Cracks in digitized paintings

178 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 15, NO. 1, JANUARY 2006

Digital Image Processing Techniquesfor the Detection and Removalof Cracks in Digitized Paintings

Ioannis Giakoumis, Nikos Nikolaidis, Member, IEEE, and Ioannis Pitas, Senior Member, IEEE

Abstract—An integrated methodology for the detection andremoval of cracks on digitized paintings is presented in thispaper. The cracks are detected by thresholding the output of themorphological top-hat transform. Afterward, the thin dark brushstrokes which have been misidentified as cracks are removed usingeither a median radial basis function neural network on hue andsaturation data or a semi-automatic procedure based on regiongrowing. Finally, crack filling using order statistics filters or con-trolled anisotropic diffusion is performed. The methodology hasbeen shown to perform very well on digitized paintings sufferingfrom cracks.

Index Terms—Anisotropic diffusion, detection of cracks, orderstatistics filters, top-hat transformation, virtual restoration ofpaintings.

I. INTRODUCTION

MANY paintings, especially old ones, suffer from breaksin the substrate, the paint, or the varnish. These patterns

are usually called cracks or craquelure and can be caused byaging, drying, and mechanical factors. Age cracks can resultfrom nonuniform contraction in the canvas or wood-panel sup-port of the painting, which stresses the layers of the painting.Drying cracks are usually caused by the evaporation of volatilepaint components and the consequent shrinkage of the paint. Fi-nally, mechanical cracks result from painting deformations dueto external causes, e.g., vibrations and impacts.

The appearance of cracks on paintings deteriorates the per-ceived image quality. However, one can use digital image pro-cessing techniques to detect and eliminate the cracks on digi-tized paintings. Such a “virtual” restoration can provide clues toart historians, museum curators and the general public on howthe painting would look like in its initial state, i.e., without thecracks. Furthermore, it can be used as a nondestructive tool forthe planning of the actual restoration. A system that is capableof tracking and interpolating cracks is presented in [1]. The usershould manually select a point on each crack to be restored. Amethod for the detection of cracks using multioriented Gabor fil-ters is presented in [2]. Crack detection and removal bears cer-tain similarities with methods proposed for the detection andremoval of scratches and other artifacts from motion picture

Manuscript received February 21, 2003; revised July 29, 2004. The associateeditor coordinating the review of this manuscript and approving it for publica-tion was Dr. Vito Cappellini.

The authors are with the Department of Informatics, Aristotle Universityof Thessaloniki, 54124 Thessaloniki, Greece (e-mail: [email protected]; [email protected]; [email protected]).

Digital Object Identifier 10.1109/TIP.2005.860311

films [3]–[5]. However, such methods rely on information ob-tained over several adjacent frames for both artifact detectionand filling and, thus, are not directly applicable in the case ofpainting cracks. Other research areas that are closely related tocrack removal include image inpainting which deals with the re-construction of missing or damaged image areas by filling in in-formation from the neighboring areas, and disocclusion, i.e., re-covery of object parts that are hidden behind other objects withinan image. Methods developed in these areas assume that the re-gions where information has to be filled in are known. Differentapproaches for interpolating information in structured [6]–[10]and textured image areas [11] have been developed. The formerare usually based on partial differential equations (PDEs) andon the calculus of variations whereas the latter rely on texturesynthesis principles. A technique that decomposes the image totextured and structured areas and uses appropriate interpolationtechniques depending on the area where the missing informa-tion lies has also been proposed [12]. The results obtained bythese techniques are very good. A methodology for the restora-tion of cracks on digitized paintings, which adapts and integratesa number of image processing and analysis tools is proposed inthis paper. The methodology is an extension of the crack re-moval framework presented in [13]. The technique consists ofthe following stages:

• crack detection;• separation of the thin dark brush strokes, which have been

misidentified as cracks;• crack filling (interpolation).A certain degree of user interaction, most notably in the

crack-detection stage, is required for optimal results. Userinteraction is rather unavoidable since the large variationsobserved in the typology of cracks would lead any fully auto-matic algorithm to failure. However, all processing steps can beexecuted in real time, and, thus, the user can instantly observethe effect of parameter tuning on the image under study andselect in an intuitive way the values that achieve the optimalvisual result. Needless to say, only subjective optimality criteriacan be used in this case since no ground truth data are available.The opinion of restoration experts that inspected the virtuallyrestored images was very positive.

This paper is organized as follows. Section II describes thecrack-detection procedure. Two methods for the separation ofthe brush strokes which have been falsely identified as cracksare presented in Section III. Methods for filling the cracks withimage content from neighboring pixels are proposed in Sec-tion IV. Conclusions and discussion follow.

1057-7149/$20.00 © 2006 IEEE

GIAKOUMIS et al.: DIGITAL IMAGE PROCESSING TECHNIQUES 179

II. DETECTION OF CRACKS

Cracks usually have low luminance and, thus, can be con-sidered as local intensity minima with rather elongated struc-tural characteristics. Therefore, a crack detector can be appliedon the luminance component of an image and should be able toidentify such minima. A crack-detection procedure based on theso-called top-hat transform [14] is proposed in this paper. Thetop-hat transform is a grayscale morphological filter defined asfollows:

(1)

where is the opening of the function (in our case,the luminance component of the image under study) with thestructuring set , defined as

(2)

In the previous equation, denotes the dilation operation. Asquare or a circle can be used as structuring element [15].The final structuring set is evaluated only once using (2)and is used subsequently in the opening operation of (1). Theopening of a function is a low-pass nonlinear filter thaterases all peaks (local maxima) in which the structuring ele-ment cannot fit. Thus, the image contains only thosepeaks and no background at all. Since cracks are local minimarather than local maxima, the top-hat transform should be ap-plied on the negated luminance image. Alternatively, one candetect cracks by performing closing on the original imagewith the structuring set and then subtracting from theresult of closing

(3)

It can be easily shown that the result of (3) is identical to that ofapplying (1) on the negated image. Use of (3) does not requirenegation of which grands it a small but not negligible com-putational advantage over (1).

In situations where the crack-like artifacts are of high lumi-nance, as in the case of scratches on photographs, negation ofthe luminance component prior to the crack detection is not re-quired, i.e., the crack detection procedure can be applied directlyon the luminance image.

The usercancontrol the resultof thecrack-detectionprocedureby choosing appropriate values for the following parameters:

• the type of the structuring element ;• the size of the structuring element and the number

of dilations in (2).These parameters affect the size of the “final” structuringelement and must be chosen according to the thicknessof the cracks to be detected. It should be noted, however,that these parameters are not very critical for the algorithmperformance due to the thresholding operation that will bedescribed in the next paragraph and also due to the existenceof the brush-stroke/crack separation procedure (Section III),which is able to remove crack-like brush strokes that have beenerroneously identified as cracks. The fact that all the resultspresented in this paper have been obtained with the sametop-hat transform parameters comes as a clear indication that

the above statement is indeed true. These parameters were thefollowing:

• structuring element type: square;• structuring element size: 3 3;• number of dilations in (2): 2.The top-hat transform generates a grayscale output image

where pixels with a large grey value are potential crackor crack-like elements. Therefore, a thresholding operation on

is required to separate cracks from the rest of the image.The threshold can be chosen by a trial and error procedure,i.e., by inspecting its effect on the resulting crack map. Thelow computational complexity of the thresholding operation en-ables the user to view the crack-detection results in real timewhile changing the threshold value, e.g., by moving a slider.This fact makes interactive threshold selection very effectiveand intuitive. Alternatively, threshold selection can be done byinspecting the histogram of for a lobe close to the max-imum intensity value (which will most probably correspond tocrack or crack-like pixels), and assigning it a value that sepa-rates this lobe from the rest of the intensities. The result of thethresholding is a binary image marking the possible cracklocations. Instead of this global thersholding technique, morecomplex thresholding schemes, which use a spatially varyingthreshold can be used. Obviously, as the threshold value in-creases the number of image pixels that are identified as cracksdecreases. Thus, certain cracks, especially in dark image areaswhere the local minimum condition may not be satisfied, can re-main undetected. In principle, it is more preferable to select thethreshold so that some cracks remain undetected than to choosea threshold that would result in the detection of all cracks butwill also falsely identify as cracks, and subsequently modify,other image structures. The thresholded (binary) output of thetop-hat transform on the luminance component of an image con-taining cracks (Fig. 1) can be seen in Fig. 2. Additional ex-amples of cracks detected using this approach can be seen inFigs. 10–12.

III. SEPARATION OF THE BRUSH STROKES FROM THE CRACKS

In some paintings, certain areas exist where brush strokeshave almost the same thickness and luminance features ascracks. The hair of a person in a portrait could be such an area.Therefore, the top-hat transform might misclassify these darkbrush strokes as cracks. Thus, in order to avoid any undesir-able alterations to the original image, it is very important toseparate these brush strokes from the actual cracks, before theimplementation of the crack filling procedure. Two methods toachieve this goal are described in the following subsections.

A. Semi-Automatic Crack Separation

A simple interactive approach for the separation of cracksfrom brush strokes is to apply a region growing algorithm on thethresholded output of the top-hat transform, starting from pixels(seeds) on the actual cracks. The pixels are chosen by the userin an interactive mode. At least one seed per connected crackelement should be chosen. Alternatively, the user can choose toapply the technique on the brush strokes, if this is more con-venient. The growth mechanism that was used implements the


Fig. 1. Original painting.

Fig. 2. Thresholded output of the top-hat transform (threshold value: 23).

well-known grassfire algorithm that checks recursively for un-classified pixels with value 1 in the 8-neighborhood of eachcrack pixel. At the end of this procedure, the pixels in the binaryimage, which correspond to brush strokes that are not 8-con-nected to cracks will be removed. The above procedure can beused either in a stand-alone mode or applied on the output ofthe MRBF separation procedure described in the next section toeliminate any remaining brush strokes.

B. Discrimination on the Basis of Hue and Saturation

Hue is associated with the dominant wavelength in a mix-ture of light wavelengths and represents the dominant color. Inthe HSV color model, hue is represented as the angle around thevertical axis, with red at 0 , green at 120 , and so on. Saturation

refers to the amount of white light mixed with a certain hue.

Hue and saturation are defined similarly in other related colordomains, e.g., in hue saturation intensity (HSI) or hue lightnesssaturation (HLS).

By statistical analysis of 47 digitized paintings (24 portablereligious icons from the Byzantine era and 23 paintings of var-ious styles and ages), it has been concluded that the hue of thecracks usually ranges from 0 to 60 . On the contrary, we ob-served that the hue of the dark brush strokes varies, as expected,in the entire gamut [0 , 360 ]. Furthermore, crack saturationusually ranges from 0.3 to 0.7, while brush-stroke saturationranges from 0 to 0.4. Thus, on the basis of these observations,a great portion of the dark brush strokes, falsely detected bythe top-hat transform, can be separated from the cracks. Thisseparation can be achieved by classification using a median ra-dial basis function (MRBF) neural network, which is a robust,order statistics based, variation of radial basis function (RBF)networks [16].

RBFs are two-layer feedforward neural networks [17], thatmodel a mapping between a set of input vectors and a set ofoutputs. The network architecture is presented in Fig. 3. RBFsincorporate an intermediate, hidden layer where each hiddenunit implements a kernel function, usually a Gaussian function

(4)where , denote the mean vector and the covariance ma-trix for kernel and denotes the number of units (kernels)in the hidden layer. Each output consists of a weighted sum ofkernels. In typical situations that involve pattern classification,the number of outputs equals to the number of classes. In sucha setting, the current vector is assigned to the class associatedwith the output unit exhibiting the maximum activation (winnertakes all approach). After the learning stage, the network im-plements the input-output mapping rule and can generalize it toinput vectors not being part of the training set.

The parameters to be estimated (learned) in a RBF networkare the center (mean) vector and the covariance matrixfor each Gaussian function and the weights correspondingto the connections between neurons in the hidden layer andoutput nodes. A hybrid technique that has been frequentlyused for the training of such networks, has been adopted forthe learning stage. According to this technique, training isperformed in two successive steps: the hidden layer parametersare estimated using an unsupervised approach and, afterwards,the output layer weights are updated in a supervised manner,using the (now fixed) hidden layer parameters evaluated in theprevious step.

In the classical version of the adopted training technique,a variation of the learning vector quantizer (LVQ) algorithmis used for the unsupervised hidden layer parameter updating.Each input vector is assigned to the Gaussian kernel whosecenter is closer (in terms of either the Euclidean or the Maha-lanobis distance) to this vector

(5)

where denotes either Euclidean or Mahalanobis distance anddenotes the class of input vectors associated with kernel .

Subsequently, the algorithm updates the center and covariance


Fig. 3. RBFs neural network architecture.

matrix of the winner kernel using running versions of the clas-sical sample mean and sample covariance matrix formulas. Onthe other hand, the MRBF algorithm which has been used in ourcase is based on robust estimation [16] of the hidden unit param-eters. It employs the marginal median LVQ [18] that selects thewinner kernel using (5) and utilizes the marginal median of theinput vectors currently assigned to this kernel for the update ofthe center vector (location parameter) of the kernel

(6)

where is the last vector assigned to kernel . The update ofthe diagonal elements of the corresponding covariance matrix isperformed using the median of the absolute deviations (MAD)[19] of the inputs currently assigned to this kernel

(7)In the previous expression, denotes the vector containing thediagonal elements of the covariance matrix and denotes thevector obtained by taking the absolute value of each componentof . The off-diagonal components of the covariance matrix arealso calculated based on robust statistics [16]. In order to avoidexcessive computations the above operations can be applied on asubset of data extracted through a moving window that containsonly the last data samples assigned to the hidden unit .

In the supervised part of the learning procedure, the weightsof the output layer, which group the clusters found by the hiddenlayer into classes, are updated. The update mechanism for theseweights is described by the following expression:

(8)

for , , and a learning factor. In the previous formula , denote the ac-

tual and desired network output for input vector . The latter isgiven by

ifif

(9)

The update formula (8) corresponds to the backpropagation forthe output weights of a RBF network with respect to the meansquare error cost function.

In our implementation, a MRBF network with two outputswas used. The first output represents the class of cracks whilethe second one the class of brush strokes. Input vectors weretwo-dimensional and consisted of the hue and saturation valuesof pixels identified as cracks by the top-hat transform. Thenumber of clusters (hidden units) chosen for each class dependson the overlap between the populations of cracks and brushstrokes. If there is a substantial overlap, the number shouldbe increased, in order to reduce the classification error. In ourimplementation three hidden units have been incorporated.Training was carried out by presenting the network with hueand saturation values for pixels corresponding to cracks andcrack-likebrushstrokes.Datafrom24digitizedportablereligiousicons from the Byzantine era were used for this purpose. Thesystem trained using this specific training set can be consideredto be optimized for paintings of this style and its use on paintingsof other style might result in somewhat suboptimal results.However, appropriately selected training sets can be used to trainthe system to separate cracks from brush strokes on paintingsof different artistic styles or content. In order to select pixelscorresponding to cracks and crack-like brush strokes the crackdetection algorithm presented in Section II was applied on theseimages. Results were subsequently postprocessed by an expertusing the semi-automatic approach presented in Section III-A.The aim of this postprocessing step was twofold: to removepixels that are neither cracks nor crack-like brush strokes and toseparate cracks and crack-like brush strokes for the supervisedstep of the training procedure. In this supervised training step,the network was presented with these labeled inputs, i.e., pairs


Fig. 4. Original painting.

of hue-saturation values that corresponded to image pixels thathave been identified as belonging to cracks and crack-like brushstrokes.

After the training session, the MRBF neural network was ableto classify pixels identified as cracks by the top-hat transformto cracks or brush strokes. The trained network has been testedon 12 images from the training set and 15 images (of the sameartistic style and era) that did not belong to the training set.Naturally, the performance of the cracks/brush-stroke separa-tion procedure was judged only in a subjective manner (i.e., byvisual inspection of the results), as ground truth data (i.e., brushstroke-free crack images) are not available. For this reason, tworestoration experts were asked to inspect several crack imagesbefore and after the application of the separation system andconcluded that in the processed crack images the great majorityof the brush strokes has been removed. A thresholded top-hattransform output containing many brush strokes, e.g., hair is il-lustrated in Fig. 5. A great part of these brush strokes is sepa-rated by the MRBF, as can be seen in Fig. 6. The original imagecan be seen in Fig. 4.

IV. CRACK-FILLING METHODS

After identifying cracks and separating misclassified brushstrokes, the final task is to restore the image using local image in-formation (i.e., information from neighboring pixels) to fill (in-terpolate) the cracks. Two classes of techniques, utilizing orderstatistics filtering and anisotropic diffusion are proposed for thispurpose. Both are implemented on each RGB channel inde-pendently and affect only those pixels which belong to cracks.Therefore, provided that the identified crack pixels are indeedcrack pixels, the filling procedure does not affect the “useful”content of the image. Image inpainting techniques like the onescited in Section I can also be used for crack filling.

Fig. 5. Thresholded output of the top-hat transform (threshold value: 19).A number of brush strokes (hair, number in the upper left corner) have beenmisidentified as cracks.

Fig. 6. Separated brush strokes after the application of the MRBF technique.

The performance of the crack filling methods presented belowwas judged by visual inspection of the results. Obviously, mea-suring the performance of these methods in an objective wayis infeasible since ground truth data (e.g., images depicting thepaintings in perfect condition, i.e., without cracks) are not avail-able. For the evaluation of the results, two restoration experts


were asked to inspect several images restored using the var-ious methods and comment, based on their experience, on thequality of the filling results, (i.e., whether cracks were suffi-ciently filled), whether the color used for filling was the correctone, whether fine image details were retained, etc.

A. Crack Filling Based on Order Statistics Filters

An effective way to interpolate the cracks is to apply medianor other order statistics filters [15] in their neighborhood. Allfilters are selectively applied on the cracks, i.e., the center ofthe filter window traverses only the crack pixels. If the filterwindow is sufficiently large, the crack pixels within the windowwill be outliers and will be rejected. Thus, the crack pixel willbe assigned the value of one of the neighboring noncrack pixels.The following filters can be used for this purpose.

• Median filter

(10)

• Recursive median filter

(11)

where the are the already computed me-dian output samples. For both the recursive median andthe median filter, the filter window (considering only rect-angular windows) should be approximately 50% widerthan the widest (thickest) crack appearing on the image.This is necessary to guarantee that the filter output is se-lected to be the value of a noncrack pixel. Smaller win-dows will result in cracks that will not be sufficientlyfilled whereas windows that are much wider than thecracks will create large homogeneous areas, thus dis-torting fine image details.

• Weighted median filter

(12)

where denotes duplication of times. For thisfilter, smaller filter windows (e.g., windows that are ap-proximately 30% wider than the widest crack appearingon the image) can be used since the probability that acolor value corresponding to a crack is selected as thefilter output (a fact that would result in the crack pixelunder investigation not being filled effectively by thefilter) can be limited by using small weights (e.g., 1) forthe pixels centrally located within the window (whichare usually part of the crack) and bigger ones (e.g., 2 or3) for the other pixels.

• A variation of the modified trimmed mean (MTM) filterwhich excludes the samples in the filter window,which are considerably smaller from the local median andaverages the remaining pixels

(13)

Fig. 7. Crack filling by using the modified trimmed mean filter (filter size 5�5).

The summations cover the entire filter window . Thefilter coefficients are chosen as follows:

ifotherwise

(14)

The amount of trimming depends on the positive param-eter . Data of small value deviating strongly from thelocal median (which correspond usually to cracks) aretrimmed out. Windows used along with this variant of theMTM filter can also be smaller than those used for themedian and recursive median filters since a portion of thecrack pixels is expected to be rejected by the trimmingprocedure.

• Another variation of the MTM filter that performs aver-aging only on those pixels that are not part of the crack,i.e., it utilizes information from the binary output image

of the top-hat transform. In this case, the filter co-efficients in (13) are chosen as follows:

ifotherwise

(15)

The median operator can be used instead of the arithmeticmean in (13). For this variant of the MTM filter, evensmaller filter windows can be used, since crack pixels donot contribute to the filter output. Thus, it suffices that thewindow is 1 pixel wider than the widest crack.

The result of the application of the second variation of the mod-ified trimmed mean filter on the painting depicted in Fig. 1(a) isshown in Fig. 7 (filter size 5 5). Another image restored bythe same crack-filling approach can be seen in Fig. 8 (filter size3 3). Extensive experimentation proved that this filter givesthe best results among all filters presented above according tosubjective evaluation by restoration experts. The superiority ofthis filter can be attributed to the fact that only noncrack pixels


Fig. 8. (a) Original painting (detail). (b) Crack filling by using the modified trimmed mean filter (filter size 3 � 3).

Fig. 9. (a) Original image with cracks (detail). (b) Crack filling using the orientation-sensitive controlled anisotropic diffusion technique.

contribute to its output. On the contrary, for all other filters pre-sented in this section the probability that crack pixels will con-tribute to the output is small but not negligible.

B. Controlled Anisotropic Diffusion

Anisotropic diffusion [20] is an image enhancement methodthat successfullycombinessmoothingofslowlyvarying intensityregions and edge enhancement. Smoothing is modeled asa diffusion that is allowed along homogeneous regions and

inhibitedbyregionboundaries.Anisotropicdiffusionisdescribedby the following PDE:

(16)

where denotes the divergence operator and , the gradientand Laplacian operators with respect to the space variables .


Fig. 10. (a) Original painting (detail). (b) Crack image (threshold value: 17). (c) Crack filling using the orientation-sensitive controlled anisotropic diffusiontechnique.

At each position and iteration, diffusion is controlled by theconduction (or diffusion) coefficients . Since diffusionshould be inhibited across regions separated by discontinuities,the conduction coefficients should obtain small values in pixelswith large intensity gradient magnitude. A similar approachnamed curvature driven diffusion (CDD) has been proposedin [9] for image inpainting applications.

In order to obtain a numerical solution to the diffusion equa-tion, discretization of the spatial and time coordinates and ap-proximation of the differential operators by finite difference op-erators should be performed in (16). We have used the same dis-cretizations as proposed in [20]. The iterative, discrete solution

to (16) is governed by the following equation:

(17)

where for the scheme to be stable, N, S, E, andW are the mnemonics for North, South, East, and West, and thesymbol indicates nearest-neighbor differences

(18)





The conduction coefficients are evaluated at every iteration asa function of the magnitude of the intensity gradient. In ourimplementation, the following approximation was used [20]:

(19)

The following function , proposed in [20], has been used inour case:

(20)

The constant was manually fixed. In order to fill the cracks,the anisotropic diffusion algorithm was applied selectively, inneighborhoods centered on crack pixels. All pixels within theseneighborhoods participate in the diffusion process. However,only the values of the crack pixels are updated in the outputimage.

Further improvements were obtained by taking into accountcrack orientation, i.e., by applying the operation only in a di-rection perpendicular to the crack direction. For example, if thecrack is horizontal, one can use only the North and the Southneighbors, since the West and the East neighbors belong also tothe crack. In order to find the directions of the cracks, the Houghtransform was applied [21]. The restoration results of this filtercan be seen in Figs. 9–12. The orientation-sensitive controlledanisotropic diffusion method gave the best results among allcrack-filling methods presented in this paper. The fact that thisfilter requires no window size selection grants it an additionaladvantage over the order statistics filters presented in the pre-vious section.

V. CONCLUSIONS AND DISCUSSION

In this paper, we have presented an integrated strategy forcrack detection and filling in digitized paintings. Cracks are de-tected by using top-hat transform, whereas the thin dark brushstrokes, which are misidentified as cracks, are separated eitherby an automatic technique (MRBF networks) or by a semi-auto-matic approach. Crack interpolation is performed by appropri-ately modified order statistics filters or controlled anisotropicdiffusion. The methodology has been applied for the virtualrestoration of images and was found very effective by restora-tion experts. However, there are certain aspects of the proposedmethodology that can be further improved. For example, thecrack-detection stage is not very efficient in detecting crackslocated on very dark image areas, since in these areas the in-tensity of crack pixels is very close to the intensity of the sur-rounding region. A possible solution to this shortcoming wouldbe to apply the crack-detection algorithm locally on this areaand select a low threshold value. Another situation where thesystem (more particularly, the crack filling stage) does not per-form as efficiently as expected is in the case of cracks that crossthe border between regions of different color. In such situations,it might be the case that part of the crack in one area is filledwith color from the other area, resulting in small spurs of color

in the border between the two regions. Such a situation is de-picted in Fig. 11. However, this phenomenon is rather seldomand, furthermore, the extent of these erroneously filled areas isvery small (2–3 pixels maximum). A possible solution wouldbe to perform edge detection or segmentation on the image andconfine the filling of cracks that cross edges or region borders topixels from the corresponding region. Use of image inpaintingtechniques [6]–[10] could also improve results in that aspect.Another improvement of the crack filling stage could aim atusing properly adapted versions of nonlinear multichannel fil-ters (e.g., variants of the vector median filter) instead of pro-cessing each color channel independently. These improvementswill be the topic of future work on this subject.

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Ioannis Giakoumis received the Diploma of Informatics in 1997.He is currently with Intracom S.A.


Nikos Nikolaidis (S’92–A’97–M’05) received theDiploma of electrical engineering and the Ph.D.degree in electrical engineering from the AristotleUniversity of Thessaloniki, Thessaloniki, Greece, in1991 and 1997, respectively.

From 1992 to 1996, he served as a TeachingAssistant in the Departments of Electrical Engi-neering and Informatics, Aristotle University ofThessaloniki, and, from 1998 to 2002, he was aPostdoctoral Researcher and Teaching Assistant withthe Department of Informatics, where he is currently

a Lecturer. He is the coauthor of the book 3-D Image Processing Algorithms(New York: Wiley, 2000). He has coauthored five book chapters, 19 journalpapers, and 56 conference papers. His research interests include computergraphics, image and video processing and analysis, and copyright protection ofmultimedia and 3-D image processing.

Dr. Nikolaidis has been a scholar of the State Scholarship Foundation ofGreece.

Ioannis Pitas (SM’94) received the Diploma of elec-trical engineering and the Ph.D. degree in electricalengineering from the Aristotle University of Thessa-loniki, Thessaloniki, Greece, in 1980 and 1985, re-spectively.

Since 1994, he has been a Professor at the De-partment of Informatics, Aristotle University ofThessaloniki, where he served as Scientific Assis-tant, Lecturer, Assistant Professor, and AssociateProfessor in the Department of Electrical and Com-puter Engineering from 1980 to 1993. He served

as a Visiting Research Associate at the University of Toronto, Toronto, ON,Canada; the University of Erlangen-Nuernberg, Nuernberg, Germany; andthe Tampere University of Technology, Tampere, Finland. He also served asVisiting Assistant Professor at the University of Toronto and Visiting Professorat the University of British Columbia, Vancouver, BC, Canada. He was aLecturer in short courses for continuing education. He has published over 380papers and contributed to 13 books in his areas of interest. He is the co-authorof the books Nonlinear Digital Filters: Principles and Applications (Norwell,MA: Kluwer, 1990), 3-D Image Processing Algorithms (New York: Wiley,2000), Nonlinear Model-Based Image/Video Processing and Analysis (NewYork: Wiley, 2001), and author of Digital Image Processing Algorithms andApplications (New York: Wiley, 2000). He is also the editor of the book ParallelAlgorithms and Architectures for Digital Image Processing, Computer Visionand Neural Networks (New York: Wiley, 1993). He was co-editor of the jour-nals Multidimensional Systems and Signal Processing and was Technical Chairof the 1998 European Signal Processing Conference. His current interests arein the areas of digital-image processing, multidimensional signal processing,watermarking, and computer vision.

Dr. Pitas has been member of the European Community ESPRIT Parallel Ac-tion Committee. He has also been an invited speaker and/or member of the pro-gram committee of several scientific conferences and workshops. He was anAssociate Editor of the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, As-sociate Editor of the IEEE TRANSACTIONS ON NEURAL NETWORKS, AssociateEditor of the IEEE TRANSACTIONS ON IMAGE PROCESSING. He was the GeneralChair of the 1995 IEEE Workshop on Nonlinear Signal and Image Processingand General Chair of IEEE International Conference on Image Processing 2001.

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Cracks in digitized paintings