Page - 21 - in Document Image Processing

J. Imaging 2018,4, 27 Theverso image is“blurred”bypassingthroughtwodifferentGaussianfilters that simulate the low-passeffectof the translucidityof theversoasseen in the frontpartof thepaper. Twodifferent parameterswereused tosimulate twodifferent classesofpaper translucidity. The“blurred”verso image isnowfadedwith a coefficientαvaryingbetween0and1 in stepsof 0.01. Then, a circular shiftof the linesof thedocument ismadeofeither5or10pixels, tominimize thechancesof the front andverso lines coincideentirely. Finally, the two imagesareoverlappedbyperforminga“darker” operationpixel-by-pixel in the images. Paper texture is added to the image to simulate the effect ofdocumentaging. Thetexturepatternwasextractedfromdocument fromlate19thcenturyto the year 2000. Theanalysis of 3450documents representativeof awidevarietyofdocuments of such aperiodwasanalyzedyielding100differentclustersof textures. Thesynthetic texture tobeapplied to the image tosimulatepaperaging isgeneratedusing those100clustersby imagequilting [11]and randomly,asexplained inreference [9]. The trainingperformedin thecurrentversionof thepresented algorithmwasmadewith16of those200 synthetic textures. The total numberof imagesused for trainingherewas thus 16 (textures), times 10 (0<α<1 in steps of 0.10), times 2blurparameters for theGaussianfilters, times100differentbinary images, totaling32,000 images.Detailsof the full generationprocessof thesynthetic imagedatabaseareoutof thescopeof thispaperandmaybefound inreference [9]. 2.3. TheBilateralFilter Thebilateral filterwasfirst introducedbyAurichandWeule [12]under thename“nonlinear Gaussianfilter”. Itwas later rediscoveredbyTomasiandManduchi [13]whocalled it the“bilateral filter”which isnowthemostcommonlyusednameaccordingtoreference [14]. Thebilateral filter is a technique to smoothen imageswhilepreserving their edges. Thefilter outputat eachpixel is aweightedaverageof itsneighbors. Theweight assigned toeachneighbor decreaseswithboththedistancevaluesamongpixelsof the imageplane(thespatialdomainS)and thedistanceonthe intensityaxis (therangedomainR).Thefilterappliesspatialweightedaveraging withoutsmoothingtheedges. It combines twoGaussianfilters;onefilterworks in thespatialdomain, while theotherfilterworks in the intensitydomain. Therefore,notonly thespatialdistancebutalso the intensitydistance is important for thedeterminationofweights. Thebilateralfiltercombines two stagesoffiltering. Theseare thegeometric closeness (i.e.,filterdomain)andthephotometric similarity (i.e., filter range)among thepixels inawindowof sizeN×N.Let I(x,y) bea2Ddiscrete imageof sizeN×N,such that {x,y}∈ {0, 1, ...,N−1}X {0, 1, ...,N−1}. Assume that I(x,y) is corruptedby anadditivewhiteGaussiannoiseofvarianceσ2n. Forapixel (x,y), theoutputofabilateralfiltercanbe asdescribedbyEquation(1): IBF(x,y)= 1 K∑ x+d i=x−d∑ x+d j=y−dGs(i;x, j;y)Gr[I(i, j), I(x,y)]I(i, j), (3) where I(x,y) is the pixel intensity in the image before applying the bilateral filter, IBF(x,y) is the resultingpixel intensityafter applying thebilateralfilter andd is anon-negative integer such that (2d+1)× (2d+1)stands for thesizeof theneighborhoodwindow.LetGs andGrbethedomainand therangecomponents, respectively,whicharedefinedas: Gs(i;x, j;y)= e −|(i−x)2+(j−y)2| 2σ2s (4) and Gr(I(i, j); I(x,y))= e −|I(i,j)−I(x,y)|2 2σ2r (5) 21