Seite - 9 - in Document Image Processing

J. Imaging 2018,4, 68 the inpaintingalgorithmalso incorporates informationofsimilarneighbouringpatches, thusmaking possible thedistinctionbetweenfalsebleed-throughpixels in thebackgroundandfalsebleed-through pixel in the foreground. 4. SparseBleed-ThroughInpainting After successful identification of the bleed-throughpixels, the next task is to find a suitable replacement for them. In thispaper,we treat thebleed-throughpixelsasmissingorcorrupt image regions,andusesparse image inpaintingtoestimateproperfill-invalues,whichareconsistentwith theknownuncorruptedsurroundingpixels. In recent years, image inpainting techniques have been widely used in image restoration, target removal, andcompression.Generally, image inpainting techniques canbedivided into two groups: diffusionbasedmethodsandexemplarbasedmethods [21]. Thediffusionbasedmethods useaparametricmodelorpartialdifferential equations,whichextend the local structure fromthe surrounding to the internalof the region tobe repaired [56]. In [57], aweightedaverageofknown neighbourhoodpixels isusedtoreplace themissingpixels,usinga fastmatchingmethod.Adiffusion basedmethod, with total variational approach, is presented in [58]. In [59], amulti-color image inpainting is outlinedusing anisotropic smoothing. Themethods in this category are suitable for non-textured imageswithsmallmissingregions. In the exemplar basedmethods, an image block is selected as a unit, and the information is replicated fromtheknownpartof the image to theunknownregion. In [20], apatchprioritybased inpaintingissuggestedthatextendsknownimagepatchestothemissingpartsoftheimage.Anon-local exemplarbasedmethod is suggested in [60],where themissingpatches are estimatedasmeansof selectednon-localpatches.Comparatively, theexemplarbasedmethodsare fasterandexhibitbetter performance, butuseonlya singlebestmatchingblock to estimate theunknownpixels. However, pure texturesynthesis fails topreserve thestructure informationof the image,whichconstitutes its basicoutline.Acombinationofdiffusionandexemplarbasedinpainting issuggestedin[61] torepair thestructureandtexture layersseparately. Thisgreedykindofapproachoften introducesartifactsand alsoconsumesmoretimeinfindingthebestmatchforeach imagepatch[21]. Recently, sparse representation based image inpainting algorithms have been reportedwith impressiveresults [62].Assparserepresentationworksonimagepatches, themain idea is tofindthe optimalsparserepresentation foreach imagepatchandthenestimate themissingpixels inapatch usingthesparsecoefficientsof theknownpixels.Asparse image inpaintingmethod,usingsamples fromtheknownimagepart, ispresented in [23].Afusionofanexemplar-basedtechniqueandsparse representation ispresented in [22] tobetterpreserve the imagestructureandtheconsistencyof the repairedpatchwith its surroundings. In [62], a sparse representationmethodbasedon structure similarity(SSIM)of imagepatchesispresented,wherethedictionarytrainingandthesparsecoefficient estimationarebasedontheSSIMindex. Mathematically, the image inpainting problem is formulated as the reconstruction of the underlyingcomplete image(inacolumnvector form)C∈RW fromitsobservedincompleteversion I∈RL,whereL<W.WeassumeasparserepresentationofCoveradictionaryD∈Rn×K:C≈DX. The incomplete image Iand thecomplete imageCare related through I=MC,whereM∈RL×W represents the layoutof themissingpixels. In formulas it is: I = MC ≈ M(DX). (8) Assumingthatawell traineddictionaryD isavailable, theproblemboilsdownto theestimation ofsparsecoefficients Xˆsuchthat theunderlyingcomplete image Cˆ isgivenby Cˆ=DXˆ. To learnthe dictionaryD, a training setY is createdbyextractingoverlappingpatchesof size √ ps×√ps from the imageat location j= 1,2,....,P,where ps is thepatchsizeandP is the totalnumberofpatches. 9