a random-valued impulse noise detector using level ...
A Random-valued Impulse Noise Detector Using Level Detection Noritaka YAMASHITA, Munenori OGURA, Jianming LU, Hiroo SEKIYA and Takashi YAHAGI Graduate School of Science and Technology, Chiba University 1-33, Yayoi-cho, Inage-ku, Chiba, 263-8522 Japan Email: n [email protected] Abstract— In this paper, we propose a new random-valued impulse noise detector from images using level detection. In our method, we use directional windows in order to search a level region in the images. One window whose variation is lowest is selected as a flat window from multi directional windows. In a flat window, random-valued impulse noise may move to the both ends of order statistics. Therefore, noise detection in selected window is easy. Consequently, the proposed method reduces undetected noise pixels without increasing mis-detections. Extensive simulations indicate that the proposed method performs significantly better than conventional methods.
I. I NTRODUCTION In the image processing, median filters have been widely used for removing impulse noise, since median filters are quite effective for the noise removal and the edge preserving. However, median filters tend to modify both noise pixels and undisturbed good pixels. Recently, switching schemes have been studied for removal impulse noise in images [1]-[3]. These schemes detect whether the current pixel is corrupted by impulse noise at each pixel. Then, filtering is activated for pixels that is detected as noise pixels, while good pixels are kept. As a switching scheme, progressive switching median (PSM) filter [1] was proposed for removal impulse noise. With the PSM filter, both the impulse noise detector and the noise filter are applied progressively. The noise detector detects an impulse noise and outputs a binary flag image. The binary flag image denotes whether pixels are corrupted or not. According to a binary flag image, the noise filter processes to only noise pixels using neighborhood good pixels. Since the noise filter processes according to the binary flag image, the PSM filter performs satisfactorily in removing impulse noise. However, in the case of random-valued impulse noise, the performance of the noise detector is significantly reduced. If the random-valued impulse noise is located in the middle of order statistics, the noise detector cannot detect the noise. Therefore, the random-valued impulse noise detection is more difficult than the fixed-valued impulse noise detection. In this paper, we propose a new random-valued impulse noise detector from images using level detection. In our method, we use directional windows in order to search level region in the images. One window whose variation is lowest is selected as a flat window from multi directional windows. In a flat window, random-valued impulse noise may move to the both ends of order statistics. Therefore, the noise detector
0-7803-8834-8/05/$20.00 ©2005 IEEE.
x(i,j)
Noise Detector
x(i,j)
P(i,j)
Noise Filter
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Output
Input Fig. 1.
Structure of the PSM filter.
can detect the noise in the selected window. Consequently the proposed method reduces undetected noise pixels without increasing mis-detection. Extensive simulations indicate that the proposed method performs significantly better than conventional methods. II. PSM FILTER [1] A structure of the PSM filter is shown in Fig.1. The PSM filter consists of the noise detector and the noise filter. In the noise detector, the current pixel x(i, j) is judged whether it is corrupted by an impulse noise or not using neighborhood pixels. First, a median value of neighborhood pixels m(i, j) is obtained. Next, a binary flag image P (i, j) is given by 1 |x(i, j) − m(i, j)| ≥ TD P (i, j) = (1) 0 otherwise where TD is a threshold of the noise detection. P (i, j) = 1 means x(i, j) is corrupted by an impulse noise. On the other hand, P (i, j) = 0 means x(i, j) may be a good pixel. If TD is small, almost noises are detected. However, good pixels are regarded as a noise pixel. On the other hand, in case that TD is large, the mis-detection is decreased with increasing the undetection. In the noise filter, x(i, j) is processed based on the binary flag image. The noise filter processes to only noise pixels using neighborhood good pixels. Since the noise filter processes based on the binary flag image, the PSM filter performs satisfactorily in removing impulse noise. Therefore, the performance of the noise filter depends on the binary flag image.
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Topology of proposed method by using level detection.
However, in the case of random-valued impulse noise, the performance of the noise detector is significantly reduced. If the random-valued impulse noise is located in the middle of order statistics, the noise detector cannot detect the noise and the undetection is increased. If TD is set to small in order to decrease the undetection, the mis-detection is increased. Therefore, the random-valued impulse noise detection is more difficult than the fixed-valued impulse noise detection.
In our method, we use directional windows in order to search a level region in the images. One window whose variation is lowest selected as a flat window from multi directional windows includes a flat region. In the noise detector, an impulse noise is detected using the flat window. In a flat window, the random-valued impulse noise may move to the both ends of order statistics even if the noise is located in the middle of order statistics. Therefore, the noise detector can detect the random-valued impulse noise. In our method, we use some directional windows for searching the flat region. Directional windows Wn (n = 1, 2, · · · , 8) are shown in Fig.3. The size of the directional window is 2×5. Since we use multi windows with various direction, searching the flat region is easy at each pixel. Consequently, the performance of the noise detector is improved. B. Flat window decision In window evaluation, first, signals in the window Wn are n n sorted and rn = {r1n , r2n , · · · , rm } (rin ≤ ri+1 ) is obtained.
W8
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In this paper, a new random-valued impulse noise detector from images is proposed. The input signal x(i, j) is given by x0 (i, j) : probability 1 − q x(i, j) = (2) h : probability q
A. Directional window
W6
W5
III. P ROPOSED M ETHOD
where (i, j) denote the pixel coordinates of an image, x0 (i, j) is the original image, q is impulse noise ratio, and h is uniformly distributed within [0,255]. A topology of the proposed impulse noise detector is shown in Fig.2. The detector consists of the window evaluation, the flat window decision and the noise detector.
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:process pixel Fig. 3.
Multi window used in this paper.
Next, the pair of k and l is searched according to n rl − rkn > T h (1 ≤ k < l ≤ m) n rl−1 − rkn ≤ T h
(3)
where T h is a threshold for flat decision.The k for maximum (l − k) is searched from these pair. The intensity of flat is defined by f latn = l − k (4) where f latn is used to select the flat window. If f latn is small, Wn includes the edge or impulse noises. On the other hand, in case that f latn is large, Wn includes a flat region. Next, in the flat window decision, the window used to detect impulse noise is defined by if f latn ≥ M Wn for maximum f latn (5) Wf = W if f latn < M 0 for maximum f latn where M is threshold in order to allow that Wn is the flat window. If f latn < M , there is no flat region in Wn . In this case, since we use pixel at the neighborhood of the current pixel, the noise detector uses the window W0 . Here, if Wn includes the flat region, TD can be set to small in order to reduce undetected noise pixels. Since the variation of Wn is low in the flat window, the noise detector generates few mis-detection for small TD . On the other hand, in case
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that Wn has no flat region, TD should be set to large in order to reduce mis-detection. If TD is set to small in non-flat, misdetection is increased.
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IV. S IMULATION RESULTS The performance of the proposed method has been evaluated by the simulations. In the simulation, windows of Fig.3 are used to search a flat region. And, the noise detector is carried out by the median-based impulse noise detector[1]. TD is set to 20 for flat region and 50 for no flat region. Boat, Lenna, Airplane, Barbara and T ext are used as processing images(256 × 256 , 8bits). This images is corrupted by random-valued impulse noise (q = 10 ∼ 40%). The performance of noise detection is quantitatively measured by the mis-detected ratio and the undetected ratio. And the performance of restoration is quantitatively measured by the peak signal to noise ratio(PSNR). In our method, two threshold T h and M are used to decide a flat window. We first study the effects of T h and M on the performance of impulse noise detection. Fig.4 shows the normalized PSNR of filtering Boat and Lenna corrupted by the random-valued impulse noise (q = 10, 40%). In Fig.4(a)(c), the PSNR depends on T h for M = 5, 6. For low probability impulse noise ratio, the window includes few impulse noises. If M is set to small, non-flat is regarded as a flat region. Therefore, mid-detection is increased, and the performance of the restoration is reduced. In Fig.4(b)(d), the PSNR obtained for M = 8, 9 is low. Since the window includes many impulse noises for high impulse noise ratio, almost windows is judged to be Wf = W0 . Therefore, better results cannot be obtained for M = 8, 9. On the other hand, in case that M is small, T h obtaining better PSNR exists. If T h is smaller than optimal threshold, the window including flat
PSM[1] FW
Airplane Barbara Boat Lenna Text
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The undetected ratio of the PSM and the FW.
region is judged as no flat window. Therefore, the performance of restoration is reduced. On the other hand, in case that T h is larger than optimal threshold, no flat region is regarded as flat region. Thus, the PSNR is declined. In Fig.4, we set T h = 15 and M = 7 in order to adapt various noise ratio. The performance of the proposed method is compared with that of the PSM filter[1]. The parameter of the PSM filter is selected to obtain better performance for different cases. Here, the proposed method is named the flat window (FW) method. Fig.5 shows the mis-detected ratio of the PSM and the FW. And, Fig.6 shows the undetected ratio. In Fig.5, the mis-detected ratio of the FW and that of the PSM almost equivalent. In Fig.6, the undetected ratio of the FW is better than that of the PSM for various noise ratio and images. That is because random-valued impulse noise are detected using a flat window searched from multi directional windows. Therefore, the undetected ratio is reduced without increasing the misdetected ratio. Next, the FW is compared with the PSM in terms of filtering results. In this simulation, images are processed using each binary flag image with the noise filter[1]. Fig.7 shows the PSNR of filtering images corrupted by random-valued impulse noise with different noise ratios. In Fig.7, the FW exceeds
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Airplane Barbara Boat Lenna Text
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Fig. 7. Performance evaluation of the PSM and the FW in filtering images corrupted by random-valued impulse noise.
the PSM in PSNR. Since the FW reduces undetected noise pixel without increasing mis-detection, the performance of the noise filtering is improved. Fig.8 shows the results of filtering Airplane corrupted by the random-valued impulse noise (q = 10%). And, Fig.9 shows the results of filtering Boat corrupted by the random-valued impulse noise (q = 40%). In Fig.8(c) and Fig.9(c), impulse noises remain in resultant images by the PSM. Furthermore, in Fig.9(c), the PSM provides inferior performance in edge preservation. Since the detection of the random-valued impulse noise is difficult, impulse noise remains in resultant images. In Fig.8(d) and Fig.9(d), better results have been achieved by the FW with more effective noise rejection and edge preservation. That is because the performance of the noise detection is improved by searching flat region.
(a)Original
(b)Noisy
(c)PSM
(d)FW
Fig. 8.
Restoration images (Airplane, q = 10%).
V. C ONCLUSION In this paper, we have proposed a new random-valued impulse noise detector from images using level detection. In our method, one window whose variation is lowest is selected as a flat window. In a flat window, random-valued impulse noise may move to the both ends of order statistics. Therefore, the performance of noise detection is increased. In the simulation, the proposed method has demonstrated superior performance in detecting impulse noise. Especially, it is note worthy that the proposed method has shown the noticeable difference from other methods in the noise detected rate as well as the image quality.
(a)Original
(b)Noisy
(c)PSM
(d)FW
R EFERENCES [1] Z. Wang and D. Zhang, “Progressive switching median filter for the removal of impulse noise from highly corrupted images”, IEEE Trans. Circuits Syst. II, Analog and Digit. Signal Process. , Vol. 46, No. 1, pp. 78-80, Jan. 1999. [2] T. Sun and Y. Neuvo, “Detail-preserving median based filters in image processing,” Pattern Recognit. Lett., Vol. 15, pp. 341-347, April 1994. [3] T. Chen, K.-K. Ma and L.-H. Chen, “Tri-state median filter for image denoising,” IEEE Trans. Image Processing, Vol. 8, pp. 1834-1838, Dec. 1999.
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Fig. 9.
Restoration images (Boat, q = 40%).
I. I NTRODUCTION In the image processing, median filters have been widely used for removing impulse noise, since median filters are quite effective for the noise removal and the edge preserving. However, median filters tend to modify both noise pixels and undisturbed good pixels. Recently, switching schemes have been studied for removal impulse noise in images [1]-[3]. These schemes detect whether the current pixel is corrupted by impulse noise at each pixel. Then, filtering is activated for pixels that is detected as noise pixels, while good pixels are kept. As a switching scheme, progressive switching median (PSM) filter [1] was proposed for removal impulse noise. With the PSM filter, both the impulse noise detector and the noise filter are applied progressively. The noise detector detects an impulse noise and outputs a binary flag image. The binary flag image denotes whether pixels are corrupted or not. According to a binary flag image, the noise filter processes to only noise pixels using neighborhood good pixels. Since the noise filter processes according to the binary flag image, the PSM filter performs satisfactorily in removing impulse noise. However, in the case of random-valued impulse noise, the performance of the noise detector is significantly reduced. If the random-valued impulse noise is located in the middle of order statistics, the noise detector cannot detect the noise. Therefore, the random-valued impulse noise detection is more difficult than the fixed-valued impulse noise detection. In this paper, we propose a new random-valued impulse noise detector from images using level detection. In our method, we use directional windows in order to search level region in the images. One window whose variation is lowest is selected as a flat window from multi directional windows. In a flat window, random-valued impulse noise may move to the both ends of order statistics. Therefore, the noise detector
0-7803-8834-8/05/$20.00 ©2005 IEEE.
x(i,j)
Noise Detector
x(i,j)
P(i,j)
Noise Filter
x(i,j)
Output
Input Fig. 1.
Structure of the PSM filter.
can detect the noise in the selected window. Consequently the proposed method reduces undetected noise pixels without increasing mis-detection. Extensive simulations indicate that the proposed method performs significantly better than conventional methods. II. PSM FILTER [1] A structure of the PSM filter is shown in Fig.1. The PSM filter consists of the noise detector and the noise filter. In the noise detector, the current pixel x(i, j) is judged whether it is corrupted by an impulse noise or not using neighborhood pixels. First, a median value of neighborhood pixels m(i, j) is obtained. Next, a binary flag image P (i, j) is given by 1 |x(i, j) − m(i, j)| ≥ TD P (i, j) = (1) 0 otherwise where TD is a threshold of the noise detection. P (i, j) = 1 means x(i, j) is corrupted by an impulse noise. On the other hand, P (i, j) = 0 means x(i, j) may be a good pixel. If TD is small, almost noises are detected. However, good pixels are regarded as a noise pixel. On the other hand, in case that TD is large, the mis-detection is decreased with increasing the undetection. In the noise filter, x(i, j) is processed based on the binary flag image. The noise filter processes to only noise pixels using neighborhood good pixels. Since the noise filter processes based on the binary flag image, the PSM filter performs satisfactorily in removing impulse noise. Therefore, the performance of the noise filter depends on the binary flag image.
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Fig. 2.
W1
Topology of proposed method by using level detection.
However, in the case of random-valued impulse noise, the performance of the noise detector is significantly reduced. If the random-valued impulse noise is located in the middle of order statistics, the noise detector cannot detect the noise and the undetection is increased. If TD is set to small in order to decrease the undetection, the mis-detection is increased. Therefore, the random-valued impulse noise detection is more difficult than the fixed-valued impulse noise detection.
In our method, we use directional windows in order to search a level region in the images. One window whose variation is lowest selected as a flat window from multi directional windows includes a flat region. In the noise detector, an impulse noise is detected using the flat window. In a flat window, the random-valued impulse noise may move to the both ends of order statistics even if the noise is located in the middle of order statistics. Therefore, the noise detector can detect the random-valued impulse noise. In our method, we use some directional windows for searching the flat region. Directional windows Wn (n = 1, 2, · · · , 8) are shown in Fig.3. The size of the directional window is 2×5. Since we use multi windows with various direction, searching the flat region is easy at each pixel. Consequently, the performance of the noise detector is improved. B. Flat window decision In window evaluation, first, signals in the window Wn are n n sorted and rn = {r1n , r2n , · · · , rm } (rin ≤ ri+1 ) is obtained.
W8
W7
In this paper, a new random-valued impulse noise detector from images is proposed. The input signal x(i, j) is given by x0 (i, j) : probability 1 − q x(i, j) = (2) h : probability q
A. Directional window
W6
W5
III. P ROPOSED M ETHOD
where (i, j) denote the pixel coordinates of an image, x0 (i, j) is the original image, q is impulse noise ratio, and h is uniformly distributed within [0,255]. A topology of the proposed impulse noise detector is shown in Fig.2. The detector consists of the window evaluation, the flat window decision and the noise detector.
W4
W2
:process pixel Fig. 3.
Multi window used in this paper.
Next, the pair of k and l is searched according to n rl − rkn > T h (1 ≤ k < l ≤ m) n rl−1 − rkn ≤ T h
(3)
where T h is a threshold for flat decision.The k for maximum (l − k) is searched from these pair. The intensity of flat is defined by f latn = l − k (4) where f latn is used to select the flat window. If f latn is small, Wn includes the edge or impulse noises. On the other hand, in case that f latn is large, Wn includes a flat region. Next, in the flat window decision, the window used to detect impulse noise is defined by if f latn ≥ M Wn for maximum f latn (5) Wf = W if f latn < M 0 for maximum f latn where M is threshold in order to allow that Wn is the flat window. If f latn < M , there is no flat region in Wn . In this case, since we use pixel at the neighborhood of the current pixel, the noise detector uses the window W0 . Here, if Wn includes the flat region, TD can be set to small in order to reduce undetected noise pixels. Since the variation of Wn is low in the flat window, the noise detector generates few mis-detection for small TD . On the other hand, in case
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that Wn has no flat region, TD should be set to large in order to reduce mis-detection. If TD is set to small in non-flat, misdetection is increased.
12 10 8 6 4 2 0 10
IV. S IMULATION RESULTS The performance of the proposed method has been evaluated by the simulations. In the simulation, windows of Fig.3 are used to search a flat region. And, the noise detector is carried out by the median-based impulse noise detector[1]. TD is set to 20 for flat region and 50 for no flat region. Boat, Lenna, Airplane, Barbara and T ext are used as processing images(256 × 256 , 8bits). This images is corrupted by random-valued impulse noise (q = 10 ∼ 40%). The performance of noise detection is quantitatively measured by the mis-detected ratio and the undetected ratio. And the performance of restoration is quantitatively measured by the peak signal to noise ratio(PSNR). In our method, two threshold T h and M are used to decide a flat window. We first study the effects of T h and M on the performance of impulse noise detection. Fig.4 shows the normalized PSNR of filtering Boat and Lenna corrupted by the random-valued impulse noise (q = 10, 40%). In Fig.4(a)(c), the PSNR depends on T h for M = 5, 6. For low probability impulse noise ratio, the window includes few impulse noises. If M is set to small, non-flat is regarded as a flat region. Therefore, mid-detection is increased, and the performance of the restoration is reduced. In Fig.4(b)(d), the PSNR obtained for M = 8, 9 is low. Since the window includes many impulse noises for high impulse noise ratio, almost windows is judged to be Wf = W0 . Therefore, better results cannot be obtained for M = 8, 9. On the other hand, in case that M is small, T h obtaining better PSNR exists. If T h is smaller than optimal threshold, the window including flat
PSM[1] FW
Airplane Barbara Boat Lenna Text
20
30
40
Noise Ratio q [%] Fig. 6.
The undetected ratio of the PSM and the FW.
region is judged as no flat window. Therefore, the performance of restoration is reduced. On the other hand, in case that T h is larger than optimal threshold, no flat region is regarded as flat region. Thus, the PSNR is declined. In Fig.4, we set T h = 15 and M = 7 in order to adapt various noise ratio. The performance of the proposed method is compared with that of the PSM filter[1]. The parameter of the PSM filter is selected to obtain better performance for different cases. Here, the proposed method is named the flat window (FW) method. Fig.5 shows the mis-detected ratio of the PSM and the FW. And, Fig.6 shows the undetected ratio. In Fig.5, the mis-detected ratio of the FW and that of the PSM almost equivalent. In Fig.6, the undetected ratio of the FW is better than that of the PSM for various noise ratio and images. That is because random-valued impulse noise are detected using a flat window searched from multi directional windows. Therefore, the undetected ratio is reduced without increasing the misdetected ratio. Next, the FW is compared with the PSM in terms of filtering results. In this simulation, images are processed using each binary flag image with the noise filter[1]. Fig.7 shows the PSNR of filtering images corrupted by random-valued impulse noise with different noise ratios. In Fig.7, the FW exceeds
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Airplane Barbara Boat Lenna Text
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Fig. 7. Performance evaluation of the PSM and the FW in filtering images corrupted by random-valued impulse noise.
the PSM in PSNR. Since the FW reduces undetected noise pixel without increasing mis-detection, the performance of the noise filtering is improved. Fig.8 shows the results of filtering Airplane corrupted by the random-valued impulse noise (q = 10%). And, Fig.9 shows the results of filtering Boat corrupted by the random-valued impulse noise (q = 40%). In Fig.8(c) and Fig.9(c), impulse noises remain in resultant images by the PSM. Furthermore, in Fig.9(c), the PSM provides inferior performance in edge preservation. Since the detection of the random-valued impulse noise is difficult, impulse noise remains in resultant images. In Fig.8(d) and Fig.9(d), better results have been achieved by the FW with more effective noise rejection and edge preservation. That is because the performance of the noise detection is improved by searching flat region.
(a)Original
(b)Noisy
(c)PSM
(d)FW
Fig. 8.
Restoration images (Airplane, q = 10%).
V. C ONCLUSION In this paper, we have proposed a new random-valued impulse noise detector from images using level detection. In our method, one window whose variation is lowest is selected as a flat window. In a flat window, random-valued impulse noise may move to the both ends of order statistics. Therefore, the performance of noise detection is increased. In the simulation, the proposed method has demonstrated superior performance in detecting impulse noise. Especially, it is note worthy that the proposed method has shown the noticeable difference from other methods in the noise detected rate as well as the image quality.
(a)Original
(b)Noisy
(c)PSM
(d)FW
R EFERENCES [1] Z. Wang and D. Zhang, “Progressive switching median filter for the removal of impulse noise from highly corrupted images”, IEEE Trans. Circuits Syst. II, Analog and Digit. Signal Process. , Vol. 46, No. 1, pp. 78-80, Jan. 1999. [2] T. Sun and Y. Neuvo, “Detail-preserving median based filters in image processing,” Pattern Recognit. Lett., Vol. 15, pp. 341-347, April 1994. [3] T. Chen, K.-K. Ma and L.-H. Chen, “Tri-state median filter for image denoising,” IEEE Trans. Image Processing, Vol. 8, pp. 1834-1838, Dec. 1999.
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Fig. 9.
Restoration images (Boat, q = 40%).
