A switching weighted vector median filter based on edge detection

Signal Processing 98 (2014) 359–369

Contents lists available at ScienceDirect

Signal Processing journal homepage: www.elsevier.com/locate/sigpro

A switching weighted vector median filter based on edge detection Jiangtao Xu, Lei Wang, Zaifeng Shi n School of Electronic and Information Engineering, Tianjin University, Tianjin, PR China

a r t i c l e i n f o

abstract

Article history: Received 13 July 2013 Received in revised form 21 November 2013 Accepted 30 November 2013 Available online 7 December 2013

An impulse noise removal method based on noise detection and image edge detection is proposed to improve the performance of vector median filter. Corrupted pixels are first discriminated from the noise-free pixels by comparing the current pixel with the corresponding pixel in a reference image. Then corrupted pixels are filtered by the proposed weighted vector median filter. The novelty of this filter lies in its weighting technique based on image edge detection. The weight of each pixel is determined by its group which is related to the image edge. This method can suppress noise and reduce edge blurring effectively. Experimental results show that the proposed method outperforms all algorithms examined in this paper in terms of MAE, MSE and PSNR values. & 2013 Elsevier B.V. All rights reserved.

Keywords: Impulse noise reduction Vector median filter Edge detection Detail preservation

1. Introduction Images are frequently corrupted by impulse noise [1] which occurs in the process of image acquisition, transmission and storage [2]. To effectively suppress noise while keeping image features such as edges and fine details is a fundamental problem in digital image processing. Median filter has become the most popular method of impulse noise removal and image restoration due to its excellent capability of suppressing impulse noise [3–5]. Scalar median filter (SMF), which replaces the gray-scale value of each pixel with the median of its neighbors, is mostly applied to single-channel or gray scale images. Vector marginal median filter (VMMF) [6] uses a scalar median filter to smooth the three channels of a color image respectively and adds the filtered single channel image as the final output image. VMMF can effectively remove noise. However, it may introduce artificial color [7] due to the irrelevancy of the filtering processes in three channels. Taking into account the correlation of R, G and B channels,

n

Corresponding author. Tel.: þ86 13682001887. E-mail address: [email protected] (Z. Shi).

0165-1684/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.sigpro.2013.11.035

nonlinear vector filters (VF) have been proposed to overcome the drawback of scalar filter by applying vector operation. The common vector filters include vector median filter (VMF) [8], basic vector directional filter (BVDF) [9] and directionaldistance filter (DDF) [10]. Among these filters, VMF represents one of the most popular approaches to remove impulse noise from color images [11]. Standard vector median filter applies filtering operation to all image pixels but a lot of them are noise-free and need not be filtered. This filter performs well in suppressing noise but introduces blurring artifacts in edges and detail areas [12]. Filters based on switching techniques have been applied to remove the impulse noise and give better performance. Switching vector median filters (SVMF) only modify those pixels which are detected as noise and keep the noise-free pixels unchanged. The key of switching filter is to detect noise correctly. Adaptive vector median filter (AVMF) [13] adopts a noise detection technique based on the set of vector-valued order-statistics with the smallest distances to the other samples in the input set. A modified AVMF is proposed in [14], which uses four one-dimensional Laplacian operators to judge the noise candidates detected by AVMF. A noise detector [15], based on quaternion unit transform theory, achieves

360

J. Xu et al. / Signal Processing 98 (2014) 359–369

a trade-off between noise suppression and detail preservation. In [16], a noise detection method combining scalar detection with vector detection achieves better performance in detail preserving but its noise removal ability is decreased. Weighted vector median filter (WVMF) can control filter behavior more precisely and improve filtering quality by assigning different weights to the samples in the observation window [17]. Many WVMFs have been proposed [12,17,18,19]. Among these filters, center-weighted vector median filter (CWVMF) [12,18], enhancing the weight of central sample of the window, is a simple weighting method with effective performance. In this paper, a noise detector is first applied to predetect corrupted pixels by calculating the similarity of current pixel and the corresponding pixel in a reference image. Then a weighted vector median filter based on image edge detection is proposed to filter the corrupted pixels. Unlike previous weighting methods which mostly pay attention to pixels' intensity information, this filter utilizes pixels' location information. Experimental results show that proposed method performs more effectively than all the other examined algorithms. The rest of this paper is organized as follows. Section 2 describes the basic theories of scalar median filter, vector median filter and weighted vector median filter. Section 3 introduces the proposed noise removal method in detail. Test images with different noise levels processed by the proposed filter and some other conventional filters are displayed in Section 4, along with the experimental results. At last conclusions are presented in Section 5.

where ‖:‖p denotes the lp norm. In this paper, l2 norm (Euclidian distance) is used. Finally, find the smallest one among all the Di values. If the ordering scheme is D(1)rD (2)rD(3)r… rD(N), and the corresponding pixel vector is X(1), X(2), X(3),…, X(N), then the central pixel of the window is replaced with X(1). The upper description can be given by

2. Basics of median filters

X WVMF ¼ arg min ∑ ωj ‖X i  X j ‖p

2.1. Scalar median filter

The center-weighted vector median filter (CWVMF), which only assigns weight to the center pixel of the filter window, is a special case of WVMF. The parameter ωj in CWVMF can be given by ( k; j ¼ ðN þ 1Þ=2 ωj ¼ ð7Þ 1; otherwise

Xi A W

j¼1

Xi A W

j¼1

N

Di ¼ ∑ ωj ‖X i  X j ‖p j¼1

8 ∂ω j < ∂δðX ;X r0 j cÞ : ωωc rα; α Z1 j

i ¼ 1; 2; 3; :::; N

j ¼ 1; 2; 3; :::; N

Using SMF, the central pixel of the window is replaced by a pixel that the sum of the distances to all the other pixels in the window is the minimum.

ð4Þ

ð5Þ

where ωj denotes the weight of pixel Xj, Xc denotes the central pixel of the filter window, ωc denotes the weight of Xc, and δ(Xj, Xc) denotes the city distance from Xj to Xc. The output of WVMF is similar to VMF and is defined as

X AW

ð1Þ

ð3Þ

2.2.2. Weighted vector median filter Weighted vector median filter (WVMF) performs better in noise suppression and detail preservation than standard VMF [12]. Different weights are assigned to pixels in the window, and pixels which are not corrupted or more similar to original pixels should be assigned higher weights. Then cumulative distances are given by

N

For an observation window W¼{X1, X2, X3, …, XN}, where N is the window size and is always odd, the output of the scalar median filter (SMF) is defined as N

X med ¼ arg min ∑
X i X j


N

X VMF ¼ arg min ∑ ‖X i  X j ‖p

j¼1

ð6Þ

Proofs can be found in [20,21] that as the value of k increases, the capability of detail preservation of the filter is improved but the noise removal performance is degraded. When k ¼1, the CWVMF is the same with standard VMF.

2.2. Vector median filter 3. Proposed switching weighted vector median filter 2.2.1. Standard vector median filter Vector median filter (VMF) is a nonlinear filter to suppress impulse noise in digital image processing. The filtering technique is as follows. W(N) is a window of finite size N, and X i ¼ ðX Ri ; X Gi ; X Bi Þ (i¼1, 2, 3, …, N) denotes the vector of a pixel in the given window. Calculate the vector distances (L1 norm or L2 norm) from each pixel to others in the window firstly. Then the sum of the vector distances can be calculated as N

N

j¼1

j¼1

Di ¼ ∑ ρij ðX i ; X j Þ ¼ ∑ ‖X i  X j ‖p

i; j ¼ 1; 2; 3; :::; Nði ajÞ ð2Þ

3.1. Noise pre-detection In a color image corrupted by impulse noise, each channel of its pixel may be corrupted with the same probability of p. VMMF, as mentioned above, filtering each channel separately using scalar median filter, has effective noise suppression ability, but may lead to color artifacts. To take advantage of VMMF and overcome its drawback, the output image of VMMF is just treated as a reference image. In the reference image, there are scarcely any corrupted pixels. This property is utilized to discriminate noise pixels from noise-free pixels in this paper.

J. Xu et al. / Signal Processing 98 (2014) 359–369

361

Fig. 1. The divided groups of the window based on image edge detection.

At first, the noised image is processed by VMMF. LetX 0i ¼ ðX 0i R; X 0i G; X 0i BÞdenote the pixel of the output image. Then calculate the similarity between Xi and X'i using the following similarity function [22,23] μQi ¼ 1 

ρðX Qi ; X 0i Q Þ k

ð8Þ

where Q¼R, G, B. k is the absolute difference between the maximal value and the minimum value of X 0i Q . ρ represents the vector distance (usually using L1 norm or L2 norm) between Xi and X'i. In this paper it denotes the Euclidian distance between X Qi and X 0i Q . If X Qi and X 0i Q are similar, which can be defined as ðμRi 4TÞ&&ðμGi 4 TÞ&&ðμBi 4TÞ

(1) Change the color image into gray-scale image. (2) Remove noise in the gray-scale image using SMF. As the size of window increases, noise removal performance is improved but the detail of the image will be more easily destroyed. Either noise or detail-hurting can affect later process of WVMF, so a trade-off is needed here. Experiments show that final results are better when using a 3  3 window for images with low noise levels (p o0.2) and a 5  5 window for images with high noise levels (p40.2) respectively. (3) Calculate the edge image using image edge detection algorithm. In this paper, a Canny edge detector is used for its efficient performance in edge detection.

ð9Þ

where T is a pre-defined threshold, the sampled pixel is considered as noise-free and output Xi directly. Otherwise it is regarded as noised and should be filtered in the next step. The output of switching VMF is given by ( X ðN þ 1Þ=2 ; ifX ðN þ 1Þ=2 is noise free ð10Þ outðN þ 1Þ=2 ¼ X WVMF otherwise

3.2. Weighted vector median filter based on edge detection If there are image edges in a filter window, the number of pixels belonging to different sides of the edge may be approximately equal. It may result in several very similar Di values in a window. So blurring occurs more easily when filter the edges of the image in comparison of the other fields of the image, and the performance of VMF near the image edges is always much worse than that on the other field of the image. Improving the processing quality near image edges will greatly improve the whole performance of the filter. 3.2.1. Image edge detection It can be concluded from Eq. (6) that increasing the weight of a pixel can enhance its probability to be the output of WVMF. In order to improve the performance of VMF especially to protect image edges, a weighting technique based on image edge detection is proposed. Large amount of noise in the image always leads to error during edge-detection, so some pre-processing must be applied to improve the accuracy of detection. The steps of edge detection in noised image are as follows:

3.2.2. Weighted vector median filter In this section, the smoothing parameter ωj in function (4) will be determined. In order to enhance the weights of pixels on or around the image edges and protect image details, the filter window is firstly divided into several groups based on the former results of image edge detection, and pixels in the same group will be assigned to the same weight. As shown in Fig. 1, this paper uses a 5  5 window to filter the noised images. The dark gray blocks in Fig. 1 represent image edges. Based on the pixels' location in relation to image edge, different weights are given as follows: (1) If the central pixel of the window is on image edge, as shown in Fig. 1(a), the pixels on the image edge are divided into the same group and their weights are set to ωe. Other pixels in the window are classified into another group with their weight set to ω3. Let ωe 4ω3, because pixels on image edge are more similar to the filtered pixel, and their probability to be the output should be increased. (2) If the central pixel is not on image edge while there are image edges in the filter window, as shown in Fig. 1(b) and (c), set the center-pixel's weight to ωc, and divide the rest pixels of the window into three groups at the same time: pixels on image edge are in the same group and their weights are set to ω2; pixels located on the same side of image edge with the center-pixel are in another group with their weights set to ω1; pixels in different side of image edge with center-pixel belong to the last group with their weights set to ω3. Considering their similarity to the center-pixel, let ωc 4ω1 4ω2 4ω3.

362

J. Xu et al. / Signal Processing 98 (2014) 359–369

(3) If the central pixel is not on image edge and there is no image edge in the filter window, as shown in Fig. 1(d), then set the weight of the central pixel to ωc and weights of the rest pixels to ω1. Let ωc 4ω1. This situation is similar to CWVMF.

corresponding to vector A. For example, if A¼{0, 1, 0}, it means the central pixel is a non-edge pixel, the second pixel is on the image edge and the third pixel is a non-edge pixel. This situation belongs to case (2). The weights are configured as follows: the weight of central pixel is set to ωc, the second pixel is set to ω2, and the third pixel is set to ω3. Scan the vector A anticlockwise over the window then all pixels in the window will be assigned with a specified weight. It can be concluded from above analysis that the relationship of ωe, ωc, ω1, ω2, ω3 is ωe 4ω3, ωc 4ω1 4ω2 4ω3. The next step is to determine the values of these weights. The five weights are defined based on function (5) and statistic experimental results. Function (5) reflects a principle to define the weights: the pixels which are closer to the center pixel should be given a higher weight. Then the five weights are defined one by one as following experiment steps:

To classify the pixels into different groups based on image edge detection, the following method is used: define a scan vector A¼{a1, a2, a3}, a1, a2, a3 ¼0 or 1, where 0 represents a non-edge pixel and 1 represents a pixel on the edge. As shown in Fig. 2(a), a1 i always at the center of the window. Fig. 2(b) shows the weight vector

1) ω3 is always set to 1; 2) keep ωc, ω1, ω2, ω3 unchanged, and change ωe from 1 to 10. Experimental results are shown in Fig. 3(a). It can be seen that when noise level is low, the influence of ωe to PSNR is little, while when noise level is high, the influence is strong. ωe ¼3 achieves best results for most cases. 3) Keep ωe, ω1, ω2, ω3 unchanged, and change ωc/ω1. Experimental results are shown in Fig. 3(b). If noise

Fig. 2. Weights assignment strategy.

29

30

28.5

29 lena p=0.2 boats p=0.1 peppers p=0.25 hat p=0.3

27.5

28

PSNR (dB)

PSNR(dB)

28

27 26.5

27 26 25

26

24

25.5

23

25

1

2

3

4

lena p=0.2 boats p=0.15 peppers p=0.25 hat p=0.3

5

6

7

8

9

10

22

1

2

3

We/W3

4

5

6

7

Wc/W1 Fig. 3. (a) ωe/ω3 versus PSNR; (b) ωc/ω1 versus PSNR.

Fig. 4. (a) R channel in the original image; (b) R channel in the noised image (p ¼0.3); (c) R channel in the filtered image.

8

9

J. Xu et al. / Signal Processing 98 (2014) 359–369

363

Fig. 5. (a) Original image; (b) noised image (p ¼0.2); (c) edge of original image; (d) edge of noised image; (e) edge of image filtered by 3  3 window; (f) edge of image filtered by 5  5 window; (g) edge of image filtered by 7  7 window.

30

11 10 9 8

26

MAE

PSNR(dB)

28

24

22

20 0.05

VMF(3*3) VMF(5*5) CWVMF VMMF proposed 0.1

VMF(3*3) VMF(5*5) CWVMF VMMF proposed

7 6 5 4 3

0.15

0.2

0.25

2 0.05

0.3

0.1

0.15

0.2

0.25

0.3

0.25

0.3

p

P

Fig. 6. Experimental results of (a) PSNR, (b) MAE when filtering Lena using different methods.

32

10 9

30

8 7

MAE

PSNR(dB)

28

26

24

22

20 0.05

VMF(3*3) VMF(5*5) CWVMF VMMF proposed 0.1

VMF(3*3) VMF(5*5) CWVMF VMMF propposed

6 5 4 3 2

0.15

0.2

p

0.25

0.3

1 0.05

0.1

0.15

0.2

p

Fig. 7. Experimental results of (a) PSNR, (b) MAE when filtering Peppers using different methods.

364

J. Xu et al. / Signal Processing 98 (2014) 359–369

Table 1 Experimental results of MAE, MSE and PSNR when filtering the Boats image corrupted by different noise density using different filters. Filter

None VMF (3  3) VMF (5  5) CWVMF (5  5) VMMF (3  3) Proposed (5  5)

5%

10%

20%

30%

MAE

MSE

PSNR

MAE

MSE

PSNR

MAE

MSE

PSNR

MAE

MSE

PSNR

6.344 5.124 7.656 5.845 4.959 3.086

853.95 102.57 202.45 144.07 102.28 97.13

18.816 28.020 25.067 26.544 28.032 28.257

13.065 5.675 7.965 6.174 5.330 3.890

1770.1 126.37 214.10 154.43 122.06 112.54

15.650 27.114 24.824 26.243 27.265 27.618

25.382 7.280 8.617 7.058 6.386 5.712

3424.1 235.33 241.64 187.89 199.45 166.43

12.785 24.414 24.299 25.391 25.132 25.918

38.19 10.480 9.538 8.297 8.596 7.488

5151.1 582.72 288.66 252.32 443.26 240.09

11.012 20.476 23.526 24.111 21.664 24.327

Table 2 Experimental results of MAE, MSE and PSNR when filtering the Hat image corrupted by different noise density using different filters. Filter

None VMF (3  3) VMF (5  5) CWVMF (5  5) VMMF (3  3) Proposed (5  5)

5%

10%

20%

30%

MAE

MSE

PSNR

MAE

MSE

PSNR

MAE

MSE

PSNR

MAE

MSE

PSNR

6.348 2.243 3.134 2.248 2.104 0.845

858.52 27.36 44.96 29.36 25.67 17.33

18.793 33.759 31.603 33.453 34.036 35.742

12.706 2.592 3.337 2.491 2.337 1.315

1717.1 39.26 50.85 35.30 34.83 24.66

15.78 32.191 31.067 32.653 32.711 34.210

25.619 3.779 3.932 3.186 3.053 2.353

3467.8 123.90 72.56 57.68 85.07 48.69

12.730 27.199 29.523 30.519 28.832 31.256

38.253 6.480 4.609 4.073 4.763 3.545

5181 426.41 98.49 95.31 273.44 94.17

10.986 21.832 28.196 28.339 23.762 28.392

Fig. 8. Experimental results for Boats in case where p ¼pr¼ pg ¼pb ¼ 0.20. (a) Original image, (b) corrupted image, (c) image edge, (d) output of VMF with a 3  3 window, (e) output of VMF with a 5  5 window, (f) output of CWVMF with a 5  5 window, (g) output of VMMF with a 3  3 window, (h) output of proposed filter.

level is low, PSNR results change little. If noise level is high, PSNR results decrease fast as the ωc/ω1 increases. To be adapted to different noise levels and to obtain better results, ωc/ω1 is set to 3.5. 4) since ω1/ω2 and ω2/ω3 have little influence on the final results they are set to 1.25 and 2 respectively.

4. Experimental results The proposed switching WVMF has been evaluated by an extensive range of tests. Some color images such as “lena”, “peppers”, “boats” and “hat” with size of 256  256  24 bits are employed as test images. In this section,

J. Xu et al. / Signal Processing 98 (2014) 359–369

365

Fig. 9. Experimental results for Lena in case where p ¼pr¼ pg ¼pb ¼ 0.10. (a) Original image, (b) corrupted image, (c) image edge, (d) output of VMF with a 3  3 window, (e) output of VMF with a 5  5 window, (f) output of CWVMF with a 5  5 window, (g) output of VMMF with a 3  3 window, (h) output of proposed filter.

Fig. 10. Experimental results for Peppers in case where p¼ pr¼ pg ¼pb ¼0.30. (a) Original image, (b) corrupted image, (c) image edge, (d) output of VMF with a 3  3 window, (e) output of VMF with a 5  5 window, (f) output of CWVMF with a 5  5 window, (g) output of VMMF with a 3  3 window, (h) output of proposed filter.

some experimental results of noise detection and image edge detection are presented, and then the performance of proposed method is compared with a number of prior-art filtering techniques in the area of color image restoration.

4.1. Results of noise detection and image edge detection Taking the Red channel of image Lena as an example, Fig. 4 shows the results of VMMF. The result proves that VMMF with a 7  7 window can almost remove all

366

J. Xu et al. / Signal Processing 98 (2014) 359–369

Fig. 11. Experimental results for Hat in case where p ¼pr¼ pg ¼ pb¼ 0.05. (a) Original image, (b) corrupted image, (c) image edge, (d) output of VMF with a 3  3 window, (e) output of VMF with a 5  5 window, (f) output of CWVMF with a 5  5 window, (g) output of VMMF with a 3  3 window, (h) output of proposed filter.

Fig. 12. Test images in this paper Table 3 PSNR results of the 8 filtered images in Fig. 12 (p ¼ 0.2).

VMF(3  3) VMF CWVMF VMMF(3  3) Proposed

a

b

c

d

e

f

g

h

28.02 32.36 33.44 28.82 33.64

26.65 28.38 29.46 27.86 29.47

27.52 29.78 30.76 27.55 31.29

27.17 28.25 29.37 28.98 29.41

22.47 22.41 23.39 22.87 23.88

24.15 23.55 24.65 25.01 25.04

25.68 26.38 27.48 26.52 28.05

22.49 22.34 23.36 23.31 23.72

J. Xu et al. / Signal Processing 98 (2014) 359–369

367

Fig. 13. Experimental results: (a) original image, (b) absolute error of noisy image (p ¼0.10), (c) absolute error of VMF with a 3  3 window, (d) absolute error of VMF with a 5  5 window, (e) absolute error of CWVMF with a 5  5 window, (f) absolute error of VMMF with a 3  3 window, (g) absolute error of VMF with proposed filter.

corrupted pixels, so the output of VMMF can be used as reference image during noise detection. In the step of image edge detection, scalar filters with different window size are used. The results of image detection with different scalar filters are shown in Fig. 5. It can be seen from Fig. 5(d) that without pre-filtering, the noised pixels can lead to error image edge detecting, and the detected error image edges can greatly affect the following process. Compared with the original image edges, the edges of image filtered by a 3  3 window remain some noise. However, the edges of image filtered by a 7  7 window, as shown in Fig. 5(g), lose a lot of details. It can be concluded that lager filter window removes more noise but destroys more details.

4.2. Performance comparison of different filters In contaminated images, noise is independently introduced in each of the three color channels with the probability of p. Noise of different densities is added to original images. As the methods for comparison, VMF with a 3  3 window, VMF with a 5  5 window, CWVMF [12] with a 5  5 widow and VMMF with a 3  3 window [23] are applied to the experiments. The objective evaluation measures, mean absolute error (MAE), mean square error (MSE) and peak signal to noise ratio (PSNR) are used to represent the quality of different filters. They are defined as MAE ¼

M ∑N i ¼ 1 ∑k ¼ 1 ‖xik oik‖1 3  NM

ð11Þ

MSE ¼

M 2 ∑N i ¼ 1 ∑k ¼ 1 ‖xik  oik‖2 3  NM

255 PSNR ¼ 20 log 10ðpffiffiffiffiffiffiffiffiffiffiÞ MSE

ð12Þ

ð13Þ

where N, M denote the width and height of the image respectively, xik is the pixel in the filtered image and oik is the pixel in the original image. ‖:‖1 denotes L1 norm, and ‖:‖2 denotes L2 norm (Euclidian distance). To compare the performance of different filters, PSNR and MAE curves of different images are plotted in Fig. 6 and Fig. 7. It can be seen that VMF with a 3  3 window performs better than that with a 5  5 window in the situation of low noise density, because for low noise images, VMF with a 3  3 window can effectively remove noise while VMF with a 5  5 window may destroy many details. However, as the noise level increases, VMF with a larger window will be more effective for its high noise reduction ability. CWVMF with a 5  5 window can protect image details to some degree, so it performs similarly to VMF with a 3  3 window when noise density is low, but its performance is still worse than VMMF. VMMF always has higher noise reduction ability for different noise density compared to VMF with the same window size, however this filter introduces many color artifacts especially near image edges [23]. Compared to those filters mentioned above, the performance of the proposed switching WVMF, using a 5  5 window, is more effective in both low noise and high noise situation. As shown in Fig. 6 and Fig. 7, the proposed method achieves higher value of PSNR and lower value of MAE than all the other methods. Objective results such as MAE, MSE and PSNR

368

J. Xu et al. / Signal Processing 98 (2014) 359–369

Table 4 MSSIM results when filtering the peppers image and lena image. Filter

VMF(3  3) VMF CWVMF VMMF(3  3) Proposed

Peppers

Lena

P¼ 0.1

P¼0.15

P¼ 0.2

P¼ 0.25

P¼ 0.3

P¼ 0.1

P ¼0.15

P¼ 0.2

P ¼0.25

P ¼0.3

0.9436 0.9182 0.9424 0.9573 0.9650

0.9268 0.9124 0.9362 0.9496 0.9557

0.8858 0.8995 0.9216 0.9286 0.9393

0.8262 0.8907 0.9089 0.8919 0.9244

0.7525 0.8715 0.8845 0.8360 0.8986

0.9110 0.8754 0.9070 0.9279 0.9423

0.8907 0.8677 0.8992 0.9208 0.9294

0.8541 0.8593 0.8890 0.8996 0.9118

0.7963 0.8460 0.8726 0.8608 0.8934

0.7181 0.8300 0.8499 0.8102 0.8664

when filtering images Boats and Hat are listed in Table 1and Table 2. Part of test images and the filtering results using different method are shown in Figs. 8–11 for further comparison. From Fig. 9 and Fig. 11, it can be seen that when noise level is low, no matter which method is adopted, the noised pixels can be removed mostly. But the proposed method achieves clearer image edges in comparison with other methods. When noise level is high, as shown in Fig. 8 and Fig. 10, filters with a 3  3 window cannot remove all noise so these filters perform less effectively than filters with a 5  5 window which can almost remove all noise. To obtain statistical performance, more test images shown in Fig. 12 were added to the filtering experiments. The PSNR results of these filtered images are listed in Table 3. The absolute error shown in Fig. 13 reflects the performance of different filters in detail protection, and it is defined as AE¼255  |I  I′|, where I is the original image and I′ is the filtered image or the noised image. Meanwhile, the mean structural similarity (MSSIM) index [24] was used to compare the ability of detail preservation with different filters. The MSSIM results are listed in Table 4. It can be seen that the proposed method destroys less details than all the other examined filters.

5. Conclusions This paper has proposed a new vector median filter to remove impulse noise in color image based on fuzzy noise detection and image edge detection. In noise detection step, pixels in noised image are compared to the corresponding pixels in a reference image which is filtered by applying a scalar median filter to each channel of noised image respectively. Whether a pixel is corrupted or not is determined by calculating their similarity. Since the conventional VMF has poor performance when filtering image edges, a weighting method based on pixels' location information is proposed. In this method, different weights are assigned to the pixels in the filter window according to their distributed groups which is classified based on image edge detection. Filtered images and objective measures demonstrate that the proposed method achieves more effective results in comparison with the conventional methods. The output images show that the proposed method has improved the performance of VMF in both detail preservation and noise suppression.

Acknowledgments This work was supported by the National High Technology Research and Development Program of China under Grant no. 2012AA012705 and International Science & Technology Cooperation Program of China under Grant no. 2012DFB10170. References [1] R.H. Chan, Chung-Wa Ho, M. Nikolova, Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization, IEEE Trans. Image Process. 14 (10) (2005) 1479–1485. [2] B. Smolka, Adaptive truncated vector median filter, in: Proceedings of the IEEE International Conference on Computer Science and Automation Engineering (CSAE), vol. 4, 2011, pp. 261–266. [3] X. Zhang, Y. Zhan, M. Ding, W. Hou, Z. Yin, Decision-based non-local means filter for removing impulse noise from digital images, Signal Process. 93 (2) (2013) 517–524. [4] S. Akkoul, Ledee Roger, R. Leconge, R. Harba, A new adaptive switching median filter, IEEE Signal Process. Lett. 17 (6) (2010) 587–590. [5] Yiqiu Dong, Shufang Xu, A new directional weighted median filter for removal of random-valued impulse noise, IEEE Signal Process. Lett. 14 (3) (2007) 193–196. [6] K.N. Plataniotis, A.N. Venetsanopoulos, Color Image Processing and Applications, Springer-Verlag, Berlin, Germany, 2000. [7] S. Morillas, V. Gregori, A. Sapena, Adaptive marginal median filter for colour images, Sensors 11 (3) (2011) 3205–3213. [8] J. Astola, P. Haavisto, Y. Neuvo, Vector median filters, Process. IEEE 78 (4) (1990) 678–689. [9] P.E. Trahanias, D.G. Karakos, A.N. Venetsanopoulos, Directional processing of color images: theory and experimental results, IEEE Trans. Image Process. 5 (6) (1996) 868–880. [10] D.G. Karakos, P.E. Trahanias, Generalized multichannel imagefiltering structures, IEEE Trans. Image Process. 6 (7) (1997) 1038–1045. [11] Lianghai Jin, Dehua Li, An efficient color-impulse detector and its application to color images, IEEE Signal Process. Lett. 14 (6) (2007) 397–400. [12] Zhonghua Ma, Hong Ren Wu, Dagan Feng, Partition-based vector filtering technique for suppression of noise in digital color images, IEEE Trans. Image Process. 15 (8) (2006) 2324–2342. [13] R. Lukac, Adaptive vector median filtering, Pattern Recognit. Lett. 24 (12) (2003) 1889–1899. [14] G. Wang, D. Li, W. Pan, Z. Zang, Modified switching median filter for impulse noise removal, Signal Process. 90 (12) (2010) 3213–3218. [15] X. Geng, X. Hu, J. Xiao, Quaternion switching filter for impulse noise reduction in color image, Signal Process. 92 (1) (2012) 150–162. [16] Fei He, Qingsong Bao, Dongchu Jiang, Detail-perservation adaptive vector median filter, in: Proceedings of the International Conference on Computer Science and Network Technology (ICCSNT), 2011, pp. 2674–2677. [17] Yuzhong Shen, K.E. Barner, Fast adaptive optimization of weighted vector median filters, IEEE Trans. Signal Process. 54 (7) (2006) 2497–2510. [18] V. Novoselac, B. Zovko-Cihlar, Image noise reduction by vector median filter, in: Proceedings of ELMAR, 2012, pp. 57–62.

J. Xu et al. / Signal Processing 98 (2014) 359–369

[19] B. Smolka, Efficient modification of the central weighted vector median filter, Lect. Notes Comput. Sci. 2449 (2002) 166–173. [20] T. Viero, Kai Oistamo, Y. Neuvo, Three-dimensional median-related filters for color image sequence filtering, IEEE Trans. Circuits Syst. Video Technol. 4 (2) (1994) 129–142. [21] R. Lukac, Adaptive color image filtering based on center-weighted vector directional filters, Multidimens. Syst. Signal Process. 15 (2) (2004) 169–196.

369

[22] A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst. 64 (3) (1994) 395–399. [23] S. Morillas, V. Gregori, Robustifying vector median filter, Sensors 11 (8) (2011) 8115–8126. [24] B. Wang, S. Sheikh, Image quality assessment: from error visibility to structural similarity, IEEE Trans. Image Process. 13 (4) (2004) 600–612.