- Email: [email protected]
Development of image fusion methodology using discrete wavelet transform for eddy current images
NDT&E International 51 (2012) 51–57
Contents lists available at SciVerse ScienceDirect
NDT&E International journal homepage: www.elsevier.com/locate/ndteint
Development of image fusion methodology using discrete wavelet transform for eddy current images Sasi Balakrishnan a, Matteo Cacciola b,n, Lalita Udpa c, Bhagi Purnachandra Rao a, Tammana Jayakumar a, Baldev Raj a a
Non-Destructive Evaluation Division, Indira Gandhi Centre for Atomic Research, Kalpakkam, TN, India University Mediterranea of Reggio Calabria, DIMET, Via Graziella Feo di Vito, I-89100 Reggio Calabria, Italy c Michigan State University, Nondestructive Evaluation Laboratory, 2214C Engineering Bldg E, Lansing, MI 48824, USA b
a r t i c l e i n f o
abstract
Article history: Received 25 July 2011 Received in revised form 20 June 2012 Accepted 22 June 2012 Available online 4 July 2012
In this paper, a method based on the discrete wavelet transform is proposed for eddy current image fusion. This method mainly involves two steps: selection of the proper wavelet filters and level of decomposition using formulated parameter, and selection of the proper fusion criterion in wavelet subband. The main aspect of the proposed method concentrates on elimination of noise while retaining defect information. This method fuses the eddy current images at two different frequencies from stainless steel cladding tube, in order to take the advantage of deep lying information effectively. The fusion results show that the selection of wavelet and fusion rule reduces the ambiguity and enhances the reliability of defect detection in both visual and qualitative evaluation. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Non-destructive testing Image fusion Wavelet analysis Information energy
1. Introduction Image fusion is a synergistic tool that serves to combine multiple-source imagery. It aims to integrate all complementary data from several images into a single image in order to enhance the apparent information in the images [1]. Fusion of images is often acquired from different instruments (or multi-sensors), or the same sensor with different measuring contexts. The recent advances in the field make it possible to implement across wide areas such as medical imaging, microscopic imaging, remote sensing, computer vision and robotics. Fusion technique includes different methodologies, starting from pixel level to feature level and symbol level. The pixel level implies algorithmic combination of vector of measurement from each images. Feature level requires post-processing of classification and segmentation of input images and fusion is based on those extracted features. This enables detection of useful feature with higher confidence. Symbol level allows information to be effectively combined at the highest level of abstraction [2]. In all the three methodologies, the knowledge of underlying physical process is required. In order to approach non-phenomenological way, that tends to ignore the physical process and attempt to fuse data regarding their statistical nature, the scientific literature presents various statistical
n
Corresponding author. E-mail address: [email protected] (M. Cacciola).
0963-8695/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ndteint.2012.06.006
techniques, like maximum amplitude signal, averaging, weighted average, Bayesian approach and Dempster–Shafer methods [3–6]. In the field of non-destructive evaluation (NDE), the main purpose is to provide information about the presence, the location and the size of potential defects on or into the inspected components [7]. Different inspection techniques and sensors are used for analyzing components in order to acquire complementary information about defects. Furthermore, for a proper exploitation of the data measured by the different sensors, or by the same sensor in different measuring contexts, it is mandatory to develop effective data fusion techniques able to take advantage of such multisensor characteristics. The definition of multi-sensor fusion is broad and the fusion can take place at pixel, feature and symbol level [8]. However, when these methods are applied, some undesired effects of contrast reduction can appear. Many fusion methods have been exploited in recent years. Some methods are based on component substitution, such as Intensity Hue Saturation (IHS) transform that distorts the spectral feature, and high pass filter (HPF) method and principle component analysis (PCA), which loose the physical features of source images [9]. Among different methods, the wavelet transform (WT) is efficiently applied to multi-sensor image fusion because of its properties such as multi-resolution analysis and accurate reconstruction [10–12]. The WT contains unique information at different resolutions that other traditional method cannot. But the selection of a particular wavelet filter and the choosing of different decomposition schemes affect the overall performance of image fusion. In
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S. Balakrishnan et al. / NDT&E International 51 (2012) 51–57
the field of NDE, fusion of images demands for the elimination of noise while retaining the information about defects. Hence, the selection of an appropriate wavelet filter and an optimum decomposition level are important for getting better results. Research on the subject of strategic combination of information while eliminating noise signals has been motivated by a desire to obtain more appropriate parameter for the selection of the wavelet filters and the level of decomposition. In this paper, we consider the case where eddy current images are obtained at two different frequencies from machined notches in stainless steel cladding tubes. For the selection of the proper wavelet filters and decomposition level, two factors have been formulated based on the removal of disturbing (noise) signal from periodic wall thickness variation and retaining defect information. In addition to the new parameters proposed for fusion, a fusing rule has been proposed in this work. This paper discusses
Fig. 1. Fusion of two images using DWT.
the experimental studies and the proposed two factors, the fusion rules and related experimental results.
2. Discrete wavelet transform fusion The fusion of two images within the wavelet domain is formally considered the discrete wavelet transform (DWT) of two registered input images and is combined with the definite fusion rule. Then the inverse DWT (IDWT) is computed and the fused image is reconstructed [13]. The process is shown in Fig. 1 and is defined as Iðx,yÞ ¼ W 1 ½jfWðI1 ðx,yÞÞ,WðI2 ðx,yÞÞg
ð1Þ
where I1, I2 are the two images to fuse, j is the fusion rule, and W and W 1 are the DWT and IDWT, respectively. Obviously, the procedure can be extended to multiple images, fusing the result coming from two images with the third image, and so on. For each one of the considered applications, the main user-related activity is based on the selection of proper wavelet filter and level of decomposition. In fact, case by case, these two parameters should be selected according to the framework, the available measurements and the aims and definite information that desired to be obtained. In general, the main aim is to emphasize the informative content of measures neglecting the noise impact. Also considering the problem we studied, our goal was to reduce the influence of noise, mainly lift-off noise in-lab measurements. In this regard, we proposed two kinds of factors for the selection of an appropriate wavelet filter, and we related to each factor a fusion rule. The details of the factors and the fusion rule are discussed below.
Fig. 2. Block diagram of the proposed fusion procedure.
S. Balakrishnan et al. / NDT&E International 51 (2012) 51–57
53
2.1. Energy risk factor Classically, the proposed risk factor related to WT, in the case of NDE, involves the energy of approximation coefficients and is mathematically designed as follows: Emin ¼ min Ea ðjÞ; j
j ¼ 1; 2, . . . ,L
ð2Þ
where Ea ðjÞ is the energy of approximation coefficient at the jth level of the step-by-step selected wavelet filters. The calculation of Emin is iterated for each decomposition level and for each desired wavelet filters. The wavelet energy represents the percentage of energy corresponding to the approximation and the detail coefficients. Minimum energy of the wavelet approximation coefficients (WAC) attributes the minimum amount of low frequency information retained after decomposition. Since we concentrate on the removal of noise, among the wavelets which shows the minimum energy of the approximation coefficients, (Emin) is considered as an optimum wavelet filter. 2.2. Weighted risk factor In the same way, our aim is retaining the useful information (defect) and removing the noise, i.e. lift-off signals. But in our proposal, we consider that useful components could be also present in lower frequencies mixed with the noise. Subsequently, the degree of usefulness assigned to information (defect) increases step by step while going from lowest towards the highest frequencies. Then, we should consider the maximized energy within the wavelet detail coefficients (WDCs) resulted among the wavelet filters. In fact, since the energy of WDCs of denoised image cannot be higher than the raw image, the energy stored within the WDCs of the denoised image must be as close as possible to the energy stored within the WDCs of the raw image. At the same time, we want to give more importance to WDCs in higher frequencies than in lower frequencies, but without avoiding the latter ones. For all these reasons, we formulated a weighted risk factor according to the following formulation: RðjÞ ¼
n 1X ðd ðjÞd^ i ðjÞÞ2 wj ; ni¼1 i
wj ¼ Lj þ 1
ð3Þ
being: di ðjÞ the ith wavelet detail coefficient of the raw image at the jth wavelet decomposition level; d^ i ðjÞ the ith wavelet denoised (using hard threshold) detail coefficient, at the ith wavelet decomposition level; n is the level by level number of detail wavelet coefficients; wj is the assigned weight, calculated according to j and L values, where L is the user-defined wavelet multiresolution level of decomposition. The closer the wavelet detail energies, the lower the RðjÞ. According to this formulation and to the previously described frequency location of noise, and varying the wavelet filter as well as the level of wavelet decomposition, we selected the filter and the level showing the minimum value of Table 1 Performance evaluation of selection of wavelet filters in terms of IQI. IQI
Fused image with Rmin BiorW 1.1, 10th level (see Fig. 3)
Fused image with Emin BiorW 3.1, 10th level (see Fig. 4)
SNR (dB) GF RMSE (with 325 kHz) UIQI (with 325 kHz) FWCF
16.278 0.058 6:15 1014
13.181 0.056 38.908
1
0.327
1.584
1.242
Fig. 3. Experimental setup showing computer interfaced eddy current instrument (vector 2d) and zy scanner with vertically mounted cladding tube and aluminium (clad) tube having machined defects simulating void (insert).
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S. Balakrishnan et al. / NDT&E International 51 (2012) 51–57
RðjÞ, i.e. Rmin ¼ minj RðjÞ. Besides, the higher the level of decomposition, the detail coefficients are closer to the lowest frequencies. This is the reason why the weighted variance of the detail coefficients is considered, with decreasing weights, in order to emphasize the contribution from the higher frequencies. Therefore, the minimum of the weighted risk factor (Rmin) is calculated for each wavelet filter, iterated on each decomposition level. The criteria of minimum weighted risk factor imply that the variances of coefficients are less and hence better denoising.
WDCs (diagonal, vertical and horizontal) having the maximal energy have been retained. Also in this case, level by level, the correspondent IDWT has been applied. In this way, the fused images have been reconstructed. Fig. 2 shows the scheme of fusion, where t is the number of images to fuse.
2.3. Implemented fusion rule
In this study, the multi-resolution analysis has been carried out using different wavelet filters, mainly using family of Daubechies wavelets (DbW) and Biorthogonal wavelets (BiorW). The test images used in our study are eddy current images obtained from an EDM (electro discharge machining) machined notches (as tabulated in Table 1) in tubes (length 30 mm, outer diameter 5.1 mm and wall thickness 0.37 mm) made of 20% cold worked AISI type 316 stainless steel. A dual frequency eddy current instrument (ECT 3100) and an absolute focused surface probe operating at 325 kHz and 75 kHz are used for obtaining the inphase (H) and quadrature (V) components of the signals. In order to obtain eddy current images of the defects in the cladding tube, a computer controlled zy scanner is used. For every 1 mm vertical movement of the probe along z-direction up to 15 mm,
Generally using DWT, all the transformed images are combined with definite fusion rules, then transformed back to the spatial domain to give the resulting fused image. Fusion of WT is defined as Eq. (1) (see Section 2). In our work, we calculated, for each image to fuse, the wavelet filter and the decomposition level according to the values of Rmin (or Emin) among wavelet family of Daubechies wavelets (DbW) and Biorthogonal wavelets (BiorW). Subsequently, the images have been decomposed by using the correspondent wavelet filters and decomposition levels. Then, considering the whole set of images to fuse, the WACs having the minimal energy have been retained and the correspondent IDWT has been applied to them. On the contrary, level by level, the
3. Application of the proposed procedure to eddy current images
Fig. 4. Eddy current images from EDM notch (transverse: 4 mm long, 0.5 mm wide and 0.1 mm deep) at (a) 325 kHz, (b) 75 kHz and fused images resulted using (c) Bior 1.1 level 10 (obtained using Rmin factor) and (d) Bior 3.1 level 10 (obtained using Emin factor).
S. Balakrishnan et al. / NDT&E International 51 (2012) 51–57
the cladding tube is rotated to 3601 in steps of 11 along the y-direction. Each z-scan (vertical scanning) of the probe along the cladding tube wall is digitized using a 16 bit ADC card at a sampling rate of 1 kHz and stored as an image of all defects for processing. The experimental setup is shown in Fig. 3. The steps involved in this methodology are: 1. The images are subjected to DWT using wavelet filters of DbW and BiorW families. 2. The energies of WACs and WDCs at each level for the different wavelet filters (DbW and BiorW) have been calculated. 3. The wavelet filter and decomposition level showing Rmin (Emin) are selected. From the calculation, Rmin results selection of the BiorW 1.1 with level 10 and Emin results the BiorW 3.1 at level 10. 4. In order to assess which best selection factor is for choosing an optimum wavelet, denoising performance of the selected wavelet are assessed: (a) The wavelet decomposition of the two images is carried out using the above selected wavelet filters and up to the optimized level (level 10) of decomposition. (b) The fusion rule is implemented by retaining the coefficients corresponding to minimum wavelet energy of WACs and maximum wavelet energy of WDCs between two test images (refer Fig. 2).
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(c) The resulted fused images obtained by using the two wavelet filters are compared by the quality of the images. The results are as follows in the next section. In this regard, the two input images are decomposed. It has been shown that choosing an appropriate wavelet filter and level of decomposition can significantly increase the quality of the fusion results. 3.1. Evaluation of the fusion methods The optimum wavelet filter among the BiorW 1.1 with level 10 and the BiorW 3.1 at level 10 is chosen based on the quality of the fused image. This quality is measured as quantitative comparison by such image quality indicators (IQIs) as the signal-to-noise ratio (SNR), the root mean squared error (RMSE), the gradient factor (GF) [9], the Universal Image Quality Index (UIQI) [14] and the Fechner–Weber contrast factor (FWCF) [15]. Typical eddy current images obtained by this method are shown in Fig. 4. The image quality factors of the fused images based on the wavelet decomposition are given in Table 1. The validation of the proposed methods has been evaluated on another set of test images, and are shown in Figs. 5 and 6, obtaining similar improvements in terms of image qualities. These results show that the proper selection of wavelet filter and level of decomposition results a satisfactory fusion results.
Fig. 5. Eddy current images from EDM notch (transverse: 4 mm long, 0.7 mm wide and 0.2 mm deep) and fused images resulted using Bior 1.1 level 10 (obtained using Rmin factor).
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S. Balakrishnan et al. / NDT&E International 51 (2012) 51–57
Fig. 6. Eddy current images from EDM notch (longitudinal: 4 mm long, 0.7 mm wide and 0.15 mm deep) and fused images resulted using Bior 1.1 level 10 (obtained using Rmin factor).
Hence, this method can be used for achieving effective image fusion in the field of eddy current NDE. Let us remark that the FWCF, according to its formulation [15], affirms that the higher the value, the higher the contrast between the considered region of interest (ROI), in our case the area of the notch, and the background. In NDE, this affirmation can be considered as: the higher the contrast, the higher the defect enhancement, and therefore the stronger the evidence of defect’s presence and the easier the calculus of its spatial extension. Moreover, as explained by Wang and Bovik [14], the closer to 1 the value of UIQI, the higher the affordability of fusion procedure. Finally, we decided to calculate RMSE and UIQI values comparing the fused images with the 325 kHz images since the depth of the notch and the skin-effect.
4. Conclusions In this paper, we approached the problem of increasing the useful information of eddy current NDE images by means of data fusion procedures. We analyzed the challenge in a multi-resolution way, and thus we solved the problem by means of the WT. Usually, such important source of noise as lift-off acts on measurements in NDE, influencing their quality and introducing
unwanted information above all at the lower frequencies of the spectrum. Therefore, WTs are classically exploited in order to erase the information lying in the lowest frequencies (i.e., in the WACs), thus considering a wavelet energy based risk factor and applying fusion rules according to the previously explained aim. On the contrary, in our work, even agreeing with the concept of noise lying in the lowest frequencies, we assumed that, in this frequency range, it is also possible to find useful component of signal. Moreover, if the multi-resolution level of analysis is pushed to a high level, not only the WACs contain the noise contribute, but also the neighboring WDCs may. In this way, a risk factor related to the ‘‘frequency location’’ of the WDCs wavelet coefficients more than to their overall energy could be more descriptive of the real mixing of noise and signal. Therefore, in this paper, we suggest the use of a weighted risk factor in order to give more importance to WDCs in higher frequencies than in lower frequencies, but without avoiding the latter ones. Here, we presented, for dissemination purposes, the test applied on eddy current images obtained from a notch simulated in an AISI type 316 stainless steel cladding tube, at 325 kHz and 75 kHz test frequencies. The values calculated for FWCFs affirm that the proposed procedure of image fusion, based on the use of weighted risk factor and the adoption of the particular fusion schema explained in Section 2.3, is able to enhance the defect’s presence
S. Balakrishnan et al. / NDT&E International 51 (2012) 51–57
than the use of the energy factor (refer Table 1). Besides, both the risk factors have been validated on different sets of NDE images, and all results confirm the better performances of our proposed weighted risk factor and fusion procedure. Finally, let us remark how the wavelet mother and the level of decomposition are automatically selected with the evaluation of energy factors. Furthermore, the latter are calculated just considering the intrinsic energy of provided wavelet coefficients, then the intrinsic energy of collected signals (i.e., images). That is why we can state that, as a general principle, the proposed automatic methodology could be applicable also to images provided by different inspection techniques, such as ultrasound or X-ray modalities. Since we dealt with eddy current inspections, and here the main source of disturbing noise (i.e. lift-off) has the frequency content above described, we formulated the energy factors according to Eqs. (2) and (3). For different inspection techniques, the formulas could be adapted according to the frequency content of the main noise sources. References [1] Gros X. Applications of NDT data fusion. New York: Springer-Verlag; 2001. [2] Farhad, S. Fusion techniques in remote sensing. In: Proceedings of the ISPRS commission IV joint workshop ‘‘challenges in geospatial analysis, integration and visualization II’’. Stuttgart, Germany.
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[3] Gros X, Strachan P, Lowden D. A Bayesian approach to NDT data fusion. Insight 1995;37:363–5. [4] Gros X, Bousigue J, Takahashi K. NDT data fusion at pixel level. NDT & E Int 1998;39:652–7. [5] Koks D, Challa S. An introduction to Bayesian and Dempster–Shafer data fusion. Technical report. Defence Science and Tech Org; 2003. [6] Memarsadeghi N, Le J, David M, Mount M, Morisette J. A new approach to image fusion based on cokriging. In: The eighth international conference on information fusion. p. 622–9. [7] Libby H. Introduction to electromagnetic nondestructive test methods. New York, NY, USA: Wiley-Interscience; 1971. [8] Simone G, Morabito F. NDT image fusion using eddy current and ultrasonic data. COMPEL: Int J Comput Math Electr Electron Eng 2001;20:857–68. [9] Chen T, Zhang J, Zhang Y. Remote sensing image fusion based on ridgelet transform. In: Proceedings of the IEEE international geoscience and remote sensing symposium, IGARSS 2005, vol. 2. p. 1150–3. [10] Li H, Manjunath B, Mitra S. Multisensor image fusion using the wavelet transform. Graph Models Image Process 1995;57:235–45. [11] Chipman L, Orr T, Lewis L. Wavelets and image fusion. IEEE Trans Image Process 1995;3:248–51. [12] Rockinger O. Pixel-level fusion of image sequences using wavelet frames. In: Mardia K, Gill C, Dryden I, editors. Proceedings of the 16th Leeds applied shape research workshop. Leeds University Press; 1996. p. 149–54. [13] Hill P, Bull D, Canagarajah C. Image fusion using a new framework for complex wavelet transforms. In: International conference on image processing, ICIP 2005; p. 1338–41. [14] Wang Z, Bovik A. A universal image quality index. IEEE Signal Process Lett 2002;9:81–4. [15] Sadjadi F. Measures of effectiveness and their use in comparative image fusion analysis. In: Proceedings of the IEEE international geoscience and remote sensing symposium, IGARSS 2003, vol. 6. p. 3659–61.
Contents lists available at SciVerse ScienceDirect
NDT&E International journal homepage: www.elsevier.com/locate/ndteint
Development of image fusion methodology using discrete wavelet transform for eddy current images Sasi Balakrishnan a, Matteo Cacciola b,n, Lalita Udpa c, Bhagi Purnachandra Rao a, Tammana Jayakumar a, Baldev Raj a a
Non-Destructive Evaluation Division, Indira Gandhi Centre for Atomic Research, Kalpakkam, TN, India University Mediterranea of Reggio Calabria, DIMET, Via Graziella Feo di Vito, I-89100 Reggio Calabria, Italy c Michigan State University, Nondestructive Evaluation Laboratory, 2214C Engineering Bldg E, Lansing, MI 48824, USA b
a r t i c l e i n f o
abstract
Article history: Received 25 July 2011 Received in revised form 20 June 2012 Accepted 22 June 2012 Available online 4 July 2012
In this paper, a method based on the discrete wavelet transform is proposed for eddy current image fusion. This method mainly involves two steps: selection of the proper wavelet filters and level of decomposition using formulated parameter, and selection of the proper fusion criterion in wavelet subband. The main aspect of the proposed method concentrates on elimination of noise while retaining defect information. This method fuses the eddy current images at two different frequencies from stainless steel cladding tube, in order to take the advantage of deep lying information effectively. The fusion results show that the selection of wavelet and fusion rule reduces the ambiguity and enhances the reliability of defect detection in both visual and qualitative evaluation. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Non-destructive testing Image fusion Wavelet analysis Information energy
1. Introduction Image fusion is a synergistic tool that serves to combine multiple-source imagery. It aims to integrate all complementary data from several images into a single image in order to enhance the apparent information in the images [1]. Fusion of images is often acquired from different instruments (or multi-sensors), or the same sensor with different measuring contexts. The recent advances in the field make it possible to implement across wide areas such as medical imaging, microscopic imaging, remote sensing, computer vision and robotics. Fusion technique includes different methodologies, starting from pixel level to feature level and symbol level. The pixel level implies algorithmic combination of vector of measurement from each images. Feature level requires post-processing of classification and segmentation of input images and fusion is based on those extracted features. This enables detection of useful feature with higher confidence. Symbol level allows information to be effectively combined at the highest level of abstraction [2]. In all the three methodologies, the knowledge of underlying physical process is required. In order to approach non-phenomenological way, that tends to ignore the physical process and attempt to fuse data regarding their statistical nature, the scientific literature presents various statistical
n
Corresponding author. E-mail address: [email protected] (M. Cacciola).
0963-8695/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ndteint.2012.06.006
techniques, like maximum amplitude signal, averaging, weighted average, Bayesian approach and Dempster–Shafer methods [3–6]. In the field of non-destructive evaluation (NDE), the main purpose is to provide information about the presence, the location and the size of potential defects on or into the inspected components [7]. Different inspection techniques and sensors are used for analyzing components in order to acquire complementary information about defects. Furthermore, for a proper exploitation of the data measured by the different sensors, or by the same sensor in different measuring contexts, it is mandatory to develop effective data fusion techniques able to take advantage of such multisensor characteristics. The definition of multi-sensor fusion is broad and the fusion can take place at pixel, feature and symbol level [8]. However, when these methods are applied, some undesired effects of contrast reduction can appear. Many fusion methods have been exploited in recent years. Some methods are based on component substitution, such as Intensity Hue Saturation (IHS) transform that distorts the spectral feature, and high pass filter (HPF) method and principle component analysis (PCA), which loose the physical features of source images [9]. Among different methods, the wavelet transform (WT) is efficiently applied to multi-sensor image fusion because of its properties such as multi-resolution analysis and accurate reconstruction [10–12]. The WT contains unique information at different resolutions that other traditional method cannot. But the selection of a particular wavelet filter and the choosing of different decomposition schemes affect the overall performance of image fusion. In
52
S. Balakrishnan et al. / NDT&E International 51 (2012) 51–57
the field of NDE, fusion of images demands for the elimination of noise while retaining the information about defects. Hence, the selection of an appropriate wavelet filter and an optimum decomposition level are important for getting better results. Research on the subject of strategic combination of information while eliminating noise signals has been motivated by a desire to obtain more appropriate parameter for the selection of the wavelet filters and the level of decomposition. In this paper, we consider the case where eddy current images are obtained at two different frequencies from machined notches in stainless steel cladding tubes. For the selection of the proper wavelet filters and decomposition level, two factors have been formulated based on the removal of disturbing (noise) signal from periodic wall thickness variation and retaining defect information. In addition to the new parameters proposed for fusion, a fusing rule has been proposed in this work. This paper discusses
Fig. 1. Fusion of two images using DWT.
the experimental studies and the proposed two factors, the fusion rules and related experimental results.
2. Discrete wavelet transform fusion The fusion of two images within the wavelet domain is formally considered the discrete wavelet transform (DWT) of two registered input images and is combined with the definite fusion rule. Then the inverse DWT (IDWT) is computed and the fused image is reconstructed [13]. The process is shown in Fig. 1 and is defined as Iðx,yÞ ¼ W 1 ½jfWðI1 ðx,yÞÞ,WðI2 ðx,yÞÞg
ð1Þ
where I1, I2 are the two images to fuse, j is the fusion rule, and W and W 1 are the DWT and IDWT, respectively. Obviously, the procedure can be extended to multiple images, fusing the result coming from two images with the third image, and so on. For each one of the considered applications, the main user-related activity is based on the selection of proper wavelet filter and level of decomposition. In fact, case by case, these two parameters should be selected according to the framework, the available measurements and the aims and definite information that desired to be obtained. In general, the main aim is to emphasize the informative content of measures neglecting the noise impact. Also considering the problem we studied, our goal was to reduce the influence of noise, mainly lift-off noise in-lab measurements. In this regard, we proposed two kinds of factors for the selection of an appropriate wavelet filter, and we related to each factor a fusion rule. The details of the factors and the fusion rule are discussed below.
Fig. 2. Block diagram of the proposed fusion procedure.
S. Balakrishnan et al. / NDT&E International 51 (2012) 51–57
53
2.1. Energy risk factor Classically, the proposed risk factor related to WT, in the case of NDE, involves the energy of approximation coefficients and is mathematically designed as follows: Emin ¼ min Ea ðjÞ; j
j ¼ 1; 2, . . . ,L
ð2Þ
where Ea ðjÞ is the energy of approximation coefficient at the jth level of the step-by-step selected wavelet filters. The calculation of Emin is iterated for each decomposition level and for each desired wavelet filters. The wavelet energy represents the percentage of energy corresponding to the approximation and the detail coefficients. Minimum energy of the wavelet approximation coefficients (WAC) attributes the minimum amount of low frequency information retained after decomposition. Since we concentrate on the removal of noise, among the wavelets which shows the minimum energy of the approximation coefficients, (Emin) is considered as an optimum wavelet filter. 2.2. Weighted risk factor In the same way, our aim is retaining the useful information (defect) and removing the noise, i.e. lift-off signals. But in our proposal, we consider that useful components could be also present in lower frequencies mixed with the noise. Subsequently, the degree of usefulness assigned to information (defect) increases step by step while going from lowest towards the highest frequencies. Then, we should consider the maximized energy within the wavelet detail coefficients (WDCs) resulted among the wavelet filters. In fact, since the energy of WDCs of denoised image cannot be higher than the raw image, the energy stored within the WDCs of the denoised image must be as close as possible to the energy stored within the WDCs of the raw image. At the same time, we want to give more importance to WDCs in higher frequencies than in lower frequencies, but without avoiding the latter ones. For all these reasons, we formulated a weighted risk factor according to the following formulation: RðjÞ ¼
n 1X ðd ðjÞd^ i ðjÞÞ2 wj ; ni¼1 i
wj ¼ Lj þ 1
ð3Þ
being: di ðjÞ the ith wavelet detail coefficient of the raw image at the jth wavelet decomposition level; d^ i ðjÞ the ith wavelet denoised (using hard threshold) detail coefficient, at the ith wavelet decomposition level; n is the level by level number of detail wavelet coefficients; wj is the assigned weight, calculated according to j and L values, where L is the user-defined wavelet multiresolution level of decomposition. The closer the wavelet detail energies, the lower the RðjÞ. According to this formulation and to the previously described frequency location of noise, and varying the wavelet filter as well as the level of wavelet decomposition, we selected the filter and the level showing the minimum value of Table 1 Performance evaluation of selection of wavelet filters in terms of IQI. IQI
Fused image with Rmin BiorW 1.1, 10th level (see Fig. 3)
Fused image with Emin BiorW 3.1, 10th level (see Fig. 4)
SNR (dB) GF RMSE (with 325 kHz) UIQI (with 325 kHz) FWCF
16.278 0.058 6:15 1014
13.181 0.056 38.908
1
0.327
1.584
1.242
Fig. 3. Experimental setup showing computer interfaced eddy current instrument (vector 2d) and zy scanner with vertically mounted cladding tube and aluminium (clad) tube having machined defects simulating void (insert).
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S. Balakrishnan et al. / NDT&E International 51 (2012) 51–57
RðjÞ, i.e. Rmin ¼ minj RðjÞ. Besides, the higher the level of decomposition, the detail coefficients are closer to the lowest frequencies. This is the reason why the weighted variance of the detail coefficients is considered, with decreasing weights, in order to emphasize the contribution from the higher frequencies. Therefore, the minimum of the weighted risk factor (Rmin) is calculated for each wavelet filter, iterated on each decomposition level. The criteria of minimum weighted risk factor imply that the variances of coefficients are less and hence better denoising.
WDCs (diagonal, vertical and horizontal) having the maximal energy have been retained. Also in this case, level by level, the correspondent IDWT has been applied. In this way, the fused images have been reconstructed. Fig. 2 shows the scheme of fusion, where t is the number of images to fuse.
2.3. Implemented fusion rule
In this study, the multi-resolution analysis has been carried out using different wavelet filters, mainly using family of Daubechies wavelets (DbW) and Biorthogonal wavelets (BiorW). The test images used in our study are eddy current images obtained from an EDM (electro discharge machining) machined notches (as tabulated in Table 1) in tubes (length 30 mm, outer diameter 5.1 mm and wall thickness 0.37 mm) made of 20% cold worked AISI type 316 stainless steel. A dual frequency eddy current instrument (ECT 3100) and an absolute focused surface probe operating at 325 kHz and 75 kHz are used for obtaining the inphase (H) and quadrature (V) components of the signals. In order to obtain eddy current images of the defects in the cladding tube, a computer controlled zy scanner is used. For every 1 mm vertical movement of the probe along z-direction up to 15 mm,
Generally using DWT, all the transformed images are combined with definite fusion rules, then transformed back to the spatial domain to give the resulting fused image. Fusion of WT is defined as Eq. (1) (see Section 2). In our work, we calculated, for each image to fuse, the wavelet filter and the decomposition level according to the values of Rmin (or Emin) among wavelet family of Daubechies wavelets (DbW) and Biorthogonal wavelets (BiorW). Subsequently, the images have been decomposed by using the correspondent wavelet filters and decomposition levels. Then, considering the whole set of images to fuse, the WACs having the minimal energy have been retained and the correspondent IDWT has been applied to them. On the contrary, level by level, the
3. Application of the proposed procedure to eddy current images
Fig. 4. Eddy current images from EDM notch (transverse: 4 mm long, 0.5 mm wide and 0.1 mm deep) at (a) 325 kHz, (b) 75 kHz and fused images resulted using (c) Bior 1.1 level 10 (obtained using Rmin factor) and (d) Bior 3.1 level 10 (obtained using Emin factor).
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the cladding tube is rotated to 3601 in steps of 11 along the y-direction. Each z-scan (vertical scanning) of the probe along the cladding tube wall is digitized using a 16 bit ADC card at a sampling rate of 1 kHz and stored as an image of all defects for processing. The experimental setup is shown in Fig. 3. The steps involved in this methodology are: 1. The images are subjected to DWT using wavelet filters of DbW and BiorW families. 2. The energies of WACs and WDCs at each level for the different wavelet filters (DbW and BiorW) have been calculated. 3. The wavelet filter and decomposition level showing Rmin (Emin) are selected. From the calculation, Rmin results selection of the BiorW 1.1 with level 10 and Emin results the BiorW 3.1 at level 10. 4. In order to assess which best selection factor is for choosing an optimum wavelet, denoising performance of the selected wavelet are assessed: (a) The wavelet decomposition of the two images is carried out using the above selected wavelet filters and up to the optimized level (level 10) of decomposition. (b) The fusion rule is implemented by retaining the coefficients corresponding to minimum wavelet energy of WACs and maximum wavelet energy of WDCs between two test images (refer Fig. 2).
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(c) The resulted fused images obtained by using the two wavelet filters are compared by the quality of the images. The results are as follows in the next section. In this regard, the two input images are decomposed. It has been shown that choosing an appropriate wavelet filter and level of decomposition can significantly increase the quality of the fusion results. 3.1. Evaluation of the fusion methods The optimum wavelet filter among the BiorW 1.1 with level 10 and the BiorW 3.1 at level 10 is chosen based on the quality of the fused image. This quality is measured as quantitative comparison by such image quality indicators (IQIs) as the signal-to-noise ratio (SNR), the root mean squared error (RMSE), the gradient factor (GF) [9], the Universal Image Quality Index (UIQI) [14] and the Fechner–Weber contrast factor (FWCF) [15]. Typical eddy current images obtained by this method are shown in Fig. 4. The image quality factors of the fused images based on the wavelet decomposition are given in Table 1. The validation of the proposed methods has been evaluated on another set of test images, and are shown in Figs. 5 and 6, obtaining similar improvements in terms of image qualities. These results show that the proper selection of wavelet filter and level of decomposition results a satisfactory fusion results.
Fig. 5. Eddy current images from EDM notch (transverse: 4 mm long, 0.7 mm wide and 0.2 mm deep) and fused images resulted using Bior 1.1 level 10 (obtained using Rmin factor).
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Fig. 6. Eddy current images from EDM notch (longitudinal: 4 mm long, 0.7 mm wide and 0.15 mm deep) and fused images resulted using Bior 1.1 level 10 (obtained using Rmin factor).
Hence, this method can be used for achieving effective image fusion in the field of eddy current NDE. Let us remark that the FWCF, according to its formulation [15], affirms that the higher the value, the higher the contrast between the considered region of interest (ROI), in our case the area of the notch, and the background. In NDE, this affirmation can be considered as: the higher the contrast, the higher the defect enhancement, and therefore the stronger the evidence of defect’s presence and the easier the calculus of its spatial extension. Moreover, as explained by Wang and Bovik [14], the closer to 1 the value of UIQI, the higher the affordability of fusion procedure. Finally, we decided to calculate RMSE and UIQI values comparing the fused images with the 325 kHz images since the depth of the notch and the skin-effect.
4. Conclusions In this paper, we approached the problem of increasing the useful information of eddy current NDE images by means of data fusion procedures. We analyzed the challenge in a multi-resolution way, and thus we solved the problem by means of the WT. Usually, such important source of noise as lift-off acts on measurements in NDE, influencing their quality and introducing
unwanted information above all at the lower frequencies of the spectrum. Therefore, WTs are classically exploited in order to erase the information lying in the lowest frequencies (i.e., in the WACs), thus considering a wavelet energy based risk factor and applying fusion rules according to the previously explained aim. On the contrary, in our work, even agreeing with the concept of noise lying in the lowest frequencies, we assumed that, in this frequency range, it is also possible to find useful component of signal. Moreover, if the multi-resolution level of analysis is pushed to a high level, not only the WACs contain the noise contribute, but also the neighboring WDCs may. In this way, a risk factor related to the ‘‘frequency location’’ of the WDCs wavelet coefficients more than to their overall energy could be more descriptive of the real mixing of noise and signal. Therefore, in this paper, we suggest the use of a weighted risk factor in order to give more importance to WDCs in higher frequencies than in lower frequencies, but without avoiding the latter ones. Here, we presented, for dissemination purposes, the test applied on eddy current images obtained from a notch simulated in an AISI type 316 stainless steel cladding tube, at 325 kHz and 75 kHz test frequencies. The values calculated for FWCFs affirm that the proposed procedure of image fusion, based on the use of weighted risk factor and the adoption of the particular fusion schema explained in Section 2.3, is able to enhance the defect’s presence
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than the use of the energy factor (refer Table 1). Besides, both the risk factors have been validated on different sets of NDE images, and all results confirm the better performances of our proposed weighted risk factor and fusion procedure. Finally, let us remark how the wavelet mother and the level of decomposition are automatically selected with the evaluation of energy factors. Furthermore, the latter are calculated just considering the intrinsic energy of provided wavelet coefficients, then the intrinsic energy of collected signals (i.e., images). That is why we can state that, as a general principle, the proposed automatic methodology could be applicable also to images provided by different inspection techniques, such as ultrasound or X-ray modalities. Since we dealt with eddy current inspections, and here the main source of disturbing noise (i.e. lift-off) has the frequency content above described, we formulated the energy factors according to Eqs. (2) and (3). For different inspection techniques, the formulas could be adapted according to the frequency content of the main noise sources. References [1] Gros X. Applications of NDT data fusion. New York: Springer-Verlag; 2001. [2] Farhad, S. Fusion techniques in remote sensing. In: Proceedings of the ISPRS commission IV joint workshop ‘‘challenges in geospatial analysis, integration and visualization II’’. Stuttgart, Germany.
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