A new class of multichannel image processing filters: vector median-rational hybrid filters

IEICE TRANS. INF. & SYST., VOL.E82–D, NO.12 DECEMBER 19991589

PAPER

A New Class of Multichannel Image Processing Filters:

Vector Median-Rational Hybrid Filters

Lazhar KHRIJI† and Moncef GABBOUJ†, Nonmembers

SUMMARY A new class of nonlinear filters called VectorMedian Rational Hybrid Filters (VMRHF) for multispectral im-age processing is introduced and applied to color image filteringproblems. These filters are based on Rational Functions (RF).The VMRHF filter is a two-stage filter, which exploits the fea-tures of the vector median filter and those of the rational opera-tor. The filter output is a result of vector rational function oper-ating on the output of three sub-functions. Two vector median(VMF) sub-filters and one center weighted vector median filter(CWVMF) are proposed to be used here due to their desirableproperties, such as, edge and details preservation and accuratechromaticity estimation. Experimental results show that the newVMRHF outperforms a number of widely known nonlinear filtersfor multispectral image processing such as the Vector Median il-ter (VMF) and Distance Directional Filters (DDf) with respectto all criteria used.key words: rational functions, vector rational filters, vectormedian filters, vector median-rational hybrid filters

1. Introduction

Multichannel image processing is investigated in thispaper using a vector approach [10]. This has beenproved to be more appropriate for vector-valued signalscompared to traditional component-wise approaches.The suitability of such a technique is often creditedto the inherent correlation that exists between the im-age channels [10]. In the vector approach, each imageelement is considered as an m-dimensional vector (mis the number of image channels). Color image pix-els are often represented by three-component vectors,m = 3, whose characteristics, i.e., magnitude and di-rection are examined. The vector’s direction signifiesits chromaticity; while, its magnitude is a measure ofits brightness. A number of vector processing filtershave been proposed in the literature for the purposeof color image processing [2], [11]. One class of filtersconsiders the distance in the vector space between theimage vectors; typical representative of this class is the“vector median filter” (VMF) [1]. A second class of fil-ters, called “vector directional filters” (VDF) [16], op-erates by considering the vectors’ direction. VMFs arederived as maximum likelihood estimators for an expo-nential distribution [1]; while, VDFs are spherical esti-mators, when the underlying distribution is a spheri-

Manuscript received November 19, 1998.Manuscript revised June 30, 1999.

†The authors are with the Signal Processing Laboratory,Tampere University of Technology, P.O. Box 553 FIN-33101Tampere, Finland.

cal one [16]. A third class of filters uses rational func-tions in its input/output relation, and hence the name“vector rational filters” (VRF) [6]. There are severaladvantage to the use of this function. Similarly to apolynomial function, a rational function is a universalapproximator (it can approximate any continuous func-tion arbitrarily well); however, it can achieve a desiredlevel of accuracy with a lower complexity, and possessesbetter extrapolation capabilities. Moreover, it has beendemonstrated that a linear adaptive algorithm can bedevised for determining the parameters of this struc-ture [9].

In this paper, a novel nonlinear vector filter classis proposed: the class of vector median-rational hybridfilters (VMRHFs). This is an extension of the nonlin-ear rational type hybrid filters called median-rationalhybrid filter’s (MRHFs) recently introduced for 1-Dand 2-D signal processing [7], [8], based on rational fil-ters [9], [15]. The VMRHF is formed by three sub-filters(two vector median filters and one center weighted vec-tor median filter) and one vector rational operation.VMRHF are very useful in color (and generally multi-channel) image processing, since they inherit the prop-erties of their ancestors. They constitute very accurateestimators in long- and short-tailed noise distributionsand, at the same time, preserve the chromaticity of thecolor image. Moreover, they act in small window andrequire few number of operations, resulting in simpleand fast filter structures.

This paper is organized as follows. Section 2 brieflyreviews rational functions and vector rational functionfilters. In Sect. 3, we define the vector median-rationalhybrid filter (VMRHF) and point out some of its im-portant properties. The proposed filter structures arepresented in Sect. 4. Section 5 includes simulation re-sults and discussion of the improvement achieved by thenew VMRHF. In order to incorporate perceptual crite-ria in the comparison, the error is measured in the theuniform L∗a∗b∗ color space, where equal color differ-ences result in equal distances [14]. Section 6 concludesthe paper.

2. Rational Function and Vector RationalFunction Filters

A rational function is the ratio of two polynomials. Tobe used as a filter, it can be expressed as:

1590IEICE TRANS. INF. & SYST., VOL.E82–D, NO.12 DECEMBER 1999

y =

a0 +n∑

i=1

a1ixj +n∑

i=1

n∑j=1

a2ijxixj + · · ·

b0 +n∑

i=1

b1ixi +n∑

i=1

n∑j=1

b2ijxixj + · · ·, (1)

where x1, x2, . . . , xn are the scalar inputs to the filterand y is the filter output, a0, b0, aij and bij are filterparameters.

The representation described in Eq. (1) is uniqueup to common factors in the numerator and denomi-nator polynomials. The RF (Rational Function) mustclearly have a finite order to be useful in solving prac-tical problems. Like polynomial functions, a rationalfunction is a universal approximator [9]. Moreover, it isable to achieve substantially higher accuracy with lowercomplexity and possesses better extrapolation capabil-ities than polynomial functions.

Straight forward application of the rational func-tions to multichannel image processing would be basedon processing the image channels separately. This how-ever, fails to utilize the inherent correlation that is usu-ally present in multichannel images. Consequently, vec-tor processing of multichannel images is desirable [10].The generalization of the scalar rational filter defini-tion to vector and scalar signals alike is given by thefollowing definition.

Definition 2.1: Let x1,x2, . . . ,xn be the n input vec-

tors to the filter, where xi =[x1

i , x2i , . . . , x

mi

]T

and

xki ∈ {0, 1, . . . ,M}, M is an integer. The VRF output

is given by

V RF = RF[x1,x2, . . . ,xn

]

=P (x1,x2, . . . ,xn)Q(x1,x2, . . . ,xn)

=[rf1, rf2, . . . , rfm

]T

(2)where P is a vector-valued polynomial and Q is a scalarpolynomial. Both are functions of the input vectors.The ith component of the VRF output is written as

rf i =[P i(x1,x2, . . . ,xn)Q(x1,x2, . . . ,xn)

]∈ {0, 1, . . . ,M} (3)

where

P i(x1,x2, . . . ,xn) = a0 +n∑

k=1

akxik (4)

+n∑

k1=1

n∑k2=1

ak1k2xik1xi

k2+ · · ·

(5)

and

Q(x1,x2, . . . ,xn) = b0 +n∑

j=1

n∑k=1

bjk‖xj − xk‖p

(6)

‖.‖p is the Lp-norm, and the square braket notationused in Eq. (3) above, [α] refers to the integer part ofα, α ∈ R+. b0 > 0, bij are constant, and ai1,i2,...,ir

used in Eq. (4) is a function of the input vectors:

ai1,i2,...,ir = f(x1,x2, . . . ,xn). (7)

When the vector dimension is 1, the VRF reduces to aspecial case of the scalar RF

3. Vector Median-Rational Hybrid Filters(VMRHF)

When extending the median-rational hybrid operationto vector-valued signals, we place some requirements onthe resulting vector median-rational hybrid operation:

• The operation should have properties similar tothose of the scalar case.

• It should have robust data smoothing ability fordifferent i.i.d. noise distributions (Gaussian, im-pulsive, mixed Gaussian-impulsive), while retain-ing sharp edges in the signal.

• It reduces to the scalar filter if the vector dimensionis 1.

3.1 Vector Median-Rational Hybrid Filters

Let f(x) : Z l → Zm, represent a multichannel signaland W ∈ Zl be a window of finite size n (filter length).l represents the signal dimensions and m the number ofsignal channels. The pixels in W will be denoted as xi,i = 1, 2, . . . , n and f(xi) will be denoted as f i. f i are m-dimensional (m ≥ 2) vectors in the vector space definedby the m signal channels. The VMRHF is defined next.

Definition 3.1: the output vector y(f i) of the VM-RHF is the result of a vector rational function tak-ing into account three input sub-functions which forman input functions set {Φ1,Φ2,Φ3}, where the “centralone” (Φ2) is fixed as a center weighted vector mediansub-filter

y(f i) = Φ2(f i) +

3∑j=1

αjΦj(f i)

h+ k||Φ1(f i)− Φ3(f i)||2(8)

where ||.||2 is the L2-vector norm, α = [α1, α2, α3] char-acterizes the constant vector coefficient of the inputsub-functions. In this approach, we have chosen a verysimple prototype filter coefficients which satisfies thecondition:

∑3i=1 αi = 0. In our study, α = [1,−2, 1]T .

h and k are some positive constants. The parameter kis used to control the amount of the nonlinear effect.

The sub-filters Φ1 and Φ3 are chosen so that an accept-able compromise is achieved between noise reduction,edge and chromaticity preservation. It is easy to ob-serve that this VMRHF differs from a linear low-pass

KHRIJI and GABBOUJ: A NEW CLASS OF MULTICHANNEL IMAGE PROCESSING FILTERS1591

filter mainly for the scaling, which is introduced on theΦ1 and Φ3 terms. Indeed, such terms are divided by afactor proportional to the output of an edge-sensingterm characterized by the Euclidean distance of thevector difference (Φ1 − Φ3). The weight of the vectormedian-operation output term is accordingly modified,in order to keep the gain constant. The behavior ofthe proposed VMRHF structure for different positivevalues of parameter k is described next.

• k � 0, the form of the filter is given as a linearlowpass combination of the three nonlinear sub-functions:

y(f i) = c1Φ1(f i) + c2Φ2(f i) + c3Φ3(f i), (9)

where coefficients c1, c2, and c3 are some constants.• k → ∞, the output of the filter is identical to the

central sub-filter output and the vector rationalfunction has no effect:

y(f i) = Φ2(f i). (10)

• For intermediate values of k, the ||Φ1(f i)−Φ3(f i)||2term perceives the presence of a detail and accord-ingly reduces the smoothing effect of the operator.

Therefore, the VMRHF operates as a linear lowpassfilter between three nonlinear suboperators, the coef-ficients of which are modulated by the edge-sensitivecomponent.

4. The Proposed Filter Structures

Vector Median-Rational Hybrid Filters (VMRHFs) arepromising detail preserving filtering structures [8] sinceit was shown that every subfilter is able to preservesignal details within their subwindows. VMRHFs aregrouped into two classes: unidirectional VMRHFs andbidirectional VMRHFs. The structures for a 3×3 win-dow unidirectional VMRHF and a bidirectional VM-RHF are shown in Figs. 1 (a) and (b), respectively.Only the points indicated in black in each window maskare used in the corresponding operation.

Unidirectional VMRHFs are designed to preserveimage details along the vertical, horizontal and the twodiagonal directions. Therefore, the samples of the samevalue neighborhood must be located along those direc-tions in order to preserve the center sample by unidirec-tional VMRHFs. On the other hand, bidirectional VM-RHFs can preserve details within the two correspondingdirections in one operation.

The central subfilter is a center weighted vectormedian filter characterized by its high detail preser-vation capability. One of the following three sets ofweights can be used depending the noise properties andthe image details [4]. Mask M1 emphasizes details inthe horizontal and vertical directions, while M2 the twodiagonal directions. On the other hand, mask M3 seeks

Fig. 1 Structures of VMRHF. (a) The unidirectional structure,(b) the bidirectional structure.

details in all of these directions simultaneously.

M1

0 1 0

1 3 10 1 0

M2

1 0 1

0 3 01 0 1

M3

1 1 1

1 3 11 1 1

5. Experimental Results

VMRHF have been evaluated, and their performancehas been compared against those of some widely knownvector nonlinear filters: the vector median filter (VMF),the distance directional filter (DDF), the generalizedvector directional filter (GVDF) [13] and the marginalmedian-rational hybrid filter (m-MRHF), using RGBcolor images.

The noise attenuation properties of the differentfilters are examined by utilizing two color images: (1)part of Lena image (256 × 256), see Fig. 2 (a); and (2)the roze image (240× 150), see Fig. 2 (b). The test im-ages have been contaminated using various noise sourcemodels in order to assess the performance of the filtersunder different scenarios:

• Gaussian noise, N (0, σ2).• Impulsive noise: each image channel is corrupted

independently using salt and pepper noise. We

1592IEICE TRANS. INF. & SYST., VOL.E82–D, NO.12 DECEMBER 1999

Fig. 2 Test color images. (a) Lena image, (b) roze image.

assume that both salt and pepper are equally likelyto occur.

• Mixed Gaussian-impulsive noise: the impulsivenoise is fixed (salt and pepper 2% in each imagechannel), while the variance of the Gaussian noiseis varied.

The original image, as well as its noisy versions,are represented in the RGB color space. This colorcoordinate system is considered to be objective, sinceit is based on the physical measurements of the colorattributes. The filters operate on the images in theRGB color space.

A number of different objective measures can beutilized for quantitative comparison of the performanceof the different filters. These criteria provide some mea-sure of closeness between two digital images by exploit-ing the differences in the statistical distributions of thepixel values [3]. The most widely used measures arethe mean absolute error (MAE), and the mean squareerror (MSE) defined as:

MAE =1

MN

M∑i=1

N∑j=1

||yi, j − di, j||1 (11)

MSE =1

MN

M∑i=1

N∑j=1

||yi, j − di, j||22 (12)

where M , N are the image dimensions, yi, j is the vec-

tor value of pixel (i, j) of the filtered image, di, j is thecorresponding pixel in the original noise free image, and||.||1, ||.||2 are the L1- and L2-vector norm, respectively.

Notwithstanding the RGB is the most popularcolor space used conventionally to store, process, dis-play and analyze color images, the human perceptionof color cannot be described using the RGB model [14].Consequently, measures such as the mean square er-ror defined in the RGB color space is not appropriateto quantify the perceptual error between images. Itis therefore important to use color spaces which areclosely related to the human perceptual characteris-tics and suitable for defining appropriate measures ofperceptual errors between color vectors. A number ofsuch color spaces are used in areas such as multimedia,video communications (e.g., high definition television),motion picture production, the printing industry, andgraphic arts. Among these, perceptually uniform colorspaces are the most appropriate to define simple yetprecise measures of perceptual errors. The Commis-sion Internationale de l’Eclairage (CIE) standardizedtwo color spaces, L∗u∗v∗ and L∗a∗b∗, as perceptuallyuniform [5].

Conversion from RGB to L∗a∗b∗ color space is ex-plained in detail in [5]. RGB values of both the orig-inal noise free and the filtered image are converted tocorresponding L∗a∗b∗ values for each of the filteringmethod under consideration. In the L∗a∗b∗ space, theL∗ component defines the lightness, and the a∗ and b∗

components together define the chromaticity.In L∗a∗b∗ color space, we computed the normalized

color difference (NCD) [12] which is estimated accord-ing to the following expression:

NCD =

M∑i=1

N∑j=1

||�ELab||

M∑i=1

N∑j=1

||E∗Lab||

(13)

where �ELab is the perceptual color error between twocolor vectors and defined as the Euclidean distance be-tween them, given by

�ELab = [(�L∗)2 + (�a∗)2 + (�b∗)2]12 , (14)

where �L∗, �a∗, and �b∗ are the differences in the L∗,a∗, and b∗ components, respectively. E∗

Lab is the mag-nitude of the original image pixel vector in the L∗a∗b∗

space and given by

E∗Lab = [(L∗)2 + (a∗)2 + (b∗)2]

12 .

The results obtained are shown in the form of plots inFigs. 3–5 for the three noise models: Gaussian, impul-sive, and Gaussian mixed with impulsive, respectively.The simulation results of the two structures of the VM-RHF are very close to each other (slight differences), we

KHRIJI and GABBOUJ: A NEW CLASS OF MULTICHANNEL IMAGE PROCESSING FILTERS1593

Fig. 3 Comparative results for the images in Fig. 2 contaminated by Gaussian noise.(a) Lena image, (b) roze image.

Fig. 4 Comparative results for the images in Fig. 2 contaminated by impulsive noise(salt and pepper). (a) Lena image, (b) roze image.

Fig. 5 Comparative results for the images in Fig. 2 contaminated by mixed noise (saltand pepper 2% in each component, and Gaussian with zero mean and variable variance).(a) Lena image, (b) roze image.

1594IEICE TRANS. INF. & SYST., VOL.E82–D, NO.12 DECEMBER 1999

Fig. 6 Results for the Lena image (Fig. 2 (a)). (a) Contami-nated image by mixed noise (impulsive 2% in each channel andGaussian with zero mean and variance 50). Images (b), (c) and(d) are the processed images by the DDF, VMF and VMRHF,respectively.

hence reported only those provided by the bidirectionalstructure given by Fig. 1 (b).

As can be verified from the plots, the VMRH fil-ters provide better results than those obtained by anyother filter under consideration. Recall that VMRHfilter uses no information about the type and the de-gree of noise corruption. Moreover, consistent resultshave been obtained when using a variety of other colorimages and the same evaluation procedure.

The filtered images are presented for visual assess-ment, since in many cases they are, ultimately, the bestsubjective measure of the efficiency of image processingtechniques. Figures 6 (a) and 7 (a) show the corruptedimages by mixed noise (impulsive 2% in each channeland Gaussian N (0, 50)) of Lena and roze, respectively.Figures 6 (b)–(d) represent the filtered images by DDF,VMF and VMRHF, respectively for Lena image. Fig-ures 7 (b)–(d) show the same representation procedurefor the roze image. All the filters considered operateusing a square 3 × 3 processing window.

Vector processing, i.e. VMRHF, produced bet-ter results compared to marginal (component-wise) fil-tering, i.e. marginal MRHF. The marginal median-rational hybrid filter fails to take into account the de-pendence between the components (i.e. the interchannelcorrelation).

The new VMRH filter outperforms the GVDFwhich uses a priori knowledge about the actual noisecharacteristics to optimize its performance.

Fig. 7 Results for the roze image [Fig. 2 (b)]. (a) Contami-nated image by mixed noise (impulsive 2% in each channel andGaussian with zero mean and variance 50). Images (b), (c) and(d) are the processed images by the DDF, VMF and VMRHF,respectively.

Fig. 8 (a) Part (128×128) of the color Lenna image corruptedwith additive (4% in each channel) impulsive noise. (b)–(f) re-sults using the DDF, the GVDF, the VMF, the marginal MRHFand the VMRHF, respectively.

An additional sample processing results are pre-sented in Figs. 8 (a)–(f). Figure 8 (a) shows a part(128 × 128) of color Lenna image corrupted with ad-

KHRIJI and GABBOUJ: A NEW CLASS OF MULTICHANNEL IMAGE PROCESSING FILTERS1595

ditive (4% in each channel) impulsive noise. Fig-ures 8 (b)–(f) present the results using the DDF, theGVDF, the VMF, the marginal MRHF and the VM-RHF respectively. A comparison of the images clearlyfavors the proposed VMRHF over its counterparts(VMF, GVDF, DDF, and Marginal MRHF). The pro-posed VMRHF can effectively remove impulses, smoothout nominal noise and keep edges, details and color uni-formity unchanged as we can see from the related errormeasures summarized in the plots.

Furthermore, it is worth mentioning that the pro-posed filter has comparable computational complexityto those used in the comparison, particularly the VMF.The vector rational operation does not introduces sig-nificant additional computational cost. In the absenceof any fancy or fast algorithms, the number of com-parators used in the median filter with a window ofsize n is Nc = n(n−1)

2 . According to Figs. 1 (a)–(b), thefirst stage of the VMRHF requires 41 comparators: 10comparators for Φ1 (n1 = 5), 10 comparators for Φ3

(n3 = 5) and 21 comparators for Φ2 (n2 = 7). Thesecond stage requires a small look-up table for the de-nominator, one multiplication, three additions and onedivision per output sample.

6. Conclusions

Median-Rational Hybrid Filters are extended in this pa-per to vector-valued signals and applied to multidimen-sional image processing. The vector median-rationalhybrid filter is a vector rational operation over threesub-filters in which the middle one is a center weightedvector median filter. These new filters exhibit very de-sirable filtering properties and utilize in an effective waythe performance of the vector rational function filtersand the features of vector median filters. Simulationresults and subjective evaluation of the filtered imagesindicate that the VMRHFs outperform all other filtersunder consideration. Vector processing has also provedto produce better results than marginal (component-wise) processing. Moreover, as it can be seen from theprocessed images, the VMRHF preserve the chromatic-ity component of the processed color images.

References

[1] J. Astola, P. Haavisto, and Y. Neuvo, “Vector median fil-ter,” Proc. IEEE, vol.78, pp.678–689, April 1990.

[2] J. Astola and P. Kuosmanen, Fundamentals of NonlinearDigital Filtering, CRC Press, Boca Raton, New York, 1997.

[3] A.M. Eskicioglo, P.S. Fisher, and S. Chen, “Image qualitymeasures and their performance,” IEEE Trans. Commun.,vol.43, pp.2959–2965, 1995.

[4] M. Gabbouj, P. Haavisto, and Y. Neuvo, “Recent advancesin median filtering,” Communications, Control and SignalProcessing, ed. E. Arikan, vol.II, pp.1080–1094, Ankara,Turkey, Elsevier Science Publishers B.V., 1990.

[5] A.K. Jain, Fundamentals of Digital Image Processing,Prentice-Hall, New Jersey, 1989.

[6] L. Khriji, F.A. Cheikh, and M. Gabbouj, “High resolutiondigital resampling using vector rational filters,” J. OpticalEngineering, Special Issue on Sampled Imaging Systems,vol.38, no.5, pp.893–901, May 1999.

[7] L. Khriji and M. Gabbouj, “Median-rational hybrid fil-ters for image restoration,” IEE Electronics Letters, vol.34,no.10, pp.977–979, May 1998.

[8] L. Khriji and M. Gabbouj, “Median-rational hybrid filters,”Proc. IEEE Int. Conf. Image Proc., ICIP ’98, Chicago, Illi-nois, Oct. 4-7, 1998.

[9] H. Leung and S. Haykin, “Detection and estimation usingan adaptive rational function filter,” IEEE Trans. SignalProcessing, vol.42, no.12, pp.3366–3376, Dec. 1994.

[10] R. Machuca and K. Phillips, “Applications of vector fieldsto image processing,” IEEE Trans. Pattern Anal. & Mach.Intell., vol.PAMI-5, pp.316–329, May 1983.

[11] I. Pitas and A.N. Venetsanopoulos, Nonlinear Digital Fil-ters - Principles and Applications, Kluwer Academic Pub-lishers, 1990.

[12] K.N.Plataniotis, D.Androutsos, and A.N. Venetsanopoulos,“Adaptive multichannel filters for colour image processing,”Signal Processing: Image Communication, vol.11, pp.171–177, 1998.

[13] K.N.Plataniotis, D.Androutsos, and A.N. Venetsanopoulos,“Colour image processing using Fuzzy vector directional fil-ters,” Proc. IEEE Workshop on Nonlinear Signal and ImageProcessing, NSIP ’95, pp.535–538, 1995.

[14] W.K. Pratt, Digital Image Processing, John Wiley & Sons,New York, NY, 1991.

[15] G. Ramponi, “The rational Filter for Image Smoothing,”IEEE Signal Processing Letters, vol.3, March 1996.

[16] P.E. Trahanias, D. Karakos, and A.N. Venetsanopoulos,“Directional processing of color images: Theory and ex-perimental results,” IEEE Trans. Image Proc., vol.5, no.6,pp.868–880, June 1996.

Lazhar Khriji received his BS degree in electronics in 1990from the Faculty of Sciences of Tunis, Tunisia, and his MS in au-tomation and control in 1992 from the Ecole Normale Seperieurede l’Enseignement Technique, Tunisia, and the Ph.D. degree in1999 from the Faculty of Sciences of Tunis, Tunisia. He is cur-rently Assistant Professor at the Electrical Engineering Depart-ment of the Ecole National d’Ingenieurs de Monastir, Tunisia.His research interests include nonlinear signal and image pro-cessing and analysis, multichannel signal processing and adaptivenonlinear filtering.

1596IEICE TRANS. INF. & SYST., VOL.E82–D, NO.12 DECEMBER 1999

Moncef Gabbouj received his BSdegree in electrical engineering in 1985from Oklahoma State University, Still-water, and his MS and PhD degrees inelectrical engineering from Purdue Uni-versity, West Lafayette, Indiana, in 1986and 1989, respectively. Dr. Gabbouj iscurrently a professor in the Signal Pro-cessing Laboratory of Tampere Universityof Technology, Tampere, Finland. From1995 to 1998 he was a professor with the

Department of Information Technology of Pori School of Tech-nology and Economics, Pori, and during 1997 and 1998 he was onsabbatical leave with the Academy of Finland. From 1994 to 1995he was an associate professor with the Signal Processing Labo-ratory of Tampere University of Technology, Tampere, Finland.From 1990 to 1993 he held was a senior research scientist withthe Research Institute for Information Technology, Tampere, Fin-land. His research interests include nonlinear signal and imageprocessing and analysis, content-based analysis and retrieval andmathematical morphology. Dr. Gabbouj is the Vice-Chairman ofthe IEEE-EURASIP NSIP (Nonlinear Signal and Image Process-ing) Board. He is currently the Technical Committee Chairmanof the EC COST 211quat. He served as associate editor of theIEEE Transactions on Image Processing, and was guest editor ofthe European journal Signal Processing, special issue on nonlin-ear digital signal processing (August 1994). He is the past chairof the IEEE Circuits and Systems Society, Technical Commit-tee on Digital Signal Processing, and the IEEE SP/CAS FinlandChapter. He was also the DSP track chair of the 1996 IEEE IS-CAS and the program chair of NORSIG’96, and is the technicalprogram chair of EUSIPCO 2000. Dr. Gabbouj is the Director ofthe International University Program in Information Technologyand member of the Council of the Department of InformationTechnology at Tampere University of Technology. He is also theSecretary of the International Advisory Board of Tampere Inter-national Center of Signal Processing, TICSP. He is a member ofEta Kappa Nu, Phi Kappa Phi, IEEE SP and CAS societies. Dr.Gabbouj was co-recipient of the Myril B. Reed Best Paper Awardfrom the 32nd Midwest Symposium on Circuits and Systems andco-recipient of the NORSIG 94 Best Paper Award from the 1994Nordic Signal Processing Symposium. He is co-author of over150 publications.