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Journal of Research and Practice in Information Technology, Vol. 41, No. 3, August 2009 195 Noisy Motion-blurred Images Restoration Based on RBFN Xinzhong Zhu, Jianmin Zhao, C. J. Duanmu and Huiying Xu College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, Zhejiang, China {zxz,zjm,duanmu,xhy}@zjnu.cn To restore a degraded image, which has been corrupted by some kinds of noise and motion blur, a model for restoration is first presented and then an algorithm based on this model and the radial basis function network (RBFN) is proposed in this paper. In the first step of this algorithm, noise is removed by using the RBFN interpolation with variable regularization parameters. In the second step, the motion blurred image is restored based on the automatic identification of the direction and length of the motion-blur. Moreover, a method, based on object extraction, for restoring local motion blurred image is given to solve the problem of the bad restoration results when the global motion-blurred characteristics are missed for local motion-blurred images. Experimental results demonstrate that the proposed method performs well when applied to general motion-blurred images, and can also be applied to the local variable speed motion-blurred images. The restoration algorithm can give accurate identification of the degraded model and good restoration results, even under the condition of a relatively large noise interference. Keywords: noisy motion blurred image restoration, local motion blurred image restoration, radial basis function network, variable regularization parameter, optimal windowed wiener filtering ACM Classification: I.4 Manuscript received: 26 November 2008 Communicating Editor: Phoebe Chen Copyright© 2009, Australian Computer Society Inc. General permission to republish, but not for profit, all or part of this material is granted, provided that the JRPIT copyright notice is given and that reference is made to the publication, to its date of issue, and to the fact that reprinting privileges were granted by permission of the Australian Computer Society Inc. 1. INTRODUCTION Restoration of noisy and blurred image is one of the hot and difficult research areas in the field of image enhancement and image processing (Zhu et al, 2006; Hsia, 2005). It has wide application areas (Hong and Zhang, 2004; Zeng et al, 2003; Wang et al, 2005), such as the car license plate recognition for identifying cars driving at an excessive speed or against the law, the image restoration of the grasped video frames of an outburst crime, the restoration and recognition of physical traces of a crime, and the restoration of a specific frame of a video monitor. Image degradation is usually generated by the defocus of a imaging system, the relative high motion between the interested object and the imaging system, the inherent defect of imaging equipments, the shaking in shooting the images, or the outside noise interferences. Among these situations, a noisy local variable-speed motion-blurred image is particularly hard to restore, since (i) the cause of the degradation of this kind of image is very complicated, (ii) there is a lot of loss of image information, and (iii) there are no reference frames for restoration in the sequence. Restoration of * Regular Paper This research has been supported by the financial support from Natural Science Foundation of China with the project 60773197 and 60772071 and Science and Technology Plan of Zhejiang Province with the project 2005C11035.

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Journal of Research and Practice in Information Technology, Vol. 41, No. 3, August 2009 195

Noisy Motion-blurred Images Restoration Based on RBFNXinzhong Zhu, Jianmin Zhao, C. J. Duanmu and Huiying XuCollege of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004,Zhejiang, China{zxz,zjm,duanmu,xhy}@zjnu.cn

To restore a degraded image, which has been corrupted by some kinds of noise and motion blur, amodel for restoration is first presented and then an algorithm based on this model and the radialbasis function network (RBFN) is proposed in this paper. In the first step of this algorithm, noise isremoved by using the RBFN interpolation with variable regularization parameters. In the secondstep, the motion blurred image is restored based on the automatic identification of the direction andlength of the motion-blur. Moreover, a method, based on object extraction, for restoring localmotion blurred image is given to solve the problem of the bad restoration results when the globalmotion-blurred characteristics are missed for local motion-blurred images. Experimental resultsdemonstrate that the proposed method performs well when applied to general motion-blurredimages, and can also be applied to the local variable speed motion-blurred images. The restorationalgorithm can give accurate identification of the degraded model and good restoration results, evenunder the condition of a relatively large noise interference.

Keywords: noisy motion blurred image restoration, local motion blurred image restoration,radial basis function network, variable regularization parameter, optimal windowed wiener filtering

ACM Classification: I.4

Manuscript received: 26 November 2008Communicating Editor: Phoebe Chen

Copyright© 2009, Australian Computer Society Inc. General permission to republish, but not for profit, all or part of thismaterial is granted, provided that the JRPIT copyright notice is given and that reference is made to the publication, to itsdate of issue, and to the fact that reprinting privileges were granted by permission of the Australian Computer Society Inc.

1. INTRODUCTIONRestoration of noisy and blurred image is one of the hot and difficult research areas in the field ofimage enhancement and image processing (Zhu et al, 2006; Hsia, 2005). It has wide applicationareas (Hong and Zhang, 2004; Zeng et al, 2003; Wang et al, 2005), such as the car license platerecognition for identifying cars driving at an excessive speed or against the law, the imagerestoration of the grasped video frames of an outburst crime, the restoration and recognition ofphysical traces of a crime, and the restoration of a specific frame of a video monitor. Imagedegradation is usually generated by the defocus of a imaging system, the relative high motionbetween the interested object and the imaging system, the inherent defect of imaging equipments,the shaking in shooting the images, or the outside noise interferences. Among these situations, anoisy local variable-speed motion-blurred image is particularly hard to restore, since (i) the causeof the degradation of this kind of image is very complicated, (ii) there is a lot of loss of imageinformation, and (iii) there are no reference frames for restoration in the sequence. Restoration of

* Regular PaperThis research has been supported by the financial support from Natural Science Foundation of China with the project 60773197 and 60772071and Science and Technology Plan of Zhejiang Province with the project 2005C11035.

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motion-blurred image has become a research hotspot in recent years (Guan et al, 2005; Rav-Achaand Peleg, 2005: Gangal et al, 2004). The key problem (Dougherty and Kawaf, 2001; Zhang et al,2000) in this research lies in the decision of a point spread function (PSF) for motion-blurredimages. For a single motion-blurred frame, the unknown parameters of PSF must be estimated fromthe degraded frame itself. A common method to estimate the motion-blur direction and length isthrough observing the spectrum of the degraded image (Cannon, 1976). Therefore, this method can -not achieve automatic identification, since some manual intervention is necessary in the restorationprocess. Recently, some automatic identification algorithms have been proposed by scholars both inChina and abroad (Yitzhaky and Kopeika, 1997; Wang and Zhao, 2001; Chen et al, 2004; He andLi, 2005). However, these algorithms have poor performance or even fail under the condition ofsome noise interference. Thus, it is necessary to suppress the noise interference before determiningthe parameters of PSF and restoring the image. However, lots of current filtering algorithms eitherhave a high computational complexity or lose the important high frequency information (Kuntssonet al, 1983; Sugiyama and Ogawa, 2002), and thus greatly degrade the restoration results.

In recent years, a special class of artificial neural networks, called the radial basis functionnetwork (RBFN), has received considerable attention and have been widely applied (Firsov andLui, 2006; Acosta, 1995; Pitas, 2000; Karageorghis et al, 2006; Girosi, 1992; Gokmen and Jain,1997; Sigitani et al, 1999). This paper chooses the RBFN method with variable regularizationparameters for removing noise. The RBFN algorithm can suppress noise without destroyingimportant image information, and it has low computational complexity of O(N3) while computingRBFN interpolation output with variable regularization parameters for each pixel through the usageof the properties of the Kronecker product. The motion-blurred image restoration model proposedcannot only give high automatic identification accuracy, but also be applied to the complicatedimaging reality such as local variable speed motion blur and high noise interferences.

2. NOISE-REMOVAL METHOD BASED ON RBFN WITH VARIABLE REGULARIZATION Assume that the motion-blurred image f(m,n) is degraded into noisy motion-blurred image y(m,n)caused by noise interference during the image acquisition and transmission process, the relationshipbetween them can be described as y(m,n) = f(m,n) + ε(m,n), where ε(m,n) represents the additiveGaussian white noise with variance σ2. This paper suppresses noise without destroying importantimage features by using the capacity of universal approximation of RBFN and selecting the variableregularization parameter of λ which is proportional to the noise level at each pixel. We choose theradial basis function (RBF) with the centre of x(m–1)N+n for the pixel at the position (m,n) and theRBF output y(n–1)N+m as the output for the pixel value. Then the denoised motion-blurred image canbe obtained from y(m,n) by using the RBFN method through this mapping information. This methodhas the following two aspects.

2.1 Adaptive Selection of Regularization ParameterRBFN generate the interpolated image that minimizes the following cost function

(1)

Where G is the (L × L) matrix whose ijth element is represented by (G)ij = g(||xi–xj||), given a set of

L observations g is the Gaussian function represented by ,

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in the above formula, the parameter σx, called the standard deviation of the Gaussian function. Thefirst term of the cost function measures the distance between the data and the desired solution, andthe second term measures the cost associated with the smoothness. The trade-off between these twoterms is controlled by the regularization parameter λ. The choice of regularization parameter isdetermined by (2)

(2)

where A and a are constants A = qσ2 (q is a proportional constant). Let us denote the minimum ofλ(m,n) and the maximum of | f '(m,n)| to be λmin and f 'max respectively, the constant a is thendetermined by: .

2.2 Fast Computation of RBFN with Variable Regularization ParametersComputing RBFN directly by (1) is costly, so it is necessary to develop fast output of RBFNinterpolated image by using the properties of Kronecker product. By utilizing the regularities ofGaussian distribution, G can be expressed as

(3)

Where Λ=diag(μ1,μ2, …,μN),V=(v1,v2, ..vN), μi and vi are the eigenvalue and eigenvector of Gs

respectively. Transform (3) and simplify it, we have

(4)

Then the computational complexity of computing the output vector fλ form the noisy motion-blurred image in reduced form O(N6) to O(N3). On the basis of (4), the RBFN output with variableregularization parameter at each pixel can be presented by

(5)

Where [(V ⊗ V)(Λ ⊗ Λ)](m–1)N+n represents the (m–1)N+n column of the matrix [(V ⊗ V)(Λ ⊗ Λ)].It can be seen that the computational complexity of computing RBFN with a variable regularizationparameter is much larger than that with a fixed regularization parameter. We thus utilize thedistribution characteristic of | f '(m,n)| to reduce the computation time. Since low frequencycomponents are predominant in the histogram of | f '(m,n)|, almost all values of | f '(m,n)| are veryclose to zero. We thus set a threshold value R, put the regularization value whose | f '(m,n)| = 0 to beλ0, then we fix the regularization parameter to λ0 at pixels whose | f '(m,n)| value is less than R whilestill computing the regularization parameter by (2) at pixels whose | f '(m,n)| value is larger than R.By the optimization carried out above, the algorithm has low computation complexity O(N3) eventhough it computes RBFN output with variable regularization parameter for each pixel.

The noise-removing method by using RBFN with variable regularization parameter is based onthe following mechanism illustrated by a one-dimensional schematic as shown in Figure 1.

Mechanism: Although the noise can be efficiently removed in flat areas, the important edgeinformation is lost as step edges are converted into smooth edges (as shown in Figure 1(a) andFigure 1(b)). Thus, the error information which is produced in this process is first saved into e(n).

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Then, the RBFN is used to extract the lost edge information from the noisy error image e(n) (asshown in Figure 1(c)). After this, the regularization parameter is small near edges so that theinterpolated image fλ(n) matches to e(n) and it is large in flat areas so that fλ(n) becomes smooth (asshown in Figure 1(c) and Figure 1(d)). Finally the denoised image is obtained by adding fλ(n) tos(n). The implementation of this process is summarized in the Algorithm1:

Algorithm 1: Noise-removal algorithm using RBFN with regularization parameter.Step 1. Generate the lowpassed smooth image s(m,n) from the noisy motion-blurred image by usingthe 2D mean filter:

Step 2. Compute the error image between the noisy motion-blurred image e(m,n) and the lowpassedsmooth image s(m,n):

e(m,n) = y(m,n) – s(m,n).

Step 3. Estimate the gradient of y(m,n) denoted by f '(m,n) by using the canny edge detector.

Step 4. Compute the regularization parameter for each pixel according to the size of f '(m,n), andthen generate the interpolated image f λ(m,n) by approximating the error image using the RBFN.

Step 5. Obtain the denoised motion-blurred image f (m,n) by adding the interpolated imagef λ(m,n) to the lowpassed smooth image s(m,n).

Figure 1: The basic idea of removing noise using the RBFN with variable regularization parameter. (a) Original image (b) Lowpassed smooth image (c) Error image (d) Interpolated image

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2.3 Experimental ResultsImplementation of algorithm 1 is shown in Figure 2 (using the Cameraman image). Figure 2(a) isthe noisy motion-blurred image y(m,n) interfered by Gaussian white noise with variance σ2 = 400.Figure 2(b) is the smooth image s(m,n) lowpassed by a 5*5 mean filter. Figure 2(c) is the errorimage e(m,n) between the noisy motion-blurred image y(m,n) and the lowpassed smooth images(m,n). Figure 2(d) is the interpolated image f λ(m,n) which approximates error image e(m,n) byusing the RBFN with regularization parameter. Figure 2(e) is the denoised motion-blurred imagef (m,n) by adding the interpolated image f λ(m,n) to the lowpassed smooth image s(m,n). Figure 2(f)is the spectrum of f (m,n). (It can been seen from Figure 2(f) that the spectrum of denoised motion-blurred image present the motion-blur characteristic of direction and length obviously.)

The proposed method can also be adapted to colour images as shown in Figure 3 using Lenaimage (the noise-removing process and mechanism of Figure 3 are the same as that of Figure 2).

3. THE IMAGE RESTORATION METHOD BASED ON AUTOMATIC IDENTIFICATION OF MOTION-BLURDIRECTION AND LENGTH

3.1 The Automatic Identification of Motion-blur DirectionThe automatic identification of motion-blur direction is based on the following theory. The originalimage is assumed to be an isotropic Markov process with rank one, that is, the autocorrelation and

(a) (b) (c)

(d) (e) (f)

Figure 2: Removing noise from ‘cameramen’ using the RBFN with variable regularization parameter. (a) Noisy and motion-blurred image (b) Lowpassed smooth image (c) Error image (d) Interpolated image

(e) Denoised motion-blurred image (f) The spectrum of Figure 2(e)

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power spectrum of the original image is isotropic. The motion blur suppresses the high frequencycomponent in the motion direction and has little influence in other directions. The more deviationfrom the motion direction, the less effect the motion blur has. Thus, there is hardly any effect in thedirection perpendicular to the motion direction. Therefore, we use the directional highpass filtering(directional derivation) for the motion-blurred image. The absolute summation of grey values in thedirectional filtered image must reach minimum when the filtering direction meets the motion direc -tion, since the blurred image contains the least high frequency components in this direction. So,after generating the directional filtered image by highpass filtering with a certain direction, thedirection, which has the minimum absolute summation of grey values in the filtered image, is justthe motion direction.

This paper employs the bi-cubic C spline interpolation method, which interpolates for threetimes in the horizontal and vertical directions respectively, we define the g = s(x) as subsectioncurve of a function, the function is constructed through bi-cubic C spline interpolation method, atthe coordinate of (i, j). Thus we get the interpolation coefficient with term hk = xk+1 – xk = 1 (xk is ior j, x is i' or j', gk is the grey value, g = Sk(x) is got through interpolation), we define dk = gk+1 – gk,uk = 6(dk+1 – dk), mk = s'' (xk) and use the boundary condition

(a) (b) (c)

(d) (e) (f)

Figure 3: Removing noise from ‘lena’ using the RBFN with variable regularization parameter. (a) Noisy and motion-blurred image (b) Lowpassed smooth image (c) Error image (d) Interpolated image

(e) Denoised motion-blurred image (f) The spectrum of Figure 3(e)

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(6)

And its interpolating function:

(7)

where v = x – xk(xk ≤ x ≤ xk+1).We adjust the directional derivative image using the weighted average method (detailed in

algorithm 2), and make the frequency of the grey scale x denoted by p(x) as its coefficient since thelow frequency components are predominant in the histogram of motion-blurred image, then thepixels in the area with low grey level could become the important factor which have an effect onthe directional derivative image. The implementation is summarized as algorithm 2:

Algorithm 2: The automatic identification algorithm of motion-blur direction. Performing Step 1 and Step 2 for each value of α in the range of α ∈ [–90°,90°]:

Step 1. Calculate the directional derivative image Δf(i, j)α = f(i', j') – f(i, j) by using bi-cubic C splineinterpolation method.Step 2. Calculate the absolute summation of grey value in directional derivative image and makethe weighted average adjusting meanwhile:

Step 3. Determine the minimum value of I(Δf)α and the corresponding value of α is just the includedangle between the motion-blur direction and the horizontal axis,

3.2 The Automatic Identification of Motion-blur LengthThe motion-blurred image can be reversely rotated to the horizontal direction after the automaticidentification of the motion-blur direction. Then, we can automatically detect its motion-blurredlength. The automatic identification of motion-blur length is based on the fact that the black regionsappear at specific intervals in the frequency domain of the motion-blurred image. Particularly, forthe denoised linear motion-blurred image, the motion-blur length can be estimated accurately byusing the positions of the black regions at regular intervals. The implementation can be summarizedin the Algorithm 3.

Algorithm 3: The algorithm for automatic identification of motion-blur length.

Step 1. Denote the Fourier transform of the motion-blurred image as F(u,v). Calculate log(|F(u,v)|)and shift it to make u=0 at the central position of the spectrum.

Step 2. Calculate

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Find the kth(k>1) minimum value of u, denoted by uLk, which lies to the left of the left centre mid = ⎣N / 2⎦. Find the kth(k>1) minimum value of u, denoted by uRk, which lies to the right of theright centre mid = ⎣N / 2⎦.

Step 3. Calculate the motion-blur length of the linear motion-blurred image f(x,y) at arbitrary angle:L ≈ Round(2k* N / |uLK – uRk).

This method uses u directional projection with the kth(k>1) minimum so that the entire staticinformation of a column can be utilized. Therefore, it reduces the random interference caused bythe original image and avoids the computational error effectively. In this method, the minimumpoints corresponds to the location of the black region, that is, u = Round(kN / a). The motion-blurredlength can be calculated automatically by the comparison between the two left and the two rightneighbouring pixels.

3.3 Optimal Windowed Wiener Filtering MethodRestoring a two-dimensional blurred image (with its width of HL and height of VL) by using theoptimal windowed Wiener filtering (Inoue, 2003) can effectively remove the restoration errorcaused by the differences of average levels at boundary locations. Thus, the optimal windowedWiener filtering can suppress the ring artifact. Divide the image area into nine regions. Therelationship between a region and the element values in the region’s optimal window is shown inFigure 4.

3.4 Experimental results To examine the results of the restoration process, which implements the automatic identificationalgorithm of motion-blur direction and length, and the optimal windowed wiener filtering for ringartifact suppression, motion blur and noise to the original clear image artificially are first added.Then the identification accuracy and restoration results are compared between the regular methodwithout the noise-removing process and the proposed method using the RBFN noise-removingmethod, as shown in the Figure 5.

The results of restoring the denoised motion-blurred images of Figure 2(e) and Figure 3(e) byusing the proposed image restoration algorithm based on the automatic identification of motion-blurdirection and length, are shown in the Figure 6.

Figure 4: The relationship between a region and the element values in the region’s optimal window

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Figure 5: The restoration process of noisy and motion-blurred image; comparision of identification accuracy andrestoration result.

(a) (b)

Figure 6: The restoration results of denoised motion-blurred image (a) Restoration result of Figure 2(e)(b)Restoration result of Figure 3(e)

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4. LOCAL MOTION BLURRED IMAGE-RESTORING METHOD BASED ON OBJECT EXTRACTION WITHMOTION-BLUR CHARACTERISTIC

4.1 Local Motion-blurred Object ExtractionIt is common in daily life that the moving body moves fast against the imaging device while thebackground stands still, or multiple objects move in different directions with variable speed. If westill apply global processing for the local motion-blurred image under this situation, not only theclear background will be blurred in an artificial way, but also most of the regular automaticidentification methods proposed at present will be failed due to the loss of global motion-blurcharacteristics in local variable speed motion-blurred images. Therefore, these methods are unableto restore this kind of image effectively.

After the local motion-blurred object extraction is performed, the characteristics of generalmotion-blurred image appear in the newly generated image which contains only the motion-blurredobject. Therefore, it is possible to effectively restore the generated image by using the imagerestoration method proposed in this paper.

The main problem for restoring a single local motion-blurred image lies in extracting themotion-blurred object without the reference information provided by the correlated frames in asequence, as for a single object image. For a video frame taken in a multi-lane highway motoringsystem, as shown in Figure 7, the problem can be simplified based on the prior knowledge of theinterested object that we want to extract. The object is a car moving fast in the lanes, and its shapeis close to a rectangle. This motion-blurred object can be extracted in the space domain based onthis assumption. The implementation can be summarized as Algorithm 4 in the following.

Algorithm 4: The local motion-blurred object extraction algorithm.

Step 1. Segment the image using fitting grey threshold.

Step 2. Generate the rectangle matching template in proportion to the size of the image.

Step 3. Perform the mathematical morphology close operation for the segmented image using thegenerated rectangle template to extract large rectangular cars, and then perform the mathematicalmorphology open operation to get rid of some smaller subjects.

The algorithm above can be implemented efficiently for its low computing time. However it ismainly applied to a video frame, where the grey levels of the object and the background are quitedifferent. For a video frame, where the grey levels of the object and the background are similar, segmen -ta tion according to grey level threshold may cause a lot of spatial segmentation errors. Under thissituation, it is better to implement the object extraction process by using the following Algorithm 5:

Algorithm 5: The local motion-blurred object extraction algorithm.

Step 1. Use the Prewitt operator and canny operator seprately. Perform the edge detection for themotion-blurred image by employing the logical “and” operation between the results from Prewittand Canny operations.

Step 2. Detect all the line segments whose length is greater than Lmin for the binary value edgeimage by employing the radon transform and save the properties of them, including the initial point,end point, and the angle between this line and the horizontal direction. (This method can overcomesome problems of the traditional Hough transform. For example, the Hough transform is inclined tobe affected by the internal points and is very time-consuming).

Step3. Sort the line segments by direction. Match the line segments pairwise whose angle are closeto each other (the absolute difference value between them is less than θmin) and whose distance isgreater than Lmin.

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Step 4. Detect whether there is a line segment between the initial point and the end point of thepaired line segments using the eight-neighbourhood connectivity method (certain discontinuouserror is allowed). ‘If there is such line segment, segment the rectangular region enclosed by the fourendpoints of the two paired line segments and save this region as a new image containing only thelocal motion-blurred object’; otherwise, keep detecting until there is no paired lines left anymore.

The method of combining statistical algorithm and pattern matching is adopted for multi-objectextraction in a sequence of video frames under a complex background. This method can locate theinterested object effectively while removing the background. The basic idea of this method isdescribed in the following. If the position of the video camera stands still, the background keepsunchanged for a short time.

Let us assume that the values of a pixel at a certain position of video frames along the time axisobey some given gauss distribution. After the means and variances of all pixels are estimated, thestatistical information of the background can be obtained. This statistical information can be utilizedin pattern matching to retrieve the background. Then the foreground image can be got by removingmatched regions which are viewed as background. The foreground image obtained in this way ismore accurate than that, which is obtained by utilizing differential equations directly, since thepattern matching is region-based. Finally, remove some regions, which are incorrectly matched,based on the information of connecting regions. Thus some post-processing for the interested objectcan be carried out after object segmentation. Detail algorithms related to this topic are not the focusof this paper, and they can be found in Hock et al (1991); Liang et al (2003) and Zhu et al (2006).

4.2 Experimental resultsFigure 7 shows the experimental results of motion-blurred object extraction and restoration process byusing Algorithm 4 for a single blurred image recorded by the motoring system under the multi-lanehighway condition. Figure 7(a) shows the original single motion-blurred image. Figure 7(b) shows thespectrum of Figure 7(a). The motion-blurred object extraction process is shown in Figure 7(c) and

Figure 7: Restoration of local motion-blurred image (a) Original blurred image (b) The spectrum of Figure 7(a) (c) Threshold segmented image (d) Main body extracted image (e) The image with only the blurred body

(f) The spectrum of Figure 7(e) (g) Restoration result of Figure 7(e)

(a) (b) (c) (d)

(e) (f) (g)

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Figure 7(d). In Figure 7(c), it gives the segmentation result by using the fitting grey level. In Figure7(d), it gives the boundary of each object by using the template matching and mathemat icalmorphology operating based on object segmentation. We filter out the object with small region andgenerate a new image which contains the blurred object only, as shown in Figure 7(e). Figure 7(f)shows the spectrum of Figure 7(e). Figure 7(g) shows the restoration result by using the auto maticidentification algorithm and restoration method proposed above (Algorithm 2 and Algorithm 3).

5. EXPERIMENTAL RESULTS AND ANALYSISThe RBFN based noisy motion-blurred image restoration model is tested under the PC Windowsdevelopment platform and the matlab 7.0 development environment using the cameraman image,the test result is given in Figure 8:

Figure 8(a) shows the different simulation results of the three automatic identification methodsof direction with certain motion-blur length of 30 pixels. Figure 8(b) shows the different simulationresults of the three automatic identification methods of length with certain motion-blur degree of45°. It can be seen from this figure that the accuracy of identifying PSF parameters, when the noiseis removed by our RBFN interpolation method with variable regularization parameters, issignificantly higher than that of identifying PSF parameters by using the general method withoutnoise-removing or the general filtering method.

By analyzing Figure 8, it can be seen that the results of automatic identification of parametersappear unsteady when the automatic identification method is applied directly without the noise-removing process. The estimated values of direction are inclined to form a stepped result, that is,the results are inclined to share the same direction value in a certain region, and the region extendsto the whole region gradually as the extent of noise interference becomes larger. Therefore, theidentification results appear to be unacceptable as the value stays at 45° among almost the wholeregion. In length identification, the automatic identification results appear to fluctuate significantlyand deviate largely from the standard value. For the general filtering method, although theidentification error is less than that of the former method, its error remains large and its accuracyremains low, since the important edge information is missing due to the loss of high frequencyinformation. Therefore, this method performs worse than the method proposed in this paper.

Figure 8: Contrast by the identification results of PSF parameters. (a) The comparison of automatic identificationof motion-blurred degrees using three different methods with certain length. (b) The comparison of automatic

identification of motion-blurred lengths using three different methods with certain degree.

(a) (b)

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CONCLUSIONThis paper has proposed a RBFN based noisy motion-blurred images restoration model, this modelmainly solves the problem of general motion-blurred image restoration under a relatively largenoise interference. Moreover, a local motion blurred image-restoring method based on objectextraction with motion-blurred characteristics is presented to solve the problem of restorationfailure caused by missing the information of global motion-blurred characteristics of local motion-blurred images. Experimental results show that the automatic identification algorithm for PSFparameters and the restoration algorithm in this model cannot only solve the problem of generalsingle motion-blurred image restoration under a relatively large noise interference, but also solvethe problem of local variable speed motion-blurred image restoration. The proposed algorithm cangive high identification accuracy and good restoration results.

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BIOGRAPHICAL NOTESXinzhong Zhu received the BSc from the University of Science and TechnologyBeijing (USTB), and his MSc degree from the National University of DefenseTechnology, China, both in Computer Science. He is currently an associateprofessor of the Zhejiang Normal University where he joined as a facultymember in 1998. He has served in numerous capacities and actively parti -cipated in over 40 (applied) research projects. His research interests includepattern recognition and image processing, manufacturing informatization,business intelligence and data mining, multimedia indexing and management,personalized e-learning and user modelling.

Jianmin Zhao is a PhD supervisor and full professor of the ZhejiangNormal University where he concurrently serves as the Dean of the College ofMathematics, Physics and Information Engineering. He is the principalinvestigator for numerous research and applied research projects, many ofwhich have been awarded by the Provincial government and State govern -ment. His research interests include pattern recognition and image processing,agent-oriented requirements engineering, business intelligence and datamining, sensor networks and e-learning.

Chunjiang Duanmu received his Bachelor and Masters degrees from theElectrical Engineering Department of the Southeast University in China in1996 and 1999, respectively. From 2000 to 2005, he was in the Electrical andComputer Engineering Department of the Concordia University in Canada.He received his PhD in 2005. Since then, he has been with the ZhejiangNormal University in China. He has published over 10 papers on IEEEconferences and journals. His research interests include video compression,digital image processing, and digital signal processing.

Huiying Xu was born in 1977, has an MSc degree and is a lecturer. She hasmembership of the China Computer Federation. Her research interests are inimage processing, pattern recognition, computer simulation, digital water -marking, and multimedia technology.

Noisy Motion-blurred Images Restoration Based on RBFN

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Xinzhong Zhu

Jianmin Zhao

Chunjiang Duanmu

Huiying Xu

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