Motion Blurred Image Restoration based on Super-resolution Method

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1 Motion Blurred Image Restoration based on Super-resolution Method Department of computer science and engineering East China University of Political Science and Law, Shanghai, China Abstract Motion blur is a typical and common degradation in surveillance system. The problem of motion estimation based on super resolution reconstruction of multiple images is addressed in this paper. This paper presents a motion projection onto convex set (POCS) algorithm to restore an image from multiple blurred images. The inter and intra pixel shifts are used to compute a joined point spread function (PSF), which determines the project model of the pixels in the moving window in each iteration. Experiments confirm the proposed algorithm outperforms single-image restored algorithms, especially for space-variant motion blurred images. 1. Introduction Keywords: Motion Blur, POCS, PSF In many applications, like surveillance, image sequences are of poor qualities. The captured images are usually blurred by many reasons. These degradations mainly include: (i) optical blur (ii) image sampling by the CCD array (iii) motion blur [1]. Moreover, motion blur is a common and typical problem in photographing fast moving objects. It can be regarded as a degraded representation of the ideal image that would have been captured at a certain instant by an ideal camera. Often changing the camera to improve the quality of the images is not an option. Because of the high cost and limitations in practice, it is important and economical to enhance the quality and resolution by post-processing technologies. Deconvolution is an important restored idea for motion deblurring. Image deconvolution can be further separated into the non-blind and blind cases. In non-blind deconvolution cases, the motion blur kernel was assumed to be known. In fact, it was limited for the use. In the case of blind deconvolution, the problem was more ill-posed. A motion blur was characterized by its point spread function (PSF) whose parameters were closely related to the motion. The solution assumed to obtain a prior parametric form by estimating a few parameters from a blurred image [2]. The simplest motion blur was the spaceinvariant motion blur, which had been studied extensively. Early works based on a single-image restoration assumed linear motion blur kernel model, which were over simplified for true motion blurring in practice [3-7]. Moreover, some methods used image priors and kernel priors to constrain an optimization for the blur kernel and the latent image. Fergus [8] used a natural image prior on image gradients in a variation Bayes framework to estimate the blur kernel. Levin [9] took a similar approach for object motion blur, where an image was segmented into several areas of different motion blur and then each area was deblurred independently. In practice, however, as motion can be quite complex, motion blurs can be much more complicated than the simple cases. For example, the blur can be spacevariant, nonlinear, local and multiple. The space-variant motion blur is motivated by the wide existence of fast object motion within every exposure period. The challenge is mainly on the space-variant property of the blur kernel. There is relatively little work on handling space-variant blur. Yosuke [10] proposed a method to translate a camera sensor circularly about the optical axis during exposure, so that high frequencies can be preserved for a wide range of in-plane linear object motion in any direction within some predetermined speed. Reference [11] proposed a method to estimate spacevariant blur kernels based on values of the alpha map. The method relied strongly on the precomputation of a good alpha matter and assumed the scene to be a foreground object moving across a background. In some practical forensic examinations, we cannot obtain all information just from one image and perhaps get inaccurate or wrong estimation. The above methods are usually computationally efficient but only work in the simple blurring cases such as symmetric optical blurring or simple motion International Journal of Digital Content Technology and its Applications(JDCTA) Volume6,Number11,June 2012 doi: /jdcta.vol6.issue

2 blurring with constant velocity. To solve more complex motion blurring, several works have utilized multiple images or videos to obtain more information of the blur kernel [12-15]. Schultz [12] used video analysis idea to estimate PSF by combing partial information. Shan et al. [13] incorporated spatial parameters to enforce natural image statistics using a local ringing suppression step and [14] used two images with PSF in different directions for deblurring problems. Furthermore, [15] presented a modified the maximum a-posteriori (MAP) estimation based on high-order non-local range Markov Random Field (MRF) prior to resolve the restoration problem. In this paper, based on super resolution algorithm, we present a modified projection onto convex set (POCS) algorithm for removing motion blur from multiple images. In the different exposure time, multiple images are chosen to estimate inter and intra shifts of the pixels. The acquired shift parameters are incorporated into the imaging motion model to construct a joined PSF, which is used to warp the sampled pixels of high-resolution (HR) image to the low-resolution (LR) grid. Based on the convex constraint sets, we determine the pixels on the HR grid and restore the blur for each iteration. 2. Image formation process Model We first briefly describe the used model of image formation in our experiments. The basic structure of the digital camera imaging pipeline is shown in Figure 1[16]. First, light from a scene enters the camera through a lens and passes through a set of filters including an anti-aliasing filter. Then the light is captured by a sensor named as CCD or CMOS and goes through a color filter array (CFA) to get color information, which is demosaiced and processed with correction and balance adjustment. Finally, the raw image is stored in the camera memory device in a user-selected image format (e.g., RAW, TIFF or JPEG). blurring The scene filtering len CFA Raw image (*.jpg, *.bmp, etc.) Color & gamma correction Figure 1. Image acquisition using a typical digital camera demosaicing From the image acquisition model, there are many reasons can reduce the image quality, such as optical defocus, atmospheric disturbance and noise. Motion blur is one of the typical degradation models. It occurs in photography whenever either the object or the camera moves during the shutter interval. Motion that occurred over this extended period of time is visible in a single snapshot, resulting in a distinctive blurry streak for fast moving objects. As for image or video acquisition systems, the object moves in successive frames. There is lots of relative information between the frames. The ideal ideal transformed version ft of the ideal image f is integrated by the camera during its exposure time T. If the object is moving significantly during this time, the resulting image gt is smeared by the motion blur. Thus, g ( x, y tt ) f ( u, v ) dτ ( t tt tt τ τ Let h denote the blur kernel, which is so-called PSF, the imaging model can be simplified as g f* h (2) where * is the convolution operator and the deconvolution is the key point to recover the clear image from the blurred one. In the blind deconvolution methods, PSF is an important factor, of which the value will directly affect the quality of the restored images. 231

3 Figure 2. The principle of the motion blurred image Figure 2 shows the simplest principle of the degraded uniform-velocity model of blurred image. In most cases, the scene A, B, C,, will image to the pixel 1, 2, 3,,respectively. But when the object moves rapidly, the scene will image at the other pixel instead. The same overlapping is operated to others scenes. So the imaging PSF for linear horizontal motion blur is given by 1 hxy (,) δ() L. (3) L Where L is the line segment of length L oriented at an angle of θ degree from the x axis. Then, the blurred image can be written as L g h* f fxy (, ) fx ( 1, y) fx ( Ly, ) fx ( ky, ). (4) This assumption is valid when the motion blur is uniform for the entire image. The blur is the trailing smear caused by the mutual covering of the pixels during the motion. Otherwise, the image can be divided into regions having approximately a constant motion blur. If supposing the motion blur is a h=(h,h,,h ) at angle α, the motion-based imaging process can be one dimensional kernel 1 2 K modeled as α def K 1 gxy (, ) f* h hk f( xkcos( α), yksin a( α)) (5) k0 3. Method Description The goal of this paper is to develop a robust numerical algorithm to recover a HR image from multiple motion-blurred images. In our setting, the input multiple images are passively captured by a commodity digital camera without any specific hardware. For spatially-invariant linear blur, the PSF can be found by multiplying the image-space object velocity with the exposure time or generated by the length L and angle α, which is defined in equation (5). Since the object moves in successive frames, the blurred images are needed to be aligned before the deconvolution. For linear constant velocity motion, the alignment corresponds to a shift in the image plane, which is computed by the shift between ( i th th and i frame. k0 232

4 ( x, y ) 0, ti1 0, ti1 ti 1 ( x, y ) 1, ti 1, ti Figure 3. The mapping trajectory of the image point Figure 3 shows the mapping trajectory of the intra-frame information of the video sequence. As the Figure 3 shown, denoting M ( M1, M2) is a shift matrix mapping from ti 1 to t i, we can describe the relationship between the successive frames as the following x1, t M1( x0, y0, t i i. (6) y1, t M2( x0, y0, t i i Where ( x0, y 0) and ( x1, y are the points at the reference time t i and ti 1, respectively. 1 M is an inverse mapping from the point ( x, y) at time t i to another point at the time ti 1, which can be estimated by optical flow method [17]. Assumed that the only changes in the scene imaging are caused by motion, we incorporate the shift model into the image acquisition process. g ( xt, ) ( f* h)( x). (7) i i v Where hv () is the joined PSF including the motion of the object and the pixel shift of the imaging plane. In this paper, we assume the blurred images are needed to be aligned before the deconvolution and the geometric transforms hv () are estimated using some existed image alignment technique during pre-processing. For linear constant velocity motion, the alignment corresponds to a shift in the image plane, which is computed by the shifts between ( i th th and i frame. Provided that the pixel ( x0, y 0) at the time ti 1 mapping onto the pixel ( x1, y at the time t i, the residual r between the actual value and the estimated value is measured by r( x0, y0, ti g( x0, y0, ti f( m, n, ti hv( mx1, ny (8) ( mn, ) Where f denotes the deblurred image. Here we use the estimated hv () as windows to the iteration, which has a p q support instead of traditional Gaussian model. So the pixel estimation is given by a sum of products of the PSF coefficients and the corresponding deblurred pixels in the area spanned by the PSF. Since the blur of the multiple images is perhaps space-variant, the PSF would be changeable for each image. The POCS method is based on pixel-by-pixel processing. We apply a moving window to a blurred source with a variable PSF. Then, the deblurred pixels estimated directly under the joined PSF are updated according to the following closed, convex constraint sets t i 233

5 f ( r) hv r Pf ( ) f r f ( r ) hv r (9) The represents the predefined threshold, which is a checkout coefficient to change the projection in each iteration. So the motion-pocs method can be summarized in the following steps: Step1: Estimate the motion parameters for the motion length L and angleθ. Step2: Estimate the pixel shifts between the sequential video frames to determine mapping vector M. Step3: According to the motion parameters and pixel shifts, map each pixel to the corresponding location of the next frame, and then compute each residual error. Step4: If the absolute value of the residual is larger than a predefined error bound, back project the residual onto the current image so that the residual can fall within the predefined bound. Step5: Update the current state until the image quality is acceptable. 4. Experimental Results We have conducted a serial synthetic experiment to demonstrate the performance of the proposed algorithm. The original mobile video sequence is blurred by the linear motion with length pixels and an angle of the theta in a counterclockwise direction. The length is 10 and the angle is 5. We choose four frames of the motion-blurred sequence shown in Figure 4. We compare with the traditional blind deconvolution method from a single image, which use cepstrum to estimate the blur parameters to generate PSF [7]. The cepstrum method gets the parameters with length 10 and angle 6. The acquired motion information is used to compute imaging PSF and restore through regularized and Lucy- Richardson method, which results are shown in Figure 5 (a) and (b), respectively. We use optical flow to estimate the pixel shifts of the video sequence [17]. Combined with the computed imaging PSF above, the restoration of our method is shown in Figure 6. Here the threshold is set to 0.1. The parameter is chosen experimentally, which can provide the best and robust restoration. As Figure 5 and Figure 6 shown, both the single-image blind deconvolution and our method can improve the image quality. But the deblurring effect of the former is limited since the imaging PSF is not accurate. Moreover, the traditional single-frame restoration remains some artifacts around the calendar digitals, while our method recovers more clearly and sharply, such as the number and 29 of the image. (a) (b) (c) (d) Figure 4. Four motion blurred images of the video sequence 234

6 (a) (b) Figure 5. The restoration of blind deconvolution: (a) Regularized method (b) Lucy-Richardson method Figure 6. The restoration of the proposed method The second experiment is a captured video from a street. One of the observations is shown in Figure7. Since the motion blur of the bus is much complicated than the synthetic experiment, we use the traditional restoration through regularized and Lucy-Richardson operator cannot give the ideal restoration. Figure8 shows the result of the proposed method for the objective bus. The image features are more distinctly visible, especially the texts of the bus are more readable on the restored images. Figure7. One of the observed blurred images Figure8. The restoration of the proposed method 5. Conclusion The relative motion between the object and camera at the exposure time will cause the motion blur. Since the path of the relative motion can be arbitrary, deblurring of motion blurred 235

7 images is a hard problem. This paper mainly focused on the estimation of multiple images based on POCS algorithm. Considering the objects moving in successive frames have much relative information between inter and intra frames, we incorporate the imaging model and pixel shifts to construct a joined PSF, which determine the moving window to the image in each iteration. Compared to the single restored methods, the proposed method can restore the images better and get clearer and sharper qualities. 6. References [1] P.A.Jansson, Deconvolution of Image and Spectra, 2nd edition. Academic Press, USA, [2] XiaoshengYu, Chengdong Wu, Li Wang, and Yuanchen Qi, An Improved Total Variation Model with Adaptive Local Constraints and Its Applications to Image Denoising, Deblurring and Inpainting, JDCTA: International Journal of Digital Content Technology and its Applications, vol.5, no.12, pp ,2011. [3] C. Mayntx, T. Aach, and D. Kunz, Blur Identification Using a Spectral Inertia Tensor and Spectral Zeros, In Proceeding of International Conference on Image Processing, pp , [4] Y. Yitzhaky, G. Boshusha, Y. Levy, and N.S. Kopeika, Restoration of an Image Degraded by Vibrations Using Only a Single Frame, Optical Engineering, vol. 39, no.8, pp , [5] A.C.Likas, N.P.Galatsanos, A variational approach for bayesian blind image deconvolution, vol.52, no.8, pp , [6] S. K. Nayar, M. Ben-Ezra, Motion-based motion deblurring, IEEE Transaction on Pattern Analysis and Machine Intelligence, vol.26, no.6, pp , [7] K. Felix, L. Youzuo, M. Bonnie, Blind Image Deconvolution: Motion Blur Estimation, Technical Report, University of. Minnesota, [8] R. Fergus, B. Singh, A. Hertzmann, S. T. Roweis, and W.T. Freeman, Removing Camera Shake from a Single Photograph, ACM Transaction on Graph, vol.25, no.3, pp , [9] Levin, A, Blind motion deblurring using image statistics, In Proceedings of Neural Information Processing System, pp , 2006 [10] Yosuke Bando, Bing-Yu Chen, Tomoyuki Nishita, Motion Deblurring from a Single Image using Circular Sensor Motion, Computer Graphics Forum, vol.30, no.7, pp , [11] S. Dai, Y.Wu, Motion from blur, In Proceedings of Internal Conference on Computer Vision and Pattern Recognition, pp.1-8, [12] R.R.Schultz, and R.L.Stevenson, Extraction of High-resolution Frames from video sequence, IEEE Trans. on Image Processing, vol.5, no.6, pp , [13] S. Qi, X.Wei, J.Y.Jia, Rotational motion deblurring of a rigid object from a single image, In Proceedings of Internal Conference on Computer Vision, pp.1-8, [14] W.Li, J. Zhang, Q.H.Dai, "Exploring Aligned Complementary Image Pair for Blind Motion Deblurring", In Proceeding of International Conference on Computer Vision and Pattern Recognition, pp , [15] Bo Zhao, Wensheng Zhang, Jin Liu, and Huan Ding, High-Order MRF Prior Based Bayesian Deblurring", JDCTA: International Journal of Digital Content Technology and its Applications, vol. 5, no. 12, pp. 383 ~ 392, [16] J. Lukas, J. Fridrich, and M. Goljan, Determining digital image origin using sensor imperfections, In Proceedings of the SPIE Electronic Imaging, pp , [17] T. Brox, A. Bruhn, A. Papenberg, High Accuracy Optical Flow Estimation Based on a Theory for Warping, In Proceedings of European Conference on Computer Vision, pp.25-36,

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