Gradient based restoration of coal mine images obtained by underground wireless transmissions

Mining Science and Technology( china)21(2011)809-813Contents lists available at SciVerse ScienceDirectMining Science and Technology( China)LSEVIERjournalhomepagewww.elsevier.com/locate/mstcgradient based restoration of coal mine images obtained by undergroundwireless transmissionsLu Zhaolina * Qian Jiansheng Li LeidabSchool of Computer Science and Technology, China University of Mining S Technology. Xuzhou 221008, ChinasChool of information and Electrical Engineering China University of Mining 8 Technology, Xuzhou 221008, ChinaARTICLE INFOABSTRACTCurvature-driven diffusion(CDD) principles were used to develop a novel gradient based image restora2011tion algorithm. The algorithm fills in blocks of missing data in a wireless image after transmissionin revised form 21 April 2011through the network. When images are transmitted over fading channels, especially in the severe circum-AcceptedAvailable online 23 December 2011stances of a coal mine blocks of the image may be destroyed by the effects of noise. Instead of using com-mon retransmission query protocols the lost data is reconstructed by using the adaptive curvature-drivendiffusion(ACDD)image restoration algorithm in the gradient domain of the destroyed image. MissingKeywords:blocks are restored by the method in two steps: In step one. the missing blocks are filled in the gradientdomain by the ACDD algorithm: in step two, and the image is reconstructed from the reformed gradientsGradient domaiby solving a poisson equation the proposed method eliminates the staircase effect and accelerates thewireless image transmissionconvergence rate. This is demonstrated by experimental resultsPoisson equationo 2011 Published by Elsevier B V. on behalf of China University of Mining Technology1 Introductionby satisfying some continuities across the boundaries of the dam-aged area. the recovered results are very smooth and this worksImages transmitted by wireless communication in a coal minewell for small damaged regions. However, when the reconstructedare typically compressed using the lossy JPEG algorithm, which area is large a blurry artifact that lacks texture will result. Chandivides the image into blocks of 8 x8 pixels. In common wireless et al. describe the total variation(Tv) based Curvature-Driven Dif-scenarios the image is transmitted over the wireless channel block fusion(CDD)model which takes into account geometric informa-by block. Due to severe fading, especially in a coal mine an entire tion of the isophotes when defining the strength of the diffusionblock may be lost or even several consecutive blocks. In the worst process [3, 4 This allows the model to function over larger areascase a whole line of the image blocks might be lost. Two common Criminisi et al. propose an exemplar-based image completion algo-techniques to make the transmission robust are the forward error rithm that operates through region filling. where the patch fillingcorrection(FEC)or the automatic retransmission query protocols order is determined by the angle between the isophote direction(ARQ Of these the FEC needs the transmission of extra error cor- and the normal direction of the local filling front (5 This meansrection packets. As noted in Reference, ARQ lowers data transmis- that missing regions with stronger structures can be filled in withsion rates and can further increase network congestion, which was higher priority. a TV model and a harmonic model were used byZhang et al in their proposed p-harmonic model, which modifiesInstead of these methods it is possible to satisfactorily recon- the index, p, of the regularization term 16). The value p actuallystruct the lost blocks by using the available information in blocks controls the diffusion direction and strength but p is set to a fixedsurrounding them. The basic idea, called image restoration, is to fill value in the p-harmonic model and can not diffuse image informa-in the missing block with information propagated from the sur- tion according to the various properties of the images.rounding pixelsWu et al. modified the filling order of the exemplar to preserveA number of schemes related to image restoration have beenthe linear structure of the image [5, 7 By combining a TV andproposed in the computer graphics or computer vision literature fourth-order filters Li et al. designed a model for restoring[2-8]. In Reference[2 Bertalmio et al. introduce a partial differen- destroyed images [8 Chen et al. introduced an operator namedtial equation(PDE)based method named"image inpainting"to re- the"difference curvature"into the Perona-Malik(P-M)and TVpair damaged images. The idea is to extend the structure inwards models used for image de-noising 9. 10). The latter approach iscalled the adaptive total variation(ATV)modelNone of these approaches use the gradient of the domain duringCorresponding author Tel +86 15150010478.image restoration 12-101 Gradient-based image processing中国煤化工1674-5264/s- see front matter o 2011 Published by Elsevier B V on behalf of China University of Mining Tecdoi:10.1016/mstc2011.11001CNMHGZ Lu et aL/ Mining Science and Technology( China)21(2011)809-813techniques have been addressed in several related areas such as where g(s)=s, s>0. p> 1. the curvature, K, at a given pixel is thehigh dynamic range compression, image de-noising, and Poisson scalar curvature of the isophotes through it. It is given by theimage matting [11-13]. The approach presented in this paper re- expressionstores missing blocks in two steps: In step one, the missing blocksare filled within the gradient domain by an adaptive curvature dri- K=V/uyven diffusion(ACDD)based algorithm: In step two the image isreconstructed from the reconstructed gradients by solving a Pois- Thus, the Cdd inpainting model can be written:son equation.The advantages of our model consist of two aspectsu=.({k)y(1)A framework is proposed for image restoration by integratAlthough the CDD model satisfies the connectivity principle, iting the techniques of CDD image inpainting, ATV image can be seen from the following experimental results that it generde-noising, and use of the poisson equation in the gradient ates obvious diffusion faults such as blurs and the staircase effect.(2)The ACDD model not only eliminates the staircase effect posed asFor convenience, a general form of the inpainting model is pro-during image inpainting but also reconstructs larger missingregions adaptivelyl=·/aV叫In Section 2 of the paper we briefly describe the classical CDDnodel. The newly proposed model for image restoration is then 3. Adaptive curvature-driven diffusion modeldescribed in Section 3. A numerical implementation of theproposed model and some experimental results are discussed inAs diffusion performance is key, the reasons for deficiencies inSection 4. Last, we conclude our discussion and point out possible the CDD or TV models, namely generation of blurs and the staircaseextensions in Section 5effect, are interpreted in local coordinates in this section2. Curvature-driven diffusion model3. 1. Cause of blurs and the staircasThe curvature-driven diffusion model is derived from the Tv An image can be represented by functioninpainting model Because the Tv model violates the connectivityprinciple the CDD model was proposed as an alternativeu(x,y):R2→Rimage,which is contaminated by noise. D the inpainting domain, in x-y coordinates for image processing. The function u(x,y)repre-uo the original image molap the available part of the image on n sents the gray value of the image. u=(ux, uy)is the gradient ofand u the restored image.u(x, y)and ux=au/ax, uy=au/ay. The x-axes is tangential to theisophote at a local point that is vertical to the gradient direction.The Lagrange multiplier, A, is introduced to define a new energy n, of the image The x-y coordinates are only concerned with thefunctional for the TV modelposition of image pixels. The 4-n coordinates represent the infor-Jr(u)=/IVuldxdy+(1) mation of the isophote that is the important geometric structure ofthe imagex∈Ω\DHence, the s-n coordinate is adopted for analysis of the diffu-0x∈D(2) sion performance of the model. The directions of the 5-and n-axesareThe Euler-Lagrange equation ofj is:vu)+如(u-)=0/(-(10)(3)And the steepest descent path gives:Vuη=m(u,4y)=atiu/+ AD(uo-uThe second-order directional derivatives of theThe first term of Eq. (4)is the regularization term, also calledthe diffusion term that diffuses the available information of u=Vu(,)={n吗-2以y+吃)Vuφmolap into the inpainting domain, D. This is also called the tv=only on the contrast or strength of the isophotes. This strength isreflected in the expression for the diffusion termSetting: p=(u) allows the diffusion term in Eq (9)to be(5)V(((Wu!)Vu)=pV. (u)+uvTherefore, the diffusion strength does not depend on the geo.ietnc information of the isophotes. A plane curve has its geometry=φ·(ux+呦)+(2φx+叫q)(14)encoded into its scalar curvature, K. this is why the TV model vio-lates the connectivity principleUsing:{,中x+uy)=「(四叫)m-ψ m and u+即=叫+Chan et al. modified the tv diffusion term, Eq. (5). to give:umm to substitute in Eq (14)gives:g(|k)中国煤化工(6) v((lVu)Vu)CNMHGZ Lu et al/ Mining Science and Technology(China)21(2011)809-8131e Eq (15)shows that the diffusion term is an anisotropic diffusion ouction and that the diffusion coefficients r(Vul)//Vul and at=v. g(k)r() uTul1)()) control the performance of the diffusion function. So theselection of the function r(Vul) determines the diffusion. For where p=2-va, and d is the normalized difference of curvatureexample, setting r(IVul)=Vu]. The diffusion term in Eq (9)turns given by d=ddmax. Here dmax is the maximum in the differenceout to be V(Vu/IVul) This is the classical TV model. Eq(15) of curvature over the image. Now as d E 10, 1], then p e[1, 2)fitsbecomes ug/Vul So the diffusion direction in the Tv model is tan- the range of p in Eq(19). while at the edges of the imagegential to the isophote. This term also perfectly explains the cause p-1, a=1 and Eq(21)becomes the classical CDD model. Inof the staircase effect in the TV model. If r(/Vu))=(Vu) then Eq. ramping or flat regions p-2, A(d)-0, g(Ix))=1, a= 1 and we(15)becomes V(Vu)=Au=o+Uyy=ug +unn namely, the get the harmonic model. So the ACDD model becomes a differentisotropic harmonic diffusion model. The expression of the diffusion diffusion model according to the property of image region whereterm shows why the harmonic diffusion model blurs the edges it is being applied. This makes the inpainted image smoothereasily3.2. A new diffusion function4. Results and discussionThis analysis suggests the optimal selection conditions are deIn this paper the half-point differential scheme is used. This isrived around the function: r(/Vu!). this is based on the desire for simple and effective for the ACDD inpainting model. Referencesmooth image diffusion.4] has additional information regarding this. After reconstructing(1)In flat or ramping regions of the image, where Vu) is small,the isotropic harmonic diffusion model should be used. Sothe function r())should be given byr(vu)imr"(Vu)=r(0)>0(16)(2)At edges, where Vul is big, it is expected that the model dif-fuses mostly along the tangent to the isophote this is toremove noise. Consequently diffusion along the normal isminimal. Now the conditions arer(VuDIWuj-+e Vy/0. lim r(IVu)=0(17)v叫→+∞Obviously, the two conditions in Eq (17)are contradictory socompromise is proposedlim u = lim r"(Vul)=0where四u|→+∞ Both diffusion coefficients tangential and normalto the isophotes decay to zero, but the latter one decays fasterThere are many functions that satisfy the conditions in Eq(17)and(18)simultaneously. In this paper a hyper surface function isused as the diffusion functionr(u)=r(s)=(a2+s2},a>0,2≥p≥1This analysis shows that the parameter p is very important forthe smoothness of image. The larger p is the more blurred theinpainted image becomes. On the contrary, the smaller p is themore distinct the staircase effect will be. So the question becomeshow to determine p according to the properties of a given imageregion. In this paper the difference curvature, d, is used to repre-sent p[10]d=lummI-lugellThe difference curvature function at the edges andis realized by(1)At the edges of the image junI is large but ug l is small so d is(2)In flat or ramping regions unnI and Jugal are both small So dis smallYH中国煤化工The final form of the aciD model is thenFig. 1.CNMHGami812Z Lu et aL/ Mining Science and Technology( China)21(2011)809-813the destroyed image in the gradient domain a modified gradient Table 1vector fieldNr, time, and number of iterations to obtain Fig. 1b-gG=[Gx, GylFig. 1:(n(g)14432.1132.1132363387is derived. Let u denote the complete image reconstructed from G.Time(s)One of the direct methods proposed in reference [11] is used to iteration500minimize VU-G. so that G& VUIntroducing Laplacian V and a divergence operator V-allowsU The classical TV model, the CDD inpainting model, the p-harto be obtained by solving the Poisson differential equation [13]: monic model, the modified ATV model and the ACDD model arev2U=V·(G,C)compared by simulation[3, 4, 6, 10]. The signal-to-noise ratio(SNR)The ACDD scheme has been implemented in Matlab 2008Ra All is given a as an objective criterion to compare the results.Thisis emplexperiments were run on a Core ll 7500 CPU with 2G ram. Betterhe pandels acesordi i were referene s serting one p rhe mers=10%山-1CDD models and p=1.3, 2=0.01 in the p-harmonic model. Inthe ATv and ACDD models these parameters are determinedIn Eq (23)(i, j)denotes the pixel position, I denotes the oriautomaticallyimage intensity, I is the mean of the original image intensity, and Iis the inpainted imageFig. 1 compares the inpainting models used on an image of aminer. The image size is 256 x 256 pixels. The damaged imagecontains many missing blocks: Several consecutive blocks are evenmissing, as Fig. 1b shows. Fig. 1c-g are the inpainted results usingthe models described. Fig. 2 is an amplified image of the local re-gion of Fig. 1a marked by a white rectangle( Note the different per-formance in the damaged regions ). Table 1 shows the SNR, thetime, and the number of iterations required to obtain Fig. 1b-gThe region marked by the white rectangle in Fig. 1d illustratesthat the CDD model generates obvious diffusion faults. the pro-posed model performs better than the other models when inpainting fine details, which is demonstrated in Fig. 2. The whiterectangles in Fig. 2c-f clearly show the staircase effect generatedby the TV model, the CDD model, the p-harmonic model, and theATV model. Similarly, Table 1 shows that the SNr using the ACDDmodel is largest, that the number of iterations for convergence isthe least, and that the time required is the least of the five model5. CoThe diffusion performance of the CDD model was analyzed inthe local coordinate space of the isophotes. The principle of smoothdiffusion and the difference curvature operator were used to devel-op a novel ACDD model It can restore the damaged images from adomain of the image the performance of the ACDD model is grealycoal mine adaptively. Because restoration occurs in the gradieimproved. Experimental results demonstrate that our model elim-inates the staircase effect and accelerates the convergence rate. Inaddition, the proposed method coupled with a fidelity term couldbe further developed to remove noise from the image.AcknowledgmentsThis paper was partially supported by the National High-TechResearch and Development Program of China (No. 2008AA062200): the National Natural Science Foundation of China(No60802077)and the Fundamental Research Funds for the CentralUniversities (No. 2010QNA43 ). The authors also gratefullyacknowledge the helpful comments and suggestions of thereviewers, which have improved the documentReferencesn.mul中国煤化工CN Ting. in: ProceedingsFig. 2. A small region of the image. marked as a box in Fig. 1a.of ACM SIGGRAPHnce on computer urapnICs: 2u00, p. 417-24ZLu et aL/Mining Science and Technology (China) 21(2011)809-813813[3] Chan T, Shen ]. Non-textureg by Curvature-Driven Diffusions(CCD)J [9] Chen Q Montesinos P, Sun QS, Xia DS. Ramp preserving Perona-Malik model.Vis Commun Image Represen[4 Chan T, Shen J. Variationm436-49.inpainting. 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