chapter 2 hybrid median filter in despeckling of...

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CHAPTER 2

HYBRID MEDIAN FILTER IN DESPECKLING OF ULTRASOUND

IMAGES

Spatial domain filtering is one of the most widely used techniques in

image processing for image enhancement, and it operates on the pixels

directly. The spatial domain filters convolve a mask with the image, and these

filters can be categorized as linear and nonlinear filters. The main drawbacks

of these filters are that, they remove lines, round off corners and blur edges.

These are the inevitable features for applications such as medical imaging and

remote sensing. To overcome these drawbacks, a corner preserving median

filter also called as Hybrid Median Filter (HMF) was proposed (Davies 2006)

in general image processing applications.

In this chapter two speckle reduction schemes are proposed based

on HMF. The first approach is a Modified HMF (MHMF) and the second

approach is Adaptive Window HMF (AWHMF).

2.1 HYBRID MEDIAN FILTER

The HMF is a three-step ranking operation. In a 5x5 pixel

neighbourhood, pixels can be formed into two sub-neighbourhoods consisting

of 45o neighbours and 90o neighbours as shown in Figure 2.1. The pixels in

these two neighbourhoods are ranked separately and the median value from

each group is computed. The filter compares these two median values with

the centre pixel and calculates the median value. Finally the centre pixel is

replaced with the median value computed in the last step.

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(a) 5 5 neighbourhood (b) 45o neighbours (c) 90o neighbours

Figure 2.1 Neighbourhood pixels used in HMF

2.1.1 HMF Algorithm

The steps of the HMF are as follows:

Step1: A window of size 5x5 is selected and two sub- neighbourhoods

(45o neighbours), and (90o neighbours) are formed.

Step2: The pixels in the two sub - neighbourhoods are arranged in

ascending order and the median value of each group is computed.

Step3: The two median values obtained in step 2 and the centre pixel are

compared and the median of the three values is computed.

Step4: Finally the centre pixel is replaced by the median value computed in

step 3.

The computational complexity is less in the three step ranking

operation when compared to the median filter. In each step, the ranking

operations take place only for a smaller number of values than used in a

square region of the same size. The main advantage of this filter is that, it

does not eliminate lines and preserves edges better than the traditional mean

and median filters.

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In this work two approaches have been proposed to improve the

edge preservation capability of the filter and to make the HMF suitable for

ultrasound image denoising.

2.2 MODIFIED HYBRID MEDIAN FILTER

A Modified Hybrid Median Filter (MHMF) is developed for speckle

reduction and edge preservation of ultrasound images. It works on the sub-

windows similar to HMF. The window size used for the proposed filter is

5x5. The pixels in 45o neighbours and 90o neighbours are represented by

and respectively. To preserve the diagonal edges, the maximum value of

the pixels in sub-neighbourhood is taken, instead of median as in HMF

and is illustrated in Figure 2.2.

The MHMF is implemented as follows:

Let W be a square filter window, and the

pixels in this window are divided into four sub-windows consisting of the

pixels in horizontal ( , vertical and diagonal ( and

directions, and are given by Equation (2.1) to Equation (2.4).

(2.1)

(2.2)

(2.3)

(2.4)

The window is a combination of the two sub-

windows , and the centre pixel and is given in Equation (2.5).

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Similarly the two sub-windows and the centre pixel are combined to

represent the pixels in as in Equation (2.6).

(2.5)

(2.6)

The output of the MHMF is represented using Equation (2.7).

(2.7)

Figure 2.2 Modified Hybrid Median Filter

"+" sub-neighbourhood

Maximum value from sub-neighbourhood

First stage Ranking

Original pixel

Original pixel and Neighbours

"x" sub-neighbourhood

Second stage Ranking

Median value from sub-neighbourhood

New pixel value

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2.2.1 MHMF Algorithm

The steps followed in the MHMF algorithm are given below:

Step1: A window of size 5x5 is selected and two sub - neighbourhoods

and are formed.

Step 2: The pixels in the sub-neighbourhoods and are arranged in

ascending order.

Step 3: Median value of the pixels in and maximum value of the pixels

in are computed.

Step 4: The values obtained from step 3 and the centre pixel are arranged in

ascending order and the median value is obtained.

Step 5: Finally the filter replaces the centre pixel with the median value

obtained in step 4.

2.3 ADAPTIVE WINDOW HYBRID MEDIAN FILTER

The major limitation of the spatial domain speckle reduction filters

is that, they are sensitive to the shape and size of the window (Loizou &

Pattichis, 2008). If a larger window size is used, the filter will be more

effective at reducing noise but will also blur edges; whereas a smaller sized

window decreases the noise reduction ability, thus making the filter

inefficient.

In this work the window size of the hybrid median filter is made

adaptive for effective speckle reduction and edge preservation.

In the proposed adaptive window hybrid median filter, the size of

the window used for filtering the noisy image is selected based on the image

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region. Since the correlation among the pixels is high in the homogeneous

regions, a window of size 5x5 is used, and as the non homogeneous regions

have less number of correlated pixels in its neighbourhood a smaller window

of size 3x3 is used in these areas. To distinguish smooth and edge regions,

edge detection operators are used. In the literature, many edge detection

operators are proposed such as Prewitt, Roberts, Sobel and Canny (Canny

1986, Maini & Aggarwal 2009). The Sobel operator is used in the proposed

algorithm, since it is less sensitive to isolated high intensity point variations. It

also gives an estimate of edge direction as well as edge magnitude at a point

which is more informative. The hardware implementation of this operator is

also relatively easier. The edge detected image is obtained by thresholding the

gradient image computed using Sobel masks. As the edges are treated

separately the edge preservation ability of the proposed algorithm is good.

The algorithm for AWHMF is given below:

2.3.1 AWHMF Algorithm

Step1: The Sobel operator is applied on the noisy image.

Step2: The edge image is obtained by thresholding the gradient image

computed using Sobel masks. The pixels belonging to smooth and

operation is shown in Figure 2.3.

Step 3: Adaptive window hybrid median filter is applied on the noisy

image. The size of the window is varied with the following

concepts.

(i) If the pixel to be processed is identified as an edge pixel then

the size of the window is 3x3.

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(ii) Else if the pixel belongs to smooth region, the size of the

window is 5x5.

Step 4: All the filtered pixels p1 and q1corresponding to p and q are

combined to obtain the denoised image as shown Figure 2.4.

Figure 2.3 Edge image extraction using Sobel operator

Figure 2.4 Filtering operation of AWHMF

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2.4 SIMULATION RESULTS AND DISCUSSIONS

The simulation is carried out in MATLAB environment to assess the

performance of the proposed filters MHMF and AWHMF. For quantitative

MATLAB. The variance ( n2) of the speckle noise is varied from 0.02 to

0.07. In this work the performance of the proposed method is compared

against the performance of the existing algorithms like median (Nixon &

Aguado 2002), Lee (Lee 1980), Kuan (Kuan et al 1985), Frost (Frost et al

1982), HMF (Davies 2006) and NCD (Abd-Elmoniem et al 2002) for

different noise variances.

The Peak Signal to Noise Ratio (PSNR), Root Mean Squared Error

(RMSE), Edge Preservation Index (EPI), Correlation Coefficient (CoC),

Feature Similarity (FSIM) Index and Execution Time (ET) are used as

performance measures.

Test Image 1: The performance of the proposed algorithm is tested using

synthetic image (Test image1) of size 128 x 128, which consists of regions

with uniform intensity and sharp edges, and is compared against the existing

denoising algorithms for the speckle noise of variance ranging from 0.02 to

0.07.

The PSNR values of various algorithms are listed in Table 2.1. The

largest PSNR value for a particular variance of speckle noise is highlighted to

show the best performance. From this table, it can be observed that for the

lowest noise variance of 0.02 the performance of MHMF is better than the

standard speckle reduction filters Lee, Kuan, Frost and the median. The

AWHMF algorithm gives 1dB PSNR better than the existing algorithms for

speckle noise of variance ranging from 0.02 to 0.05 and above 0.05 it

performs more or less similar to the existing filters.

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Table 2.1 PSNR values obtained for Test Image 1

Peak Signal to Noise Ratio (PSNR) in dB

Filters Noise variance

0.02 0.03 0.04 0.05 0.06 0.07

Speckled image 28.93 27.21 25.97 25.09 24.20 23.51

Median(3x3) 29.90 29.28 28.61 28.16 27.51 27.18

Median(5x5) 27.97 27.43 27.18 26.82 26.42 26.01

HMF(3x3) 31.44 29.70 28.62 27.50 26.96 26.21

HMF(5x5) 31.17 29.84 28.79 28.17 27.54 27.02

Lee 29.86 29.51 29.13 28.85 28.73 28.30

Kuan 29.90 29.47 29.10 28.87 28.69 28.35

Frost 30.62 29.77 29.04 28.69 28.10 27.52

NCD 31.98 29.51 27.63 26.43 25.51 24.65

MHMF 30.85 29.11 27.96 26.97 26.50 26.13

AWHMF 32.59 31.05 30.09 29.07 28.42 27.73

The proposed algorithms are also tested with the Root Mean Square

Error (RMSE), which is the square root of the squared error averaged over the

M x N (size of the image) array. The RMSE values of the MHMF, AWHMF

and existing algorithms for synthetic image are given in Table 2.2. The

smallest (best) RMSE value for a particular noise variance of speckle noise is

highlighted for analysis purpose. From the table it is evident that the RMSE

value of AWHMF is smaller for noise variance from 0.02-0.05 and above

0.05 the performance of standard speckle filters Lee and Kuan is better when

compared to the other filters.

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Table 2.2 RMSE values obtained for Test Image 1

Root Mean Square Error (RMSE)


0.02 0.03 0.04 0.05 0.06 0.07 Speckled image 0.0506 0.0617 0.0711 0.0787 0.0872 0.0944 Median(3x3) 0.0452 0.0486 0.0525 0.0553 0.0596 0.0619 Median(5x5) 0.0575 0.0594 0.0634 0.0650 0.0672 0.0742 HMF(3x3) 0.0379 0.0463 0.0524 0.0597 0.0635 0.0692 HMF(5x5) 0.0391 0.0455 0.0514 0.0552 0.0594 0.0630 Lee 0.0455 0.0473 0.0495 0.0511 0.0518 0.0544 Kuan 0.0453 0.0475 0.0496 0.0509 0.0520 0.0541 Frost 0.0416 0.0459 0.0499 0.0520 0.0556 0.0581 NCD 0.0356 0.0473 0.0587 0.0675 0.0750 0.0828 MHMF 0.0406 0.0496 0.0569 0.0631 0.0663 0.0721 AWHMF 0.0332 0.0396 0.0443 0.0498 0.0537 0.0571

Table 2.3 EPI values obtained for Test image 1

Edge Preservation Index (EPI) Filters Noise variance


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Table 2.4 CoC values obtained for Test Image 1

Correlation Coefficient(CoC)



Table2.5 FSIM values obtained for Test Image 1

Feature Similarity (FSIM) Index



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Edge Preservation Index (EPI) is used to test the edge preservation

ability of the filters. The highest value of EPI indicates that the filter is good

in preserving edges. The EPI values of various speckle reduction filters for

different noise variances are listed in Table2.3. From the Table, it is clear that

the MHMF preserves edges better than the standard speckle filters (Lee, Kuan

and Frost) and NCD. The proposed AWHMF outperforms the other

algorithms in terms of EPI.

The Correlation Coefficient (CoC) is a quantitative measure, which

provides the correlation between the original image and the denoised image.

The CoC of various filters is given in Table 2.4. The value of CoC is higher,

if both the images are perfectly identical. From the table it can be observed

that the AWHMF performed better than the existing filters up to noise

variance of 0.05. At higher noise variance the performance of Lee and Kuan

was found to be good. The FSIM values in Table 2.5 show that the AWHMF

is able to preserve the features only at lower noise levels and at higher noise

levels the Frost filter performs well.

For subjective evaluation, the output images of different spatial

domain filters for noise variance of 0.02 are shown in Figure 2.5. From the

figures it is evident that the proposed filters are able to preserve edges and

fine details.

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`

Figure 2.5 Original, noisy and denoised images for Test Image 1

Test Image 3 and Test Image 4: The performance of the proposed algorithm

MHMF and AWHMF is tested using Brain images (Coronal View - Test

Image 3 and Sagittal View - Test Image 4).

The plot of PSNR values of the proposed and the existing denoising

algorithms against different noise variances for Test image 3 is given in

Figure 2.6. From this plot, it is inferred that the proposed AWHMF algorithm

performs better than the other denoising algorithms. Table 2.6lists the RMSE

values of different algorithms and the lower values of RMSE obtained by

AWHMF indicates that the error is less in the despeckled image.

(c) Median (3x3) (d)Median (5x5)

(e) HMF (3x3) (f) HMF (5x5) (g) Lee filter (h)Kuan filter

(a)Test Image 1 (b)Noisy-0.02

(i) Frost filter (k) MHMF (l) AWHMF (j)NCD

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Figure 2.6 Plot of PSNR values for Test Image 3


Root Mean Square Error (RMSE)



0.02 0.03 0.04 0.05 0.06 0.075

10

15

20

25

30

35

40

Noise Variance

HMF(3x3)LeeFrostNCDMHMFAWHMF

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Table 2.7 EPI values obtained for Test Image 3

Edge Preservation Index (EPI)



Figure 2.7 Plot of CoC values for Test Image 3

0.02 0.03 0.04 0.05 0.06 0.070.8

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

Noise Variance

HMF(3x3)LeeFrostNCDMHMFAWHMF

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Table 2.8 FSIM values obtained for Test Image 3

Feature Similarity Index (FSIM) Filters Noise variance


The EPI values for Test Image 3 at different noise levels are

presented in Table 2.7. The highlighted values indicate that the proposed filter

AWHMF is good in preserving edges. From the plot of CoC in Figure 2.7, it

can be observed that the performance of AWHMF is better than the other

filters. In Table 2.8, the higher values of FSIM indicate that the AWHMF is

able to preserve features effectively at lower noise levels.

For subjective evaluation, the output images of different spatial

domain filters are shown in Figure 2.8. From the figure, it is observed that the

AWHMF improves the quality of the image.

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Figure 2.8 Original, noisy and despeckled images for Test Image 3

Table 2.9 shows the PSNR values obtained for the Test image 4 and is observed that the AWHMF gives better PSNR values under different noise conditions. For higher noise variance (0.07), the MHMF yields better performance in terms of PSNR values.

The RMSE values of different filters obtained for Test Image 4 are shown in Table2.10. From the table, it is observed that the filters AWHMF and MHMF give better performance as compared to others.

The EPI values of different filters are listed in Table 2.11. For low and moderate noise levels the proposed filter AWHMF exhibits high performance and when the noise level is high, the standard filters Lee and Kuan perform well.

(c) Median (3x3) (d) Median (5x5)

(e) HMF (3x3) (g) Lee filter (h) Kuan filter (f) HMF (5x5)

(l)AWHMF (i) Frostfilter

(b)Noisy -0.02 (a)Test image 3

(k) MHMF (j)NCD

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Table 2.9 PSNR values obtained for Test Image 4

Peak Signal to Noise Ratio (PSNR) in dB Filters Noise variance



Root Mean Square Error (RMSE) Filters Noise variance


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Table 2.11 EPI values obtained for Test Image 4

Edge Preservation Index (EPI) Filters Noise variance


Table 2.12 CoC values obtained for Test image 4

Correlation Coefficient (CoC) Filters Noise variance

0.02 0.03 0.04 0.05 0.06 0.07

Speckled image 0.9352 0.9071 0.8805 0.8599 0.8366 0.8089

Median(3x3) 0.9703 0.9609 0.9494 0.9384 0.9305 0.9178

Median(5x5) 0.9484 0.9423 0.9321 0.9267 0.9188 0.9096

HMF(3x3) 0.9642 0.9480 0.9337 0.9204 0.9057 0.8907

HMF(5x5) 0.9666 0.9558 0.9438 0.9339 0.9213 0.9130

Lee 0.9221 0.9194 0.9127 0.9074 0.9047 0.8983

Kuan 0.9227 0.9204 0.9140 0.9110 0.9023 0.9004

Frost 0.9741 0.9633 0.9535 0.9441 0.9347 0.9258

NCD 0.9541 0.9285 0.9033 0.8805 0.8588 0.8338 MHMF 0.9724 0.9612 0.9511 0.9428 0.9340 0.9255

AWHMF 0.9940 0.9921 0.9888 0.9840 0.9831 0.9792

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Figure 2.9 Plot of FSIM for Test Image 4

Table 2.12 lists the CoC values of different speckle reduction

filters. The CoC values of AWHMF indicate that its performance is better

than the other filters.

The performance of the proposed filters and some high performing

filters in terms FSIM is illustrated in Figure 2.9. From the figure it is obvious

that the proposed filter AWHMF gives better performance than the other

filters.

The despeckled images of different spatial domain filters are given

in Figure 2.10, and it is clear from the figure that the image quality is

improved by the AWHMF when compared to other filters.

0.02 0.03 0.04 0.05 0.06 0.070.975

0.98

0.985

0.99

0.995

1

Noise Variance

Median(3x3)HMF(3x3)LeeFrostMHMFAWHMF

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Figure 2.10 Original, noisy and despeckled images for Test Image 4

Ultrasound Images: The proposed methods are tested with ultrasound

imagesof Liver, Breast and Gall bladder. The original and despeckled images

obtained using some high performing filters are illustrated in figures from

Figure 2.11 to Figure 2.13. Speckle Suppression Index (SSI) is used to

measure the quality of the resultant images.

(a)Test image 4

(h) AWHMF

(b)Noisy -0.02 (c)Median (3x3)

(e)HMF (3x3) (g) MHMF (f) NCD

(d) Lee Filter

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.

Figure 2.11 Original and despeckled images of ultrasound image of Liver

(b)Frost (c) NCD

(d) MHMF (e) AWHMF

(a) Original image - Liver

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Figure 2.12 Original and despeckled images of ultrasound image of Breast

(c) NCD (b) Frost

(d) MHMF (e) AWHMF

(a)Original image - Breast

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Figure 2.13 Original and despeckled images of ultrasound image of Gall bladder

(d) MHMF

(a) Original Image

(b) Frost (c) NCD

(e) AWHMF

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Figure 2.14 shows the plot of SSI values obtained for ultrasound

images of Liver, Breast and Gall bladder. From the figure, it is observed that

the SSI values of AWHMF are less when compared to the other filters such as

Frost, NCD and MHMF and indicates that the AWHMF suppresses speckle

noise effectively.

Figure 2.14 Plot of SSI for ultrasound images

Execution Time: The execution time taken by a filter is an important

measure to find its computational complexity, and depends on the computing

-period. In addition to the clock-period, it also depends on

the memory-size, the input data size, and the memory access time, etc. The

proposed algorithm has been implemented in MATLAB 7.12.0 environment

with Intel core i3@ 2.40 GHz processor with 2GB RAM. The execution time

of the proposed and the existing spatial domain speckle reduction algorithms

for different test images with speckle noise of variance 0.04 is illustrated in

Table 2.13. From the table, it is evident that the execution time of MHMF is

less than the standard filters for speckle reduction and higher than the

traditional median filter.

0.95

0.96

0.97

0.98

0.99

1

Fros

t

NCD

MH

MF

AW

HM

F

Fros

t

NCD

MH

MF

AW

HM

F

Fros

t

NCD

MH

MF

AW

HM

F

Liver Breast Gall Bladder

SSI

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Table 2.13 Execution Time

Execution Time in Seconds

Method Test image1

( 128 x 128)

Test image3

(128x128)

Test image4

(128x128)

Median(3x3) 0.366 0.379 0.378

Median(5x5) 0.382 0.399 0.379

HMF(3x3) 0.886 0.882 0.881

HMF(5x5) 0.917 0.916 0.926

Lee(3x3) 1.531 1.544 1.526

Kuan(3x3) 1.524 1.524 1.545

Frost(3x3) 0.875 0.896 0.882

NCD 0.635 0.624 0.623

MHMF (5x5) 0.689 0.691 0.684

AWHMF 0.991 0.994 0.993

2.5 CONCLUSION

In this chapter two spatial domain filters MHMF and AWHMF are

proposed for speckle reduction in ultrasound images. The experimental results

reveal that the AWHMF gives better performance for different levels of

speckle noise. PSNR values are higher (1dB) for low noise levels and under

such noise conditions the filters have smaller RMSE values. AWHMF also

gives superior performance in terms of EPI and which can be observed from

the tables. From the FSIM and CoC values obtained, it is clear that the

proposed filter AWHMF is good in feature preservation when compared to

the other spatial filters. It is also observed from the tables that the other

proposed filter MHMF shows only moderate performance in terms of PSNR,

RMSE and EPI. But its execution time is minimal as compared to the standard

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filters. The performance of AWHMF is good at lower levels of speckle noise

(0.02 to 0.05). The time taken to execute AWHMF is slightly higher than the

HMF and Frost filters and less than the standard filters namely Lee and Kuan.

The proposed filters efficiency is tested for the ultrasound images

collected from hospitals and taken from repository. The effectiveness of the

filters is proved with the computation of SSI, which is less in case of

AWHMF. Based on the above data and the related discussions, it may be

concluded that AWHMF works well when the speckle noise variance is low

and also preserves the edges and minute details effectively. When the noise

variance increases, it merges with the high frequency information of the

image content and hence it is difficult for AWHMF to perform better at

higher noise levels.

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