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International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.

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  1. 1. Vipul pathak, Deepali Kaushik, Pawan Verma, Rohit Pathak / International Journal ofEngineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1264-12701264 | P a g eAn Efficient Algorithm For Deblurring A Natural ImageVipul pathak, Deepali Kaushik2, Pawan Verma3and Rohit Pathak41Department of Electronic Communication Engineering, Teerthanker Mahaveer University, Moradabad (U.P.),India2Department of Computer Science & Engineering, Krishna College of Engineering and Technology Ghaziabad(U.P.), India3Department of Master in Computer Application, Sharda University G.Noida (U.P.), India4Department of Electronic Communication Engineering, Moradabad Institute of Engineering andTechnology Moradabad (U. P.), India1. INTRODUCTIONBlurred image has always been a bottleneckfor investigating agencies. Deblurring from a singleimage has been an ill-posed and challenging problemdue to the large number of unknowns in theestimation process. The unknowns are the type ofblur, the extent of blur and the noise, which degradethe image further. There does not exist any efficientalgorithm that can deblur any given image. Thispaper attempts to deblur blindly a given naturalimage with an assumption of uniform blurthroughout the image. The algorithm uses theVariation Bayesian approach for optimizing theposterior probability and deriving the most probablePoint Spread Function (PSF). Once the PSF isestimated, a modified Lucy Richardson algorithm isused to do the deconvolution operation and to get thedeblurred image. The algorithm is found to be veryeffective for natural images and the results arequantified using the Cumulative Probability of BlurDetection (CPBD) values. Most of the naturalimages are acquired in neither controlledenvironments nor using professional camera. By aprofessional camera, we mean that it has thecapabilities to detect, motion and rectifies it oncapture. Although images are captured to recorduseful information, degraded version of theoriginal image results in practical cases. Most ofthe on-field cameras are hand held and thus,acquiring a good quality image with the help of sucha camera is challenging, especially whenthe lighting conditions and environment are notcontrolled. Many hardware techniques have beenincorporated now days in cameras to stabilize theoptical system. Optically stabilized lenses are used inboth video and still cameras but are quite expensivein nature. They make use of gyroscopes and inertialsensor systems to stabilize the optical system.Another hardware approach is to usecustomized CMOS image detectors that selectivelycan stop image integration more quickly in areaswhere movement is detected. However, thesehardware techniques are effective only in removingsmall camera shakes at relatively short exposures. Inmany practical cases, long exposures are needed tocapture low light images. The imperfections incapturing introduce blur and noise to the image1.1 PROBLEM STATEMENTRestoration of blurred images is a vitalproblem especially in tracking and identification ofcriminals. The available image can be used toidentify a human face or a moving vehicle’s numberplate taken in hit and run situation or in a bomb blastsite. To restore a blurred image successfully,blurring function needs to be estimated accurately.Blurring function is referred to as Point SpreadFunction (PSF) which is the response of animaging system to a point source or it can be saidas the impulse response of a focused optical system[1]. It is non-parametric and spatially varying.Deblurring is an ill-posed problem because of thenumber of unknown parameters is more than theavailable parameters. This paper discusses some ofthe available deblurring algorithms and proposes anefficient approach to deblur issue. The aim is toidentify the PSF and to apply the restoring algorithmto get the latent image. Some of the reasons for theseimperfections are as follows:- Relative motion between camera and thesubject being captured: During the exposuretime of the camera, this type of motion causesthe pixels being spread over a distance in thedirection of the motion. It can be said thatthe image gets integrated over time duringthe exposure; thus causing a single pixelrecorded from each point of the scenecontributing to several different pixels in thereal image. This degradation of image can betermed as motion blur. Atmospheric turbulences: It can becaused dueto temperature variations and windthat causes the light rays to refract anddegraded the image received on the camerasensor. Imperfect focus: Wrong focal point of thecamera lenses leads to blurred version of theimage. Even after taking care of focal pointadjustment, use of a shallow depth of fieldmay cause blur to some parts of the image. Bad capturing device: Damaged camerasensor, shutter or lenses can induce blurringeffect by scattering the light falling on thesensor.Noise plays a major role in aggravating the
  2. 2. Vipul pathak, Deepali Kaushik, Pawan Verma, Rohit Pathak / International Journal ofEngineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1264-12701265 | P a g edegradation. It may be introduced by the followingsources Measurement errors of the sensor/camera:Measurement errors of the camera arecaused due to damages in the cameracircuitry, sensor or lenses. Quantization noise while digital storage:Digital images are quantized while beingstored in a storage device. This introduces aquantization noise depending upon thesampling rate selected by the system. The bitdepth of the digitization process limits theSignal to Noise Ratio (SNR) of a digitalsystem. Noise introduced by the medium: Noise isalso introduced by the medium due toscattering effects and random absorption. Thisis very common in the case of distantphotography. Electronic Noise: Even without incominglight, the electrical activity of the sensor itselfgenerates some signal. For understanding, thiscan be compared with backgroundhumming sound of audio equipment, which isswitched on without playing any music. Thisis caused by the electronic components likeamplifiers in the circuit. This additional signalis noisy because it varies per pixel andincreases with temperature and adds to theoverall image noise. Photoelectric noise: Each pixel in a camerasensor contains one or more light sensitivephotodiodes, which convert the incominglight (photons) into an electrical signal,which is processed into the color value of thepixel in the final image. If the same pixelwould be exposed several times by the sameamount of light, the resulting color valueswould not be identical but have smallstatistical variations and can be called asnoise. Relative motion between camera andthe subject is one of the prime player whichcauses blurring in an image. The real relativemotions can take convoluted paths and thusmaking the restoration more complex.Restoring of blurred image involve twocomponents, namely identification of blurand restoration of image using the obtainedblurring parameters1.2 GENERAL BLUR MODELDegradation of sharpness and contrast of animage, which cause loss to the higher frequencies, iscalled as blur. The observed image is a result of theconvolution of the latent image with a point spreadfunction and some added noise. Figure 1 shows thegeneral model of blur which shows the blurredastronomical image. In the image, it is evident thatthe observed image is blurred and classification oridentification of the object in it is difficult. Theblurred image is formed as a result of the degradationcaused by the Unknown Point Spread Function asshown in Figure 1. The unknown noise adds to thetrouble by making the operation difficult to reverse.Figure 1 General Model of BlurLet g(x,y), f(x,y) ,h(x,y) and n(x,y) be the measured image, the true image, the point spread function (PSF) andthe additive random noise respectively where (x,y) represent the position of the pixels.Then, (x,y) can be defined asWhere * is convolution operation. Now if one considers in frequency domain, then one gets
  3. 3. Vipul pathak, Deepali Kaushik, Pawan Verma, Rohit Pathak / International Journal ofEngineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1264-12701266 | P a g eIt can be seen that all the parameters on the righthand side of the Equation 1.3 are unknown. Thereare two types of deblurring approaches namely, non-blind deblurring and blind deblurring which areclassified according to the context or application. Innon-blind deblurring, knowledge of the PointSpread function (PSF) is available whereas in caseof blind deblurring, any prior knowledge aboutthe PSF or type of blur is not available. This paperaddresses the blind deblurring operation. For aperfect motion blur, the parameters to be consideredare the length and the direction of blur. In this case ifit is assumed that there is no noise, it is easy toreconstruct the PSF using the length and the angleparameters and to do a non blind deblur operation.Some of the typical PSFs are shown in Figure 1.2.There are four different types of Point SpreadFunctions, namely Motion Blur, out of Focus Blur,Gaussian Blur and Scatter Blur that are very basicand generic in nature. Out of those four, twofunctions belong to the category of sharp edged PSFsand the other two belong to the category of smoothedged PSFs. These illustrations of these PSF modelsare in time domain. In practical cases, such estimatedmodels might not be as perfect as shown in figure1.2.Figure 1.2 Graphical Interpretations of Different Types of Blurs2. RELATED WORKAttempts have been made to address theproblem of blind deconvolution for deblurring of anatural image. Recent algorithms have achieveddramatic progress. However, there exist yet manyaspects of the problem which are still challengingand hard to solve. Lokhande et. al. have worked onidentification of motion blur parameters [2] usingfrequency domain analysis and tried to reconstructthe PSF using the length and angle information.This approach may not perform well for naturalimages because the algorithms assumes PSF to beperfectly box (linear) which is not the case in manynatural images. The algorithm also does not caterfor varying noise levels. Joshi et. al. have tried toestimate the PSF using sharp edge prediction [3].They have tried to predict the ideal edge by findingthe local maximum and minimum pixel values. Thisalgorithm has given good results for smaller blursbut has not performed well for larger blurs. Levin et.al. have proposed an algorithm to deblur a blurredimage using image statistics [4]. They have provedthat the direction of motion blur is the direction withminimal derivative variation and the value whichgives the maximum likelihood of the derivatives isthe blur length. This algorithm has given good resultsonly for box kernels. Box kernels are characteristicsof perfect motion blurs. Blurs are not always motionblurs alone and most of the motion blurs do not haveperfect box PSF. Fergus et. al. [5] have approachedthe problem using a variational Bayesian approachfor PSF estimation. Shan et. al. [6] have used asemi maximum a-posteriori (MAP) algorithmwhich is used to get a point estimate of the unknownquantity based on empirical data. They have used aGaussian prior for natural image and edgereweighting and iterative likelihood update for
  4. 4. Vipul pathak, Deepali Kaushik, Pawan Verma, Rohit Pathak / International Journal ofEngineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1264-12701267 | P a g eapproximation of latent image. This algorithm doesnot work well for all images which is sparse or a bitaway from Gaussian. Yuan et. al. have used of twosets of images (one blurry and one noisy) to recoverthe original image [7]. A comprehensive literaturereview to approach a deconvolution problem can befound in [8]. Miskin and Mackay have usedensemble learning algorithm to extract hiddenimages from a given image [9]. They have usedVariational Bayesian approach to do ensemblelearning.2.1 CHALLENGESThe major challenge in deblurring anatural image is the determination of the unknownparameters like type of blur, extend of blur (PSF)and the approximation of noise. The number ofunknowns is more than the number of knownparameters making the problem ill posed. Evenminor reduction in accuracies in PSF estimationleads to degradation of image quality whiledeblurring.3. PROPOSED WORKThis paper work started with the approachof estimating the blur parameters using thealgorithms discussed below. The algorithm aims atdetermining the Blur parameters such as length ofblur in pixels and the angle of blur in degrees. Thisalgorithm used for estimating the blur parameters,deblurring of the image using the estimatedparameters, its limitations and the proposedEfficient Deblurring Algorithm for natural images.following is our proposed model figure 3.Figure:- Proposed model3.1 DESIGNINGLokhande et. al have introduced the use of frequencydomain to estimate the blur parameters length andangle. The algorithm uses the spectrum of the imagefor analyzing the blur and Hough transform todetermine the blur angle. Spectrum of an image doesnot reduce all the noise parameters introduced andhence display lines which are not representing theblur direction in the image. Hough transform alsodoes not perform well in such a case and iscomputationally intensive. This paper uses thecestrum of the image instead of spectrum andradon transforms instead of Hough transforms.While taking radon transform, binary image of thespectrum is used to make computations easy. Radontransform gave accurate results and is easy toimplement. Once the blur direction is obtained, thebinary cepstrum image is rotated by the estimatedangle and average of each column is taken. Thedistance between the zero-crossings represents theinverse of the length parameter. The algorithm is asfollows:- Read the image Convert to grayscale Calculate Log and square of the image. Calculate Inverse Fast Fourier Transform toget the cepstrum. Convert to binary Apply radon transform for various angles. Find the angle at which the radon transformvalue is maximum to get θ. Calculate average along each column. Find the distance between the zerocrossings to get the periodicity and hence L.3.2 DEBLUR USING THE BLURPARAMETERSUsing the parameters, blur length and angle,the PSF can be constructed. Once the approximatePSF is available, the latent image can be
  5. 5. Vipul pathak, Deepali Kaushik, Pawan Verma, Rohit Pathak / International Journal ofEngineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1264-12701268 | P a g ereconstructed using any of the deconvolutionalgorithms explained in above This paper uses thewiener filter, which is faster and computationallyless expensive. Approximating the correct value ofNoise to Signal Ratio dictates the quality of theoutput of the Wiener Filter. We have approximatedNoise to Signal Ratio (NSR) as follows:-NSR=1/ (2log base10 (max pixel value-min pixelvalue)/ standard derivation)3.3 LIMITATIONThis algorithm works well for syntheticallygenerated blurs but fails for natural blurs. The mainreason for this is the fact that most of the naturalblurs are not perfect motion blurs which have anangle and length. These blurs are either out of focusblurs or non-linear motion blurs due to camera shake,or random blurs. The biggest challenge is to knowthe type of blur and then decide the way to obtain thePSF. Most of the naturally blurred images havePoint Spread Functions which have random shapeand estimating such a PSF is a big challenge. Imageprocessing problems do not have fixed solutions. Allproblems are specific to the image and thus one needto look for a solution that can generalize some of therestrictions and come to a common conclusion orwork individually on each input images. Theseresults also suffer from the phenomenon of ringingartifacts.4. EXPERIMENTAL RESULTSExperiments have been carried out using theproposed algorithms in this paper. The User assisteddeblurring algorithm using radon transform andcestrum gave excellent results for syntheticallygenerated blurs. The results of the angle and lengthestimated are illustrated in Table 4.1 as well as in theimages.Image Name Actual Theta Estimated Theta Actual Length Estimated LengthCar1 30 34 60 62Car2 30 33 50 50Bike 45 48 65 66Gate 30 32 45 45Ground 10 11 55 55Face 9 10 31 30Peacock 2 3 50 49TABLE 1
  6. 6. Vipul pathak, Deepali Kaushik, Pawan Verma, Rohit Pathak / International Journal ofEngineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1264-12701269 | P a g e5. CONCLUSION & FUTURE WORKIt is difficult to generalize image-processingproblems. Every image is different from each otherand thus needs human intelligence and interventionto approach a problem. Therefore, it can beconcluded that every image-processing problem isunique. This paper has improved upon the algorithmsuggested by Lokhande et. al. [2] by increasing theaccuracy of blur parameters detection and reducedthe computational complexity by using radontransform and cestrum domain. It also proposesan efficient algorithm using machine-learningapproach to come to an accurateestimation of PSF. The algorithm requires userintervention to select the Region of Interest (ROI)which does not have saturated pixels. The resultsdepend largely on the area of interest selected and
  7. 7. Vipul pathak, Deepali Kaushik, Pawan Verma, Rohit Pathak / International Journal ofEngineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1264-12701270 | P a g ethe degree of non-saturation in the image. It isdifficult to incorporate all possible type of imagedegradation in a single model. However, thisalgorithm gives good results for natural blurs and itcaters for most types of blurs. There is a scope forimprovement in the deconvolution algorithm likeLucy-Richardson algorithm and wiener filter.Reduction of ringing artifacts has been a challengewhile working in frequency domain. Modeling ofnoise is very important while approaching ill-posedproblems. The algorithm can perform better if noisecan be modeled in a better manner. Gaussianapproximation is used for noise in this algorithm andthat might not be ideal for camera noises. Thealgorithm assumes images to have linear tone scale.However, cameras generally have sigmoid shape totheir tone response curve. The selection of ROI isdone manually to avoid saturated regions and thusthe consistency of the algorithm varies. If somestatistical or heuristic approach can be implementedfor the selection of ROI, better results can beobtained. Use of shallow depth of field in manycameras cause blur only to certain areas of theimage. Using the same PSF to deblur the wholeimage may cause the unblurred parts to degradefurther. It is possible to segment the image based onsome energy function or blur measurement functionand carry out deblurring for different segments usingdifferent PSFs. This may make the recovered imagealso look segmented. The algorithm has beenimplemented as a serial code and there is a scope ofparallelizing it for larger images.REFERENCES[1] Wikipedia, Point spread function ---Wikipedia[2] R. Lokhande, K. V. Arya, and P. Gupta,"Identification of parameters andrestoration of motion blurred images," inProc. of the 2006 ACM symposium onApplied computing, 2006, pp. 301-305.[3] N. Joshi, R. Szeliski, and D. J. Kriegman,"PSF estimation using sharp edgeprediction," in Proc. IEEE Conf.Computer Vision and Pattern RecognitionCVPR 2008, 2008, pp. 1-8.[4] Anat Levin, "Blind motion deblurring usingimage statistics," i Advances in NeuralInformation Processing Systems (NIPS),2006.[5] Rob Fergus, Barun Singh, AaronHertzmann, Sam T. Roweis, and WilliamT.Freeman, "Removing camera shake froma single photograph," in SIGGRAPH 06,2006, pp. 787-794.[6] Qi Shan, Jiaya Jia, and Aseem Agarwala,"High-quality motion deblurring from asingle image," in ACM SIGGRAPH 2008papers, 2008, pp. 73:1--73:10.[7] Lu Yuan, Jian Sun, Long Quan, and Heung-Yeung Shum, "Image deblurring withblurred/noisy image pairs," in ACMSIGGRAPH 2007 papers, 2007.[8] D. Kundur and D. Hatzinakos, "BlindImage Deconvolution," IEEE SignalProcessing Magazine, vol. 13, no. 3, pp. 43-64, 1996.[9] James Miskin and J. C. David,"Ensemble Learning for Blind ImageSeparation and Deconvolution,"inIndependent Component Analysis, M.Girolani, Ed.: Springer-Verlag, 2000.AuthorsVipul PathakThe author is pursuing PostGraduation in engineering fromTeerthanker Mahaveer University,Moradabad (U.P.). He had completedengineering from MoradabadInstitute of Technology;Moradabad(U. P.) affiliated toGautam Buddha Technical University in 2011.Deepali KaushikThe author is pursuing Post Graduationin engineering from Krishna Instituteof Engineering and TechnologyGhaziabad (U.P.). She had completedengineering from VenkateshwaraInstitute of engineering & Technology;MEERUT (U.P.) affiliated to GautamBuddha Technical University in 2011.Pawan VermaThe author is pursuing PostGraduation in Master In computerApplication from Sharda University,Greater Noida (U.P.).Rohit PathakThe author had completedengineering from Moradabad Instituteof Technology; Moradabad(U. P.)affiliated to Gautam BuddhaTechnical University in 2011.