shouldrepresent the same range. Consequently, the processidentifies the pixel Iði; jÞ as noise-free if it belongs tothe range ðBl;BuÞ, and noisy otherwise.

This method works well in the case of fixed-valued noise since noisy pixels can have only twovalues of 0 or 255, or only one value in each subsetX 1 or X 2. Hence there exists only one drasticchange between noisy pixels and noise-free pixels,allowing for easy noise identification. However, inthe case of random-valued noise, certain noisypixels might lie remotely close to the noise-freepixels which produce differences with values smallerthan the maximum difference. Such pixels might goundetected, as demonstrated in the example illu-strated in Fig. 1 for a 3� 3 window. Theuncorrupted pixels in white cells have values of101, 103, 104, 107 while the gray cells represent thenoise pixels. It can be easily shown for this examplethat the maximum differences in L and U are 40 and55, respectively. These differences correspond topixel values 10 and 205 generating the noise-free-accepted range of ð10; 205Þ. The noisy center pixel,80, nevertheless stays well within the said range,thus being kept undetected.

3. Proposed method

The proposed solution consists of two impulsedetection stages and one noise filtering stage. The

second impulse detection stage refines the findingsfrom the first stage.

3.1. Initial impulse detection

The proposed solution first obtains L and U fromthe samples inside the local 7� 7 window. In eachsubset, L or U, for 2pap25, both LðaÞ and UðaÞ

should be tested using the set of thresholds:

aðaÞ ¼ LðaÞoT1;

bðaÞ ¼ LðaÞ � Lða� 1ÞoT2;

gðaÞ ¼ LðaÞ=Lða� 1ÞoT3:

8><>: (6)

The first criteria is the difference value, LðaÞ,which should not exceed Rmax � Rmin, the maximumdifference between any two noise-free pixels. Thesecond criteria involves calculating the second-orderdifference between two adjacent difference values,i.e. LðaÞ � Lða� 1Þ. Similarly to second-order deri-vative for a function, this calculation helps pacifythe contrast between noise-free pixels from smoothand edgy regions while still separates them from theimpulsive noise values. The third criteria considersthe rate at which the differences change, i.e.LðaÞ=Lða� 1Þ for Lða� 1Þ40. A sudden jump witha large enough factor could also indicate a possiblenoise behavior. Utilizing these criteria to find thefirst disqualified difference, each subset can separateall extreme differences as well as locate thecorresponding pixel values in X 1 and X 2. Toefficiently adapt with the region of interest, the teststops at a difference that does not qualify any two ofthe three criteria. Extensive experiments on stan-dard test images [38] show that T1 belongs to arange ½10; 40�. A local window of size 7� 7 providesenough data, i.e. 49 pixel values, so that the averagedifference between values should remain relativelysmall. Therefore, for the sake of simplicity, T1 ¼ 15is used here. Similarly, common ranges for T2 andT3 are ½2; 10� and ½5; 15�, respectively. For ourtesting purposes, T2 ¼ 5 and T3 ¼ 10 were used.The process proceeds to the next step if LðaÞ fails atleast two of the three criteria or repeats itself foraþ 1 otherwise.

For each difference value equal to or greater thanLðaÞ, mark the corresponding pixel value in X 1 asnoise (or in X 2 for UðaÞ). Let Bl denote the largestnoise value in X 1 and Bu denote the smallest noisevalue in X 2. Identify Iði; jÞ as noise-free ifBloIði; jÞoBu and as noise otherwise.

ARTICLE IN PRESS

Table 3

Comparative results in PSNR (dB) for image Lena corrupted by

20% fixed-valued impulse noise and random-valued impulse

noise, respectively

Algorithm Fixed-

valued

impulses

Random-

valued

impulses

Median filter 28.57 29.76

Rank conditioned rank selection filter [7] 31.36 30.78

Switch I median filter [8] 31.97 31.34

Switch II median filter [8] 29.96 32.04

Median filter with adaptive length [9] 30.57 31.18

SD-ROM (M ¼ 1296, outside training

set) [11]

34.65 32.95

SD-ROM (M ¼ 1296, inside training set)

[11]

35.70 33.37

Tri-state median filter [14] 30.57 32.20

Decision-based median filter [15] 32.20 30.57

Fuzzy filter [16] 30.75 28.66

FM [12] with previous training 34.83 34.32

Long-range correlation method [20] 36.95 33.43

BDND [22] 36.13 21.96

The proposed approach 39.43 35.07

D. Dang, W. Luo / Signal Processing 87 (2007) 2017–20252020

3.2. Refined impulse detection

If the pixel Iði; jÞ did not pass the first noisedetection stage, it is a possible noise candidate.However, to eliminate extreme cases, more mea-sures need to take place before assuring thecorruption of the pixel. The extreme case entailsthe first stage identifying a noise-free pixel whichbelongs to an extreme edge as noisy. Therefore, ifIði; jÞ correlates to its neighbors with a certaindegree it can still qualify as an uncorrupted pixel.To determine whether its neighbors also possesssimilar characteristics the second stage utilizes thesimilar test described in the first stage, however,with a smaller 3� 3 window and different thresholdvalues. Hence, this stage repeats all the steps listedin the first stage with the exception of altering thecriteria set in step 5 as follows:

LðaÞ4H1;

LðaÞ � Lða� 1Þ4H2;

((7)

with H1 ¼ 25 and H2 ¼ 13. In this case, thealgorithm finishes if LðaÞ fails both criteria. Thefirst pixel that fails either criteria will set the noiseboundary for each subset. The algorithm then

Table 1

Undetected positives and false alarms for image Lena corrupted with fi

Noise (%) Undetected positives

Number Percentage (%)

10 0 0

20 0 0

30 0 0

40 0 0

50 0 0

60 0 0

70 0 0

Table 2

Undetected positives and false alarms for image Lena corrupted with r

Noise % Detection mises

Number Percentage (%)

10 3368 1.28

20 3264 1.25

30 3569 1.36

40 4105 1.57

50 5310 2.02

60 8371 3.19

70 12577 4.80

determines all noise pixels as well as the largestlow-intensity noise value, Bl, (for L) and thesmallest high-intensity noise value, Bu (for U) in a

xed-valued noise with ratio of 10–70%

False alarms Total noise

Number Percentage (%) Number

73 0.028 26 215

78 0.029 52 428

147 0.056 78 643

230 0.084 104 858

349 0.133 131 072

660 0.25 157 286

1054 0.4 183 501

andom-valued noise with ratio of 10–70%

False alarms Total noise

Number Percentage(%) Number

3996 1.52 26 215

9108 3.47 52 428

14 831 5.66 78 643

21 966 8.38 104 858

30 160 11.50 131 072

39 117 14.92 157 286

47 895 18.27 183 501

ARTICLE IN PRESSD. Dang, W. Luo / Signal Processing 87 (2007) 2017–2025 2021

similar fashion as in the first stage. The newthree regions constituted by the new values of Bl

and Bu will finally conclude the definite integrityof Iði; jÞ.

3.3. Noise filtering

The noise detection process resulted in dividing thelocal window pixels into two groups: good pixels G

and noise pixels N. Let Mði; jÞ denote the median ofgood pixels G in the local window since the exclusionof corrupted pixels in the filtering process reduces thedistortion generated in the restored image. Thismedian filter can be expressed as follows:

Mði; jÞ ¼ medianfIði � s; j � tÞ j Iði � s; j � tÞ 2 Gg.

(8)

Fig. 2. A comparison of restored images of Lena from the proposed me

of Lena, (b) Lena corrupted by 40% random-valued impulse noise, res

BDND.

The algorithm applies Mði; jÞ to all Iði; jÞ identifiedas corrupted while leaving the rest of the pixelsidentified as noise-free intact. In other words, therestoration of the image Y of size l1 � l2 appears asfollows:

Y ði; jÞ ¼Iði; jÞ if Iði; jÞ is noise-free;

Mði; jÞ if Iði; jÞ is noisy:

((9)

4. Experimental results

To test the performance of the proposed method,experiments were performed on standard 512� 512gray-scale images [38] and the results evaluatedusing two approaches. The first approach identifiesthe accuracy of the proposed detection, in other

thod and BDND for random-valued noise: (a) the original image

tored images of Lena utilizing (c) our proposed method, and (d)

ARTICLE IN PRESSD. Dang, W. Luo / Signal Processing 87 (2007) 2017–20252022

words, the number of unidentified noise pixels(undetected positives) and noise-free pixels mista-kenly identified as noisy (false alarms). This bench-

10 20 30 40 50 60 70

10

15

20

25

30

35

40

45

Noise ratio

PS

NR

BDND

Proposed Method

Fig. 3. Image Lena: comparison of the proposed method versus the BD

valued noise and (b) random-valued noise.

BDND

Proposed Method

10 20 30 40 50 60 70

10

15

20

25

30

35

40

Noise ratio

PS

NR

Fig. 4. Image Peppers: comparison of the proposed method versus the

fixed-valued noise and (b) random-valued noise.

mark identifies the perfect binary decision imagemapping the locations of noisy pixels during thenoise injection process to verify our proposed

BDND

Proposed Method

10 20 30 40 50 60 70

10

15

20

25

30

35

40

Noise ratio

PS

NR

ND algorithm with noise ratio from 10 to 70% for both (a) fixed-

BDND

Proposed Method

10 20 30 40 50 60 70

10

15

20

25

30

35

Noise ratio

PS

NR

BDND algorithm with noise ratio from 10 to 70% for both (a)

ARTICLE IN PRESSD. Dang, W. Luo / Signal Processing 87 (2007) 2017–2025 2023

algorithm. Two following tables display the totalmisdetection including both undetected positivesand false alarms of our algorithm.

Tables 1 and 2 display the detection rate includingthe numbers of undetected positives and falsealarms and their respective percentage against thetotal amount of pixels in the image Lena [38] forfixed-valued and random-valued noise, respectively.Table 1 clearly demonstrates that the proposedmethod performs extremely well on images con-taminated with fixed-valued noise since it treats thistype of noise as a special simplified case of generalimpulse noise. The perfect noise pixel detection ratesuggests that our proposed algorithm locates andcorrectly identifies every single noise pixel. Thenumber of false alarms has a minuscule contribu-tion to the total noise detection. Table 2 also showsexcellent detection results. The performance onrandom-valued noise cannot exceed that of fixed-valued noise due to certain noise pixels whose valuesstay well in the vicinity of the original pixels.Nevertheless, they contribute little effect to thecorruption of the image. Therefore, convincing datafrom Tables 1 and 2 confirm the extreme efficiencyof our detection scheme which performs closely toan ideal detection.

10 20 30 40 50 60 70

10

15

20

25

30

35

40

Noise ratio

PS

NR

BDND

Proposed Method

Fig. 5. Average of ten images: comparison of the proposed method vers

(a) fixed-valued noise and (b) random-valued noise.

The second quantitative evaluation of the experi-mental results involves calculating the peak signal-to-noise ratio (PSNR). Table 3 lists the results ofsome existing algorithms and includes our methodat the end of the table. The experiments utilize thetest image Lena corrupted by both 20% fixed-valued and random-valued noises. Table 3 clearlysuggests that for both fixed-valued and random-valued impulse noise, our method provides signifi-cant improvement over all the other approaches.Experiments with other images and different noiseratios also provide similar results.

Fig. 2 displays the results from processing a Lena

image corrupted with 40% random-valued noise,demonstrating the superior visual results obtainedby our proposed method when compared toBDND. Figs. 3–5 display comparative resultsbetween the recently developed method, BDND,with our proposed method under different testconditions including varying noise ratio from 10 to70% for both fixed-valued and random-valuednoise. We have tested 10 images, from which Lena,Peppers, and the average result of 10 images arechosen for demonstrations. Figs. 3–5 reveal that ourproposed method consistently outperforms BDNDfor fixed-valued noise and produces extremely

BDND

Proposed Method

10 20 30 40 50 60 70

14

16

18

20

22

24

26

28

30

32

34

Noise ratio

PS

NR

us the BDND algorithm with noise ratio from 10 to 70% for both

ARTICLE IN PRESSD. Dang, W. Luo / Signal Processing 87 (2007) 2017–20252024

superior results in comparison to those obtainedfrom BDND in the case of random-valued noise.This confirms the significant improvement that ourproposed method successfully achieves.

5. Conclusion

In this paper, we present an efficient algorithmthat efficiently detects and removes impulse noise ofboth categories: fixed-valued and random-valuednoise. By detecting the difference and the rate of thechanging difference in each local window, thismethod effectively isolates the noisy pixels fromthe uncorrupted contents. Only a lightweight, fast,and robust filtering is required in order to achieveexcellent results. Extensive testing and experimentalresults show the significant improvement that theproposed method provides over many other well-known algorithms.

Acknowledgments

We would like to thank the anonymous reviewersfor their helpful comments to improve the quality ofthis paper.

References

[1] R.C. Gonzalez, R.E. Woods, Digital Image Processing,

second ed., Prentice-Hall, Englewood Cliffs, New Jersey,

2001.

[2] I. Pitas, A.N. Venetsanooulos, Nonlinear Digital Filters:

Principles and Applications, Kluwer, Boston, MA, 1990.

[3] R. Lukac, K.N. Plataniotis, A Taxonomy of color image

filtering and enhancement solutions, in: P.W. Hawkes (Ed.),

Advances in Imaging and Electron Physics, vol. 140,

Elsevier, Academic Press, June 2006, pp. 187–264.

[4] A. Nieminen, P. Heinonen, Y. Neuvo, A new class of detail-

preserving filters for image processing, IEEE Trans. Pattern

Anal. Machine Intell. PAMI-9 (1) (1987) 74–90.

[5] J. Astola, P. Kuosmanen, Fundamentals of Nonlinear

Digital Filtering, CRC Press, Boca Raton, Florida, 1997.

[6] S.J. Ko, Y.H. Lee, Center weighted median filters and their

applications to image enhancement, IEEE Trans. Circuits

Syst. 38 (9) (1991) 984–993.

[7] R.C. Hardie, K.E. Barner, Rank conditioned rank selection

filters for signal restoration, IEEE Trans. Image Process. 3

(2) (1994) 192–206.

[8] T. Sun, Y. Neuvo, Detail-preserving median based filters in

image processing, Pattern Recognition Lett. 15 (April 1994)

341–347.

[9] H. Lin, A.N. Willson, Median filter with adaptive length,

IEEE Trans. Circuits Syst. 35 (6) (1988) 675–690.

[10] H. Hwang, R.A. Haddad, Adaptive median filters: new

algorithms and results, IEEE Trans. Signal Process. 4 (4)

(1995) 499–502.

[11] E. Abreu, M. Lightstone, S.K. Mitra, K. Arakawa, A new

efficient approach for the removal of impulse noise from

highly corrupted images, IEEE Trans. Image Process. 5 (6)

(1996) 1012–1025.

[12] K. Arakawa, Median filters based on fuzzy rules and its

application to image restoration, Fuzzy Sets Syst. 77 (1996)

3–13.

[13] T. Chen, H.R. Wu, Space variant median filters for the

restoration of impulse noise corrupted images, IEEE Trans.

Circuits Syst. II 48 (8) (2001) 784–789.

[14] T. Chen, K. Ma, L. Chen, Tri-state median filter for image

denoising, IEEE Trans. Image Process. 8 (12) (1999) 1834–1838.

[15] D. Florencio, R.W. Schafer, Decision-based median filter

using local signal statistics, Proc. SPIE 2308 (September

1994) 268–275.

[16] F. Russo, G. Ramponi, A fuzzy filter for images corrupted

by impulse noise, IEEE Signal Process. Lett. 3 (6) (1996)

168–170.

[17] T. Chen, H.R. Wu, Application of partition-based median

type filters for suppressing noise in images, IEEE Trans.

Image Process. 10 (6) (2001) 829–836.

[18] R. Garnett, T. Huegerich, C. Chui, W. He, A universal noise

removal algorithm with an impulse detector, IEEE Trans.

Image Process. 14 (11) (2005) 1747–1754.

[19] T. Chen, H.R. Wu, Adaptive impulse detection using center-

weighted median filters, IEEE Signal Process. Lett. 8 (1)

(2001) 1–3.

[20] Z. Wang, D. Zhang, Restoration of impulse noise corrupted

images using long-range correlation, IEEE Signal Process.

Lett. 5 (1) (1998) 4–7.

[21] S. Zhang, M.A. Karim, A new impulse detector for

switching median filters, IEEE Signal Process. Lett. 9 (11)

(2002) 360–363.

[22] P. Ng, K.K. Ma, A switching median filter with boundary

discriminative noise detection for extremely corrupted

images, IEEE Trans. Image Process. 15 (6) (June 2006)

1506–1516.

[23] R.H. Chan, C.W. Ho, M. Nikolova, Salt-and-pepper noise

removal by median-type noise detectors and detail-preser-

ving regularization, IEEE Transactions on Image Process.

14 (10) (October 2005) 1479–1485.

[24] Z. Wang, D. Zhang, Progressive switching median filter for

the removal of impulse noise from highly corrupted images,

IEEE Trans. Circuits Syst. 46 (1) (1999) 78–80.

[25] H.L. Eng, K.K. Ma, Noise adaptive soft-switching median

filter, IEEE Trans. Image Process. 10 (2) (2001) 242–251.

[26] R. Lukac, V. Fischer, G. Motyl, M. Drutarovsky, Adaptive

video filtering framework, Int. J. Imaging Syst. Technol. 14

(6) (December 2004) 223–237.

[27] Y. Hashimoto, Y. Kajikawa, Y. Nomura, Directional

difference-based switching median filters, Electron. Com-

mun. Jpn. 85 (2002) 22–32.

[28] A. Beghdadi, K. Khellaf, A noise-filtering method using a

local information measure, IEEE Trans. Image Process. 6

(1997) 879–882.

[29] J. Park, L. Kurz, Image enhancement using the modified

ICMmethod, IEEE Trans. Image Process. 5 (1996) 765–771.

[30] R. Berstain, Adaptive nonlinear filters for simultaneous

removal of different kinds of noise in images, IEEE Trans.

Circuits Syst. 34 (1987) 1275–1291.

[31] R. Lukac, B. Smolka, K.N. Plataniotis, A.N. Venetsano-

poulos, Vector sigma filters for noise detection and removal

ARTICLE IN PRESSD. Dang, W. Luo / Signal Processing 87 (2007) 2017–2025 2025

in color images, J. Visual Commun. Image Representation

17 (1) (February 2006) 1–26.

[32] Z. Ma, D. Fenga, H.R. Wu, A neighborhood evaluated

adaptive vector filter for suppression of impulse noise in

color images, Real-Time Imaging 11 (5–6) (October–

December 2005) 403–416.

[33] R. Lukac, K.N. Plataniotis, A.N. Venetsanopoulos, B.

Smolka, A statistically-switched adaptive vector median

filter, J. Intelligent Robotic Syst. 42 (4) (April 2005) 361–391.

[34] B. Smolka, A. Chydzinski, Fast detection and impulsive

noise removal in color images, Real-Time Imaging (Special

Issue on Multi Dimensional Image Processing) 11 (5–6)

(October–December 2005) 389–402.

[35] R. Lukac, Adaptive color image filtering based on center-

weighted vector directional filters, Multidimensional Syst.

Signal Process. 15 (2) (April 2004) 169–196.

[36] R. Lukac, Adaptive vector median filtering, Pattern Recog-

nition Lett. 24 (12) (August 2003) 1889–1899.

[37] S. Hore, B. Qiu, H.R. Wu, Improved vector filtering for

color images using fuzzy noise detection, Opt. Eng. 42 (6)

(June 2003) 1656–1664.

[38] hhttp://sipi.usc.edu/services/database/Database.htmli.