A Bilateral Filtering Based Ringing Elimination Approach for Motion-Blurred Restoration Image

Current Optics and Photonics ISSN: 2508-7266(Print) / ISSN: 2508-7274(Online) Vol. 4, No. 3, June 2020, pp. 200-209 DOI: https://doi.org/10.3807/COPP.2020.4.3.200

A Bilateral Filtering Based Ringing Elimination Approach for Motion-blurred Restoration Image

Weiqing Wang1, Weihua Wang2*, and Jiao Yin3 1Business College, Southwest University, Rongchang 402460, China 2School of Artificial Intelligence, Chongqing University of Arts and Sciences, Yongchuan 402160, China 3Department of Computer Science and Information Technology, La Trobe University, Victoria 3083, Australia

(Received October 29, 2019 : revised February 12, 2020 : accepted February 14, 2020)

We describe an approach that uses a bilateral filter to reduce the ringing artifact in motion-blurred restoration image. It takes into account the specific physical structure of the ringing artifact combined with the properties of the human visual system. To properly reduce the ringing artifact, each of the adjacent pixels is limited in a straight line which has a given direction. To protect the edges and the texture regions of an image, our algorithm divides the image into texture regions and flat regions, and the artifact reduction algorithm is only applied to the flat region. Finally, we use 8 typical images and 5 objective quality evaluation indices to evaluate our algorithm. Experimental results show that our algorithm can obtain better results in subjective visual effect and in objective image quality evaluation.

Keywords : Image restoration, Bilateral filtering, Ringing OCIS codes : (100.0100) Image processing; (100.2980) Image enhancement; (100.3020) Image reconst- ruction-restoration

I. INTRODUCTION will generate ringing artifacts [1-3]. The ringing artifact is a byproduct of the lineal space-invariable regularization Vision is an important sense by means of which people scheme in suppressing the noise amplification [4, 5]. The can understand and perceive the real world, and studies suppression for the ringing artifacts has two steps: Firstly, show eighty percent of information is gained through the to detect and mark the ringing-regions in a restored image, visual system. An image is a picture with visual effects, and secondly, to reduce the ringing artifact. In the past 20 and it is a vivid description of the outside world. An years, much of the research on ringing artifact detection image contains a wealth of information and plays an and elimination has been published. important role in the information exchange. The clearer the Different methods were adopted to eliminate different image, the more accurate the information obtained from kinds of ringing artifact. Lee et al. [6] present a blur the image, however for the process of collecting images, kernel computational method based on bi-directional motion the image quality will decline for several reasons, such as compensation. The problem with this approach is that an the aperture and focal length of the camera, the intensity image cannot be restored from a single frame image and a of illumination, the exposure time, the movement of clear reference image is needed. Chen et al. [7] introduce acquisition equipment and so on. To obtain the accurate a restoration method based on bringing out the strongest information of an image, the collected degraded images line fuzzy kernel for the motion blurred image. This need to be restored, and the traditional image restoration method can effectively decrease the ringing, but it is techniques such as least squares filtering, Wiener filtering, difficult to find the best light-line regions. Deshpande et Lucy Richardson filtering and blind image restoration all al. [8] propose a method for restoring the motion blurred

*Corresponding author: [email protected], ORCID 0000-0003-4160-2668 Color versions of one or more of the figures in this paper are available online. This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/ licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. Copyright 2020 Current Optics and Photonics

- 200 - A Bilateral Filtering Based Ringing Elimination Approach for … - Weiqing Wang et al. 201 image and eliminating ringing, but the definition of the where  is the convolution operation. As we know the weight matrix for the algorithm is complex. El-Regaily et convolution operation in the spatial domain is the same as al. [9] put forward a restoration method based on a the multiplication operation in the frequency domain, genetic algorithm for the motion blurred image, it is therefore, in order to simplify the calculation, the Eq. (2) suitable for images whose moving distance is small, while in the airspace can be converted to the following formula the restored image suffers from distortions and has strong in the frequency domain ringing. Li et al. [10] describe a method of compensating for restoring the motion blurred image by the near infrared G(v,v)  H (u,v)F(u,v)  N(u,v), (3) image, but it needs a multi-spectral camera. A restoration method, based on multi-scale, for motion blurred images is where G(u,v), H (u,v) and N(u,v) are the Fourier trans- proposed by Duan et al. [11], to remove the ringing forms of g(x, y), h(x, y) and n(x, y), respectively. If the artifact, constraints are added in the smooth regions at noise N(u,v) is ignored, the image restoration can be different scales. Yang et al. [12] present a gradient expressed as attenuation Richardson-Lucy algorithm for image motion deblurring, the algorithm improves the speed of the pixels, G(u,v) F(u,v)  . (4) and can effectively eliminate ringing, but it does not H (u,v) objectively assess the quality for the restored image. Aim at the above problems, to eliminate the ringing It is worth noting that the restoration of an image is artifacts produced by restoring the motion-blurred image, closely related to the degradation reasons of that image, we propose an image ringing elimination method based on which means that solving the point spread function H (u,v) improved bilateral filtering. The principle and experimental depends upon the degradation reasons. results of our algorithm are illustrated in detail below. To In this paper we fully research on the restoration of verify the effect of eliminating ringing artifacts, we have motion blur caused by uniform rectilinear motion. Li [19], evaluated the restoration results from the subjective and Zhao [20] and Zhao [21] conduct their own research on objective aspects. There are many objective quality the kernel of motion blur caused by uniform rectilinear evaluation methods to evaluate the restored images motion. In this, set the exposure time to T, the motion [13-16], so we chose 5 common indexes to do this. distance to L and the motion angle to  , then the blurring kernel can be expressed as II. RELATED WORKS  1 L y  x 2  y 2  and tan  h(x, y)  (5) In this section, we will show you the principle and  L 2 x 0 otherwise . process of images blurred and restored by uniform  rectilinear motion, and will show you the principle that generates ringing during the restoring of the motion For a 2D image, in discrete space, its kernel of motion blurred image. blur caused by uniform rectilinear motion can also be represented as 2.1. The Degradation Mode of the Motion Images N The degradation model of natural images is detailed in x  [ y], y  0,1,2,..., M 1, (6) the literature [6, 17, 18], and it can be expressed as M

' ' M g(x, y)   h((x  x , y  y ),(x, y)) y  [ x], x  0,1,2,..., N 1, (7) (x'  y' ) (1)N  f (x  x ' , y  y ' )  n(x, y) , where M is the number of the blurred points in the x direction, N is the number of the blurred points in the y where h((x  x ' , y  y ' ),(x, y)) is the point spread function direction and [] is the integer-valued function. When M <= (PSF),  is a set of neighboring points around the pixel N, PSF is calculated by Eq. (6), and when M > N, PSF is f (x, y) in the input image, g(x, y) is the pixel value of calculated by Eq. (7). pixel f (x, y) in a degraded image, and n(x, y) is the noise of pixel f (x, y) . So by standardizing the expression (1), 2.2. Ringing Artifact we can obtain In a restored image, the direct cause of the ringing artifact is the information, especially the high frequency information lost during the restoration. In image processing, g(x, y)  h(x, y)  f (x, y)  n(x, y), (2) an image is filtered. If the selected frequency-domain filter has a steep change, the filtered image will generate ringing. 202 Current Optics and Photonics, Vol. 4, No. 3, June 2020

(a) (b) (c) (d) (e) FIG. 1. Ringing artifact and its classification. (a) Original image. (b) Blurred image. (c) Boundary ringing. (d) and (e) Edge ringing.

The so-called ringing refers to the shock caused by the 1(e). Experiments show that there are 3 obvious ringing sharp change in the gray level of the output image. edges near the edges as to the Richardson-Lucy method, According to the location of the ringing artifact, the ringing while the ringing artifacts in farther distance are not artifact can be clarified into edge ringing and boundary obvious and so they could be ignored. The above detected ringing [22]. Boundary ringing is a parasitic ripple that ringing artifacts can be detected by edge detectors, but the occurs near the edge of the recovered image, Edge ringing difference of the visual effects of ringing artifacts in artifacts are a kind of pseudo-wave which appears near the different regions is not considered. Based on the sensitivity edges, and they are also parallel stripes which appear near of vision to image signal, an image can be classified into the edges. So edge ringing artifacts are caused directly by two parts: texture regions and flat regions [24]. In texture the edges especially by the discontinuity of the sharp regions, such as foreground of the image shown in Fig. edges. Figure 1 shows an example of the ringing artifact 1(a), the gray scale changes very rapidly and the gradient and its classification. changes uniformly in various directions, so the changes of ringing in various directions can be offset, and the ringing artifact is not obvious, therefore, one’s vision is not III. METHODS sensitive to the ringing artifact in texture regions and the ringing artifact can be ignored. In contrast, the ringing Our algorithm for eliminating ringing artifacts consists artifact in flat regions, such as background of the image of three steps: (1) ringing detection; (2) calculating filter; shown in Fig. 1(a), has stronger orientation, so the results (3) eliminating ringing artifact. So following are details are very obvious, and one’s vision is very sensitive to the about its principle and implementation process. ringing artifact in flat regions, thus the ringing artifact cannot be ignored. This paper makes use of the region 3.1. Ringing Detection detection algorithm proposed by Liu and others [24] for Ringing detection is to detect and to mark ringing the detection of ringing regions. artifact regions, and it involves in two parts, the edge The detection and marking process of ringing regions is detection and the ringing detection. divided into the following several steps: The first step is Edge detection: Ringing artifacts usually appear near the edge detection, and the edge is detected by a Canny edge sharp edges, which are the regions with violent changes of detector; the second step is edge processing, its intent is to gradient. However, there are no obvious ringing artifacts detect out the smooth and real edges, and this process in the regions where gradient changes slowly. Therefore, includes two steps that are expansion and filtering. we need to detect the sharp edges before detecting and Expansion is meant to get smooth edges, filtering is meant eliminating the ringing artifacts. Here, we use the mature to eliminate the shorter edges and noise to get the real edge detector Canny [23, 24] to detect image edges. edges; the third step is to detect texture regions, its aim is Ringing detection: The characteristics of the ringing to segment the ringing regions which are not sensitive to artifact in motion-blurred images are: (1) ringing is a kind human vision; and the fourth step is to mark out ringing of edge ringing; (2) The edge ringing artifacts appear near regions, and here express them by black pixels. An the sharp edges in an image, in the meantime, they are example is illustrated in Fig. 2, (a) shows a clear image, parallel to the edges and distributed on the two sides of (b) is the motion blurred image of (a), (c) shows the image the edges, at the same time, the distance between ringing restored with ringing by the Richardson-Lucy algorithm, and edge is the integral multiple of moving distance len; the ringing is shown as the regions with dotted blue line, (3) ringing intensity decreases with the increasing of the (d) gives the results of edge detection, (d) provides the distance between ringing and edge. An example of the texture regions of Lena detected by the PRARDD ringing artifact caused in motion-blurred images with algorithm, and (f) marks out the ringing marking regions Richardson-Lucy and Levin are shown in Figs. 1(d) and (RMR) in (b). A Bilateral Filtering Based Ringing Elimination Approach for … - Weiqing Wang et al. 203

(a) (b) (c)

(d) (e) (f) FIG. 2. Ringing region detection. (a) Clear image. (b) Motion blurred image. (c) Image with ringing. (b) Edge detecting. (e) Texture detection. (f) Ringing marking regions.

3.2. Filtering Operation on an image plane, and it is expressed as r (i, j) , its Based on the above analysis, we may draw a conclusion value decreases with the increases of the difference of the that the ringing artifact of the restored image of motion luminance values between the center point and its adjacent blur caused by uniform rectilinear motion is related to the pixels, and it can be calculated as follows: location and intensity of edge. For those reasons, we choose a bilateral filter to eliminate the ringing artifact. As f (i, j) f (x, y) 2 ( ) 2 2 we know, a bilateral filter [25, 26] is a kind of nonlinear r  r (i, j)  e (i, j) S , (9) filter, it has the characteristics such as non-iteration, locality and realization, and its weight coefficient consists of two where f (x, y) is the luminance value of the center point parts: spatial proximity factors and luminance-similarity (x, y) , and f (i, j) is the luminance value of the adjacent factors. Spatial proximity factor  describes the position s point (i, j) of the center point (x, y) . Then, the weight relationship between the center pixel (x, y) and its adjacent coefficient of the filter is the product of the spatial pixels (i, j) , and its value decreases with the increasing of proximity factor and the luminance-similarity factor, the the Euclidean distance between (x, y) and (i, j) . In the weight coefficient of the filter for a pixel (x, y) is calculated discrete case, the spatial proximity factors of the adjacent as follows: pixels (i, j) of a certain pixel (x, y) in an image can be expressed with the following Gauss function ω(i, j) = ωs (i, j) * ωr (i, j) (i, j) S . (10)

ix 2  j y 2 ( ) 2 3.3. Eliminating the Ringing Artifact 1 2 s  s (i, j)  e (i, j)  S , (8) 2 s Ringing-effect elimination is a filter, and it uses the above bilateral filter to calculate the local weighted value. where  s is the standard deviation of the spatial proximity For each pixel (x, y) in the ringing marking region, its factor. pixel value can be calculated as follow:

Luminance-similarity factor  r for a certain pixel (i, j) describes the similarity degree of luminance between the (i, j)*g(i, j) (x, y) (i, j) f (x, y)  (i, j )S . (11) center pixel and its adjacent pixels i.e. the (i, j) difference of their luminance values, it reflects the (i, j )S continuity of the luminance values in the adjacent space 204 Current Optics and Photonics, Vol. 4, No. 3, June 2020

IV. EXPERIMENTS 4.1. Subjective Evaluation To validate the validity of our algorithm above, we do An imagery processing result can be validated from simulation with several different styles of blurred images subjective and objective aspects, subjective validation such as hat, house, Beach, chimney, play, bird, bike, means that restored effects are viewed directly through village, wall, etc. These images stored as png were taken human visual system, and objective validation means that directly from Kodak Lossless True Color Image Suite, and restored effects are validated via some objective indices. their sizes are 768 × 512. The results of our experiments So we analyze and validate our algorithm subjectively and are shown in Fig. 3. The first column is the original objectively. images. The second column is the results restored with the deconvblind function in matlab2014a tools. The third

Hat

House

Beach

Chimney

Play

Bird

Bike

Village

Wall

(a) (b) (c) (d) (e) (f) FIG. 3. Visual effects. (a) Original image, (b) Ringing image, (c) Edge detection, (d) Texture region, (e) Ringing Mark, (f) Ringing removing. A Bilateral Filtering Based Ringing Elimination Approach for … - Weiqing Wang et al. 205 column is the edge images detected out with the Canny intuitively, the Hotelling T2 test is performed. Since the operator, and the edge threshold used in the experiment is indexes of RM are opposite to the others, in order to keep 0.2. The fourth column is the texture regions detected out consistent with others the value of the RM need to be with the method proposed by Liu et al. [24]. The fifth modified to 1-RM during the test, then the mean vector column is the ringing regions. And the sixth column is the before the ringing elimination is u0 = [27.3896, 0.92038, results where the ringing artifacts were eliminated with our 0.91968, 0.87293, 0.76698]’, and the mean vector after algorithm. As you can see from Fig. 3, our algorithm that is u1 = [27.4514, 0.9286, 0.9358, 0.88122, 0.82049]’, removes some of the ringing artifacts. suppose H0:u0 = u1, H1:u0 < u1. Then, the F is computed as 18.1501, and F0.05(5, 8) = 3.69, so, F > F0.05(5, 8), the 4.2. Objective Evaluation suppose H1 is accepted. So, taken as a whole, our In this experiment, the quality of the restored images is algorithm enhances the quality of the restored images. evaluated by PSNR (Peak Signal to Noise Ratio), FSIM (Feature Similarity Index for Image Quality Assessment) [27], MSSIM (Mean Structural SIMilarity) [28, 29], MSSIM V. DISCUSSIONS (Ringing Metric RM) [28, 29], etc. PSNR refers to the difference between the signal-noise ratios of two images, 5.1. The Performance Comparison of Different Algorithms and researchers tend to think: the bigger the PSNR, the Out algorithm has strong robustness. To verify the higher the quality of the restored image. But experiment robustness of our algorithm, we perform experiments with results show that PSNR cannot be completely consistent the hat images, in which we add the additive Gauss noise with visual quality, it is possible that, the bigger the PSNR with the variance   0.001,   0.01,   0.05 and   0.1 is, the lower visual effect the image has. FSIM represents respectively, in the meantime, set the motion angle is the similarity of the feature structures between two images,   20 , the motion distance is len  15. These images are the bigger the FSIM is, the better the quality of image restored with different algorithms, and the experimental restoration will be. FSIMC is similar to FSIM, but FSIMC results are shown in Fig. 4. The additional noise is shown can be used to evaluate color images. RM is mainly used in the first row, the hat images with different noise are to evaluate the ringing artifacts of the restored images, the shown in the second row, the images from the third to the greater the RM value is, the more obvious the ringing seventh of the rows are respectively restored by different artifact of the restored image is, so, the smaller the RM filters such as least square filter, Wiener filtering, Lucy- is, the better the image quality is. Table 1 showed the Richardson, blind convolution and our algorithm. experiment results of the restored images in Fig. 3, in The objective evaluation indices of image are used to the experiments, the parameter values are: motion angle evaluate the quality of the images in Fig. 4, the experi-   60 , moving distance len  20 , edge detection threshold mental results are shown in Table 2. From the table we

threshold  0.2, spatial proximity standard deviation  s  3, can see, in all noise conditions, our algorithm is better and the standard deviation of luminance  r  6 . than the other algorithms. In Table 1, the arrow “↑” shows that the bigger the index value is, the better the quality of the restored image 5.2. Filter Performance Evaluation is, whereas: the arrow “↓” shows that the smaller the The quality of our bilateral filter has a great deal to do index value is, the better the quality of image restoration with its parameter  s and  r , the bigger the parameter  s is. To describe the performance of the algorithm more and  r are, the more smooth the image is, so the more

TABLE 1. Objective assessment

PSNR ↑ FSIM ↑ FSIMC↑ MSSIM ↑ RM ↓ Images Before After Before After Before After Before After Before After Hat 30.7606 30.9340 0.9400 0.9490 0.9395 0.9485 0.8902 0.9080 0.1170 0.1060 House 22.5965 22.6198 0.8898 0.9089 0.8888 0.979 0.8467 0.8524 0.2231 0.2132 Beach 29.5914 29.8910 0.9207 0.9357 0.9201 0.9351 0.8481 0.8699 0.3330 0.2327 Chimney 26.6767 26.6775 0.9063 0.9118 0.9057 0.9112 0.8784 0.8836 0.2472 0.2249 Play 28.4585 28.5831 0.9122 0.9227 0.9117 0.9222 0.8951 0.9058 0.1502 0.1294 Bird 31.1455 31.0455 0.9538 0.9589 0.9533 0.9584 0.9294 0.9369 0.2956 0.2767 Bike 24.3458 24.3759 0.9185 0.9205 0.9172 0.9192 0.8638 0.8664 0.1955 0.1820 Village 28.3324 28.3169 0.9279 0.9296 0.9272 0.9289 0.8695 0.8706 0.2904 0.2507 Wall 24.5993 24.6190 0.9142 0.9203 0.9136 0.9197 0.8352 0.8374 0.2452 0.2026 206 Current Optics and Photonics, Vol. 4, No. 3, June 2020

Gaussian noise

Noise image

Least square filter

Wiener filtering

Lucy-Richardson

Blind convolution

Our method

(a) (b) (c) (d) FIG. 4. Different image restoration algorithms have different effectiveness. noise parameter: (a) 0.001, (b) 0.01, (c) 0.05, (d) 0.1.

TABLE 2. The quality of the restored images with different methods and noises

TABLE 2. The quality of the restored images with different methods and noises (Continue)

Image quality assessment Noise Restoration method PSNR↑ FISM↑ FSIMC↑ MSSIM↑ RM↓ Least square filter 33.3502 0.9010 0.9008 0.8669 0.2462 Wiener filtering 17.3004 0.5978 0.5724 0.2404 0.9029 1.0*E-2 Lucy-Richardson 35.3900 0.9346 0.9344 0.8926 0.1411 Blind filter 35.3834 0.9345 0.9343 0.8924 0.1402 Our method 35.5693 0.9450 0.9448 0.9115 0.1289 Least square filter 33.3627 0.9015 0.9012 0.8672 0.2477 Wiener filtering 16.9689 0.5854 0.5595 0.2258 0.9058 5.0*E-2 Lucy-Richardson 35.3864 0.9345 0.9343 0.8923 0.1403 Blind filter 35.3798 0.9344 0.9342 0.8922 0.1441 Our method 35.5597 0.9447 0.9445 0.9110 0.1297 Least square filter 33.4047 0.9030 0.9027 0.8685 0.2388 Wiener filtering 16.4186 0.5602 0.5332 0.1920 0.9120 1.0*E-1 Lucy-Richardson 35.3726 0.9344 0.9342 0.8917 0.1376 Blind filter 35.3665 0.9343 0.9341 0.8915 0.1426 Our method 35.5639 0.9450 0.9448 0.9112 0.1242

1 6

2 7

3 8

4 9

5 10

(a) (b) (a) (b)   FIG. 5. The results of eliminating the ringing artifact with different parameter s and r . (a)  s  110, r  10 , (b)

 s  10, r  110 . 208 Current Optics and Photonics, Vol. 4, No. 3, June 2020

in the other directions. It uses a bilateral filter to eliminate Sigma_S Curve Sigma_R Curve ringing, and the pixel is associated with not only the 1.2 1.2 positions of its adjacent pixels but also the luminance of its adjacent pixels. Its goal is to avoid the dramatic 1 1 changes of pixel values and to improve the filtering effect. It also takes into account the relation between the ringing 0.8 0.8 artifact and the textures. For a texture region is not sensitive to ringing artifact, it needs to detect out the PSNR PSNR FSIM 0.6 0.6 FSIM textures in an image, and our algorithm has no need to FISMC FSIMC Value Value MMSIM MSSIM perform in the texture regions. After the experiments on RM RM various images such as Lena, hat, play, etc., we could see 0.4 0.4 that our algorithm eliminates the ringing artifacts evidently, and significantly improves the objective evaluation indices. 0.2 0.2 In short, our algorithm is able to effectively eliminate the ringing artifacts in the motion-blurred restoration images,

0 0 and to effectively improve the quality of the motion-blurred 1 5 9 13 17 21 25 29 1 5 9 1317212529 restoration images. Sigma_S Sigma_R (a) (b) FIG. 6. The performance evaluation of our algorithm. (a) The ACKNOWLEDGMENT curve of the space adjacent proximity. (b) The curve of the luminance similarity. This study was funded by the Natural Science Foundation of Chongqing under grant no.cstc2019jcyj-msxm2486, the the ringing artifacts are eliminated, but the fuzzier the Science and Technology Research Program of Chongqing image is. The hat images are restored with different spatial Municipal Education Commission of China grant no. KJQN proximity parameters and luminance similarity parameters, 201901306, the Talent Introduction Project of Chongqing as shown in Fig. 5. The left column is the results when University of Arts and Sciences under grant no. R2019FRJ34,   10 and  equals 1 to 10, and right column is the and the Scientific Research Fund of Chongqing University r s of Arts and Sciences under grant no. Z2018RJ08. results when  s  10 and  r equals 1 to 10. As before, the objective evaluation indices of the image are also used to evaluate the quality of the images in Fig. 5, the experimental results are shown in Fig. 6. Where, Fig. REFERENCES 6(a) analysis changing trends of the objective evaluation 1. J. Jiang, J. Huang, and G. Zhang, “An accelerated motion indices when the parameter  s changes, Fig. 6(b) analysis changing trends of the objective evaluation indices when blurred star restoration based on single image,” IEEE Sensors J. 99, 1306-1315 (2017). the parameter  changes. Due to the difference of r 2. B. Dong, Z. Shen, and P. Xie, “Image restoration: a general objective evaluation indices, the ranges of evaluation value wavelet frame based model and its asymptotic analysis,” may differ greatly, to compare these evaluation indices in Siam J. Math. Anal. 49, 421-445 (2017). the same image, the objective evaluation indices are 3. C. Cruz, R. Mehta, V. Katkovnik, and K. O. Egiazarian, normalized via dividing each index by the maximum “Single image super-resolution based on wiener filter in index. The “Value” in Fig. 6 is the normalized indices. similarity domain,” IEEE Trans. Image Process. 27, 1376- From Fig. 6 we can see, the filtering effect of the bilateral 1389 (2018). filter changes according to  s and  r , when  s  6 and 4.M. E. Eldib, M. Hegazy, Y. J. Mun, M. H. Cho, M. H.

 r  7, the curve reaches the peak value, at this point, the Cho, and S. Y. Lee, “A ring artifact correction method: filtering performance is the best. validation by micro-CT imaging with flat-panel detectors and a 2D photon-counting detector,” Sensors 17, 269 (2017). 5. W. Vågberg, J. C. Larsson, and H. M. Hertz, “Removal of VI. CONCLUSION ring artifacts in microtomography by characterization of scintillator variations,” Opt. Express 25, 23191-23198 (2017). 6. D. B. Lee, B. Y. Heo, and B. C. Song, “Video deblurring The article focuses on the ringing artifact of the based on bidirectional motion compensation and accurate blur restoration of a motion blurred image. We present an kernel estimation,” in Proc. IEEE International Conference edge-ringing-elimination algorithm for the restoration of on Image Processing (Melbourne, Australia, Sep. 2013). the motion blurred image. Our algorithm is only related to 7. X. Chen and Y. Zhang, “Kernel refinement based on best the motion parameters and the adjacent pixels in the light streak for motion deblurring,” in Proc. 2014 Inter- motion direction, and it is irrelevant to the adjacent pixels national Conference on Orange Technologies (Xi’an, China, A Bilateral Filtering Based Ringing Elimination Approach for … - Weiqing Wang et al. 209

Sep. 2014). 18. R. Chen, H. Jia, X. Xie, and W. Gao, “Blind restoration for 8. A. M. Deshpande and S. Patnaik, “Single image motion non-uniform aerial images using non-local Retinex model deblurring: an accurate PSF estimation and ringing reduction,” and shearlet-based higher-order regularization,” J. Electron. Optik 125, 3612-3618 (2014). Imaging 26, 033016 (2017). 9. S. El-Regaily, M. A. El-Aziz, H. El-Messiry, and M. 19. H. S. Li, Y. N. Zhang, R. Yao, and J. Q. Sun, “Parameter Roushdy, “Using GPU-accelerated Genetic Algorithm for estimation of linear motion blur based on principal compo- non-linear motion deblurring in a single image,” in Proc. nent analysis,” Opt. Precis. Eng. 21, 2656-2663 (2013). 8th International Conference on Informatics and Systems 20. Y. Y. Zhao, Y. Yuan, and L. Su, “Point spread function (INFOS) (YanTai, China, May 2012). estimation of blurring due to uniform linear motion in arbi- 10. C. Wang, L. F. Sun, Z. Y. Chen, S. Q. Yang, and J. W. trary direction,” Chin. J. Lasers 39, 809003-809628 (2012). Zhang, “Robust inter-scale non_blind image motion deblur- 21. P. Zhao, J. Chao, and X. Z. Wei, “Identification of robust ring,” in Proc. 16th IEEE International Conference on Image blur parameter for uniform linear motion blurred images,” Processing (ICIP) (Cairo, Egypt, Nov. 2009). Opt. Precis. Eng. 21, 2430-2438 (2013). 11. Z. Wang, E. P. Simoncelli, and A. C. Bovik, “Multi-scale 22. J. S. Li, S. J. Zhang, Y. W. Yang, M. Li, and J. L. Wang, structural similarity for image quality assessment,” in Proc. “Edge-detached image restoration with ringing reduction,” The Thrity-Seventh Asilomar Conference on Signals, Systems Opt. Precis. Eng. 22, 797-805 (2014). & Computers (Pacific Grove, CA, USA, Nov. 2003). 23. J. Canny, “A computational approach to edge-detection,” 12. H. L. Yang, P. H. Huang, and S. H. Lai, “A novel gradient IEEE Trans. Pattern Anal. Mach. Intell. 8, 679-698 (1986). attenuation Richardson-Lucy algorithm for image motion 24. H. Liu, N. Klomp, and I. Heynderickx, “A perceptually deblurring,” Signal Process. 103, 399-414 (2014). relevant approach to ringing region detection,” IEEE Trans. 13. Y. Ding, Y. Zhang, X. Wang, X. L. Yan, and A. S. Krylov, Image Process. 19, 1414-1426 (2010). “Perceptual image quality assessment metric using mutual 25. Q. Yang, “Hardware-efficient bilateral filtering for stereo information of Gabor features,” Sci. Chin. Info. Sci. 57, 1-9 matching,” IEEE Trans. Pattern Anal. Mach. Intell. 36, 1026- (2014). 1032 (2014). 14. Y. Ding, Y. Zhang, X. Yan, and A. S. Andrey, “Information- 26. K. N. Chaudhury and S. D. Dabhade, “Fast and provably based reduced reference image quality assessment incorpo- accurate bilateral filtering,” IEEE Trans. Image Process. 25, rating non-tensor product wavelet filter banks,” Chin. Sci. 2519-2528 (2016). Bull. 59, 1917-1924 (2014). 27. L. Zhang, L. Zhang, X. Mou, and D. Zhang, “FSIM: a feature 15. F. Guan, G. Jiang, Y. Song, M. Yu, Z. Peng, and F. Chen, similarity index for image quality assessment,” IEEE Trans. “No-reference high-dynamic-range image quality assessment Image Process. 20, 2378-2386 (2011). based on tensor decomposition and manifold learning,” 28. Z. Wang, E. P. Simoncelli, and A. C. Bovik, “Multiscale Appl. Opt. 57, 839-848 (2018). structural similarity for image quality assessment: signals,” 16.M. Liu, K. Gu, G. Zhai, P. L. Callet, and W. J. Zhang, in Proc. The Thrity-Seventh Asilomar Conference on Signals, “Perceptual reduced-reference visual quality assessment for Systems & Computers (KS, USA, Nov. 2003). contrast alteration,” IEEE Trans. Broadcast. 63, 71-81 (2017). 29. J. Chu, Q. Chen, and X. C. Yang, “Review on full reference 17. B. Hu, L. Li, and J. Qian, “Perceptual quality evaluation for image quality assessment algorithms,” Appl. Res. Comput. motion deblurring,” IET Comput. Vision 12, 796-805 (2018). 31, 13-22 (2014).