Trans. Tianjin Univ. 2014, 20: 060-065 DOI 10.1007/s12209-014-2124-y

Accepted date: 2013-04-23. *Supported by the National Natural Science Foundation of China (No. 60872065), Open Foundation of State Key Laboratory of Advanced Weld-

ing and Connection, Harbin Institute of Technology (AWPT-M04), and Priority Academic Program Development of Jiangsu Higher Education Institutions.

Wu Yiquan, born in 1963, male, Dr, Prof. Correspondence to Wu Yiquan, E-mail: nuaaimage@163.com.

Noise Reduction of Welding Defect Image Based on NSCT and Anisotropic Diffusion*

Wu Yiquan(吴一全)1,2，Wan Hong(万 红)1，Ye Zhilong(叶志龙)1，Gang Tie(刚 铁)2

(1. College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics,

Nanjing 210016, China;

2. State Key Laboratory of Advanced Welding and Connection, Harbin Institute of Technology, Harbin 150001, China)

© Tianjin University and Springer-Verlag Berlin Heidelberg 2014

Abstract：In order to reduce noise effectively in the welding defect image and preserve the minutiae information, a noise reduction method of welding defect image based on nonsubsampled contourlet transform (NSCT) and anisot-ropic diffusion is proposed. Firstly, an X-ray welding defect image is decomposed by NSCT. Then total variation (TV) model and Catte_PM model are used for the obtained low-pass component and band-pass components, respec-tively. Finally, the denoised image is synthesized by inverse NSCT. Experimental results show that, compared with the hybrid method of wavelet threshold shrinkage with TV diffusion, the method combining NSCT with P_Laplace diffu-sion, and the method combining contourlet with TV model and adaptive contrast diffusion, the proposed method has a great improvement in the aspects of subjective visual effect, peak signal-to-noise ratio (PSNR) and mean-square error(MSE). Noise is suppressed more effectively and the minutiae information is preserved better in the image. Keywords：welding defect detection; noise reduction; nonsubsampled contourlet transform; total variation model; Catte_PM model

Welding technology is widely applied to aerospace, petrochemical, machinery manufacturing, electronics industries, etc. However, welding defects such as cracks, slag, tungsten inclusion, lack of penetration and incom-plete fusion, may appear due to the influence of parame-ters setting, operation process, materials and some ran-dom factors in the course of welding. To ensure the qual-ity of welding products, effective detection of welding defects is necessary. The automatic welding defect detec-tion based on digital image processing technology can greatly improve the efficiency and accuracy of detection. Unavoidable noise introduced in the course of X-ray welding image formation and transmission includes Gaussian noise, little salt and pepper noise. It will lead to false detection of welding defects[1]. Therefore, the noise reduction of welding defect image is essential to preproc-essing of automatic detection.

At present, the noise reduction methods of welding defect image mainly include averaging filtering[2], mean filtering[3], median filtering and morphological filtering. Edge details of image are blurred while noise is removed

by these methods, which will inevitably cause false re-sults of subsequent defect detection. With the develop-ment of multi-scale transform, more effective noise re-duction methods based on wavelet transform [4-6], con-tourlet transform [7] and nonsubsampled contourlet trans-form(NSCT) [8] emerge successively, which have better performance in detail preservation. However, wavelet transform is not the sparsest representation for an image and lacks of directionality, which limits its application in two-dimensional image processing [9]. Although contour-let transform can capture the singular points of image better, Gibbs effect may be introduced [10]. With the ap-pearance of NSCT, the above problem can be solved per-fectly by iterative nonsubsampled filter banks. Though NSCT can remove noise more effectively, it loses some information of high-frequency components, which leads to blurred edge. On the other hand, noise reduction method based on anisotropic diffusion is widely con-cerned and it has advantage in detail preservation by us-ing adaptive selection of diffusion coefficients, which can make up for the shortage of multi-scale transform [11].

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Thus combining multi-scale transform with anisotropic diffusion is expected to achieve better noise reduction performance. It is proved by the hybrid method of wave-let threshold shrinkage with TV diffusion (denoted as WSTV) [12]. However, threshold shrinkage used for high-frequency components is likely to lead to the loss of some image minutiae. Similarly, the method combining NSCT with P_Laplace diffusion (denoted as NSPL) re-moves noise insufficiently, since there is no processing for high-frequency components [13]. The method combin-ing contourlet with TV and adaptive contrast diffusion (denoted as CPMTV) improves the noise reduction per-formance by using TV diffusion and PM diffusion for low-pass component and band-pass components, respec-tively[14]. But PM diffusion is likely to lead to staircase effect and is unsuitable for the environment of intense noise.

In view of the above-mentioned analysis, a noise re-duction method of welding defect image based on NSCT and anisotropic diffusion is proposed. Firstly, an X-ray welding defect image is decomposed by NSCT. Then the low-pass component with the main information of image and little noise is processed by TV model, which can re-move noise and remain the minutiae. Band-pass compo-nents with most noise and detail information are proc-essed by Catte_PM diffusion model which is an im-provement of PM diffusion model. Finally, the denoised image is synthesized by inverse NSCT. In order to evalu-ate the performance of noise reduction, experimental re-sults are given. Comparisons are made with methods of WSTV[12], NSPL[13] and CPMTV[14] according to subjec-tive visual effect, peak signal-to-noise ratio (PSNR) and mean-square error (MSE).

1 Noise reduction method of welding defect images

1.1 NSCT As same as contourlet transform, NSCT has the

characteristics of multi-scale and multi-direction. Besides, it is shift-invariant and can effectively eliminate Gibbs effect [15].

There are two steps in the NSCT of an image. (1) An image is decomposed into a low-pass component and a band-pass component by a single-layer nonsubsampled pyramid filter. The obtained low-pass component is fur-ther decomposed by nonsubsampled pyramid filter to get

the low-pass component and band-pass components of the next level. The process is repeated. (2) Every band-pass component is decomposed by nonsubsampled direc-tional filter banks. The whole two-dimensional frequency domain is divided into J (the number of decomposition directions) wedge-shaped sub-bands and the singular points of the same direction are synthesized into one co-efficient.

Fig. 1 shows the schematic diagram of NSCT.

（a）Block diagram

（b）Ideal frequency partition

Fig. 1 Schematic diagram of NSCT

1.2 TV model In TV model, the total variation of image is used to

measure the optimal scale, and the nonlinear diffusion operator is obtained by minimizing the total variation in certain conditions [16].

Two constraints of the differential equations are given as

2 2

0 0( )d d 0, d dx y x y

I I I I (1)

where is the image region; 2 is noise variance; 0I is the value of noisy welding defect image I when 0t ; and t is diffusion time. Noise reduction problem aims at obtaining the processed images by solving the condi-tional extremum of Eq. (1) under the condition of noise statistics.

The image energy function of TV model is defined as

2

0( ) d d d d2

E x y R x y

I I I I (2)

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where ( )E I is the energy of I ; is gradient operator; and is the Lagrange constant which defines the weight of the latter item in the right side of Eq. (2) and deter-mines the relative strength of two constraints; R is degra-dation operator; and d dx y

I is the total variation of

I . The second integral is the fidelity term, which ex-presses the approximation to the original noisy image.

The Euler-Lagrange equation of ( )E I under the

boundary condition of 0n

I

at the outside normal di-

rection is

0div ( ) 0R R R

II I

I (3)

where R is the conjugate adjoint operator of R ; and div is divergence operator. Considering

divt

III

(4)

Eq. (4) is the diffusion model of TV stream. TV stream is a kind of stable diffusion function between for-ward and backward diffusion. By solving Eq. (4) to get the global optimal solution, the best effect of diffusion can be achieved. 1.3 Catte_PM model

Considering Gaussian noise introduced in the form-ing process of welding image, an improved PM model called Catte_PM model with Gaussian smoothing func-tion is adopted. It can control the diffusion process ac-cording to the gradient norm after Gaussian smoothing instead of the original gradient norm [17]. Catte_PM model can be expressed as

0 0

div [ ( ( ) ) ]

t

c Gt

II I

I I (5)

where “*” is convolution; G x is the Gaussian sm-oothing function with zero mean and standard variance ,

1 2 2( ) exp( 4 )G x C x , C is a constant. The form of diffusion equation is selected according to the relation between gradient value and diffusion coefficient.

2

1( ( ) )

1 ( ( ) / )c G

G k

II

(6)

where k is diffusion threshold and

( )G I can be seen as the edge detector. If ( )G I is much larger than k , ( ( ) )c G I is close to 0 and the diffusion is suppressed; on the contrary, the diffusion is strengthened.

Assuming that at time t , the value of ( ( ) )c G I is t

p and tq at point p and point q , respectively, then

the discrete expression of Catte_PM model is 1

,( )p

t t t t tp p p q p q

q

t

I I I (7)

where tpI and 1t

pI are the discrete samples of image at

time t and 1t , respectively; is a constant which con-trols the diffusion strength; and p is the neighborhood of the pixel p . The value of gradient norm is ,

tp q I

t tp qI I .

1.4 Algorithmic steps of noise reduction for weld-ing defect images

On the basis of the analysis on NSCT, TV model and Catte_PM model, and considering the noise charac-teristics of welding defect images, a noise reduction method of welding defect images is proposed. The spe-cific steps are as follows.

Step 1 A welding defect image is decomposed by NSCT.

An X-ray welding defect image is decomposed by single-layer nonsubsampled pyramid filter to obtain a low-pass component and a band-pass component. The nonsubsampled pyramid filter is selected to be “maxflat”. The band-pass component is processed by two-layer non-subsampled directional filter, which is selected as “dmax-flat7” to get four band-pass directional components. Each component has the same size as the original image.

Step 2 Low-pass component is processed by TV dif-fusion model.

Since the low-pass component contains most infor-mation and little noise of the image, TV diffusion model is used, which can remove noise and preserve the minu-tiae. Meanwhile, diffusion equation in Eq. (4) can be rewritten as

1

t

I II I

I I I (8)

where ( , )x y I I I , xx yy I I I , 2 2x y I I I .

The step sizes of time and space in TV diffusion model are 0.2 and 1, respectively. The diffusion filter ends till iterative MSE is smaller than 0.01.

Step 3 The noise reduction of band-pass compo-nents is achieved by Catte_PM diffusion model.

The band-pass components contain most noise and minutiae information of the image. Catte_PM model is applied to process band-pass components, and the de-noised components can be obtained by the diffusion equation in Eq. (6). The value of k is calculated by [18]

1

( )0.674 5 I Ik m m I I (9)

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where Im is the median operator. The diffusion step size is 1/7 and the number of iteration is 30.

Step 4 The welding defect image is synthesized by inverse NSCT.

Finally, inverse NSCT is applied to reconstruct the

denoised welding defect image by synthesizing the re-sults of Step 2 and Step 3.

The flowchart of the proposed noise reduction method of welding defect image based on NSCT, TV model and Catte_PM model is shown in Fig. 2

Fig. 2 Flowchart of the proposed method

2 Experimental results and analysis

A large number of experiments on different welding defect images were done by the proposed method. In or-der to evaluate the noise reduction performance, some comparisons were made by the related methods proposed recently such as WSTV, NSPL and CPMTV. Evaluation criteria of the noise reduction performance include the subjective visual effect, PSNR and MSE. The experi-ments were carried out in the following environment: Intel(R) Core(TM) 2, 1.80 GHz, 3 GB memory, Matlab R2007b. The parameters of the above-mentioned meth-ods are set as follows. In WSTV, the image is decom-posed by single-layer Haar wavelet transform. The ob-tained high-frequency components are processed by threshold shrinkage with threshold 22 logT N , where N represents the number of image pixels and is the noise standard variance. Generally, /0.674 5q , where q is the median of wavelet coefficients. Mean-while, the obtained low-frequency component is diffused

by TV model. The step sizes of time and space are 0.2 and 1, respectively. The diffusion filter ends as iterative MSE is smaller than 0.5. In NSPL, after NSCT, the low-pass component is diffused by P_Laplace model with iteration step size 0.1 and band-pass components remain unchanged. As for CPMTV, the image is decomposed by contourlet transform. The low-frequency component and high-frequency components are processed by TV diffu-sion model and adaptive contrast diffusion, respectively. The parameters of TV diffusion model are identical to WSTV, while the step size of adaptive contrast diffusion is 1/7 and iteration number is 30.

X-ray welding images usually are polluted by Gaus-sian noise and little salt and pepper noise. Here two im-ages of different welding defects are taken as examples. Noise reduction results of a slag defect image are given in Fig. 3. The noisy image is shown in Fig. 3(a). Mean-while, the denoised images obtained by WSTV [12], NSPL[13], CPMTV [14] and the proposed method can be seen from Fig. 3(b) to Fig. 3(e). Noise reduction results of a tungsten inclusion defect image are given in Fig. 4.

（a）Noisy image （b）WSTV （c）NSPL （d）CPMTV （e）The proposed method

Fig. 3 Noise reduction of slag defect image

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（a）Noisy image （b）WSTV （c）NSPL （d）CPMTV （e）The proposed method

Fig. 4 Noise reduction of tungsten inclusion defect image

From Fig. 3 and Fig. 4, it can be seen that the image obtained by the proposed method is clearer than other images. Minutiae information of the image is preserved more completely while noise is removed. The image ob-tained by NSPL still contains a lot of noise since the band-pass components are not processed. As for CPMTV, some noise in low-frequency component is residual be-cause PM diffusion model cannot remove Gaussian noise well. And some detail information is lost through WSTV while noise is smoothed.

In order to evaluate the noise reduction performance objectively, one noise-free X-ray slag defect image is chosen as the original image. Three groups of welding slag defect images with different Gaussian white noise and the same salt and pepper noise are considered as ex-amples in the experiments. The mean is 0 and variances are 0.005, 0.010 and 0.015, respectively. The PSNR and MSE of images processed by the above-mentioned meth-ods are listed in Tab. 1. PSNR and MSE can be calcu-lated by

1 2

21 2

2

1 1

255PSNR 10 lg

[ ( , ) ( , )]M M

i j

M M

i j i j

I I

(10)

1 2

2

1 11 2

1MSE [ ( , ) ( , )]

M M

i j

i j i jM M

I I (11)

where ( , )i jI and ( , )i jI are the denoised image and the original image, respectively; and 1 2M M is the size of image.

Tab. 1 Comparison of the performances of four methods Noise variance 2

PSNR/dB MSE Noise reduction

method 0.005 0.010 0.015 0.005 0.010 0.015

Noisy image 10.12 07.39 05.79 360 680 990

WSTV 18.97 15.90 13.90 045 088 140

NSPL 17.89 14.64 12.68 058 120 180

CPMTV 18.81 15.72 13.71 047 092 140

The proposed

method 19.51 16.31 14.24 040 079 130

PSNR and MSE can reflect the practical effect of noise suppression. The larger value of PSNR and the smaller value of MSE indicate that the noise reduction performance is better.

From Tab. 1, it is shown that the PSNR of image processed by the proposed method is the largest and MSE is the smallest among all the four methods. The PSNR of image obtained by the proposed method increases by 0.7 dB compared with CPMTV, which means that Catte_PM diffusion model can remove Gaussian noise better than PM diffusion model. Compared with NSPL, the PSNR can increase by at least 1.58 dB. Besides, the smallest MSE indicates that the noise reduction performance of the proposed method is superior to other three methods.

Lots of experimental results show that the proposed method has the best noise reduction performance for dif-ferent welding defect images in terms of both subjective visual quality and objective evaluation criteria. The pro-posed method can capture the directional information more accurately, remove the noise more effectively and preserve the minutiae information better.

3 Conclusions

(1) A noise reduction method of welding defect im-age based on NSCT, TV diffusion model and Catte_PM diffusion model is proposed. TV diffusion and Catte_PM diffusion model are used for the low-pass component and band-pass components obtained by NSCT, respectively. Then inverse NSCT is applied to synthesize the de-noised welding defect image.

(2) A large number of experiments for different welding defect images are done by using the proposed method. Comparisons are made with the related methods proposed recently, such as WSTV, NSPL and CPMTV. Experimental results show that the proposed method can achieve better noise reduction performance in terms of subjective visual quality and objective evaluation criteria such as PSNR and MSE. The Stronger the capability of

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noise reduction is, the better the minutiae information of the welding defect image is preserved.

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(Editor: Zhao Yang)