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This paper aims to propose a novel improved complex shock filter for image enhancement of real time transformer oil images. An improved theoretical equation was introduced for the analysis in order to normalize the complex diffusion shock filter. This was accomplished through multiplying each term of complex shock filter by scalar correction constant to crumbling into three cases of improved complex shock filter. The results of all the cases are validated using image performance metrics such as Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR) and Similar Structure Index Mean (SSIM).Through this study, it was found that the proposed noise elimination method can be effectively used for synthetic as well as real time transformer oil images without affecting the structure of the object. The findings of this research may serve as a new filtering technique for the analysis of an image.
CSF, ICSF, MSE, OSF, PSNR, SSIM, transformer oil
Transformer is a static device used transfer energy from one voltage level to other with a constant frequency and power. Performance of this continuously working equipment is based on the insulation and cooling characteristics. In general, mineral oil from crude petroleum used as dielectric as well as cooling medium in all the power transformers [13]. Gases produced and dissolved in the transformer oil due to operation of transformer at various temperatures for different loads minimize the cooling as well as insulation efficiency. Hence transformer oil chemical, structural and thermal characteristics are to be monitored to improve the effectiveness performance of the transformer [46]. There are many timeconsuming classical methods are available to measure the performance of transformer oil. The digital image processing is an emerging nondestructive method for diagnosis of internal faults occurred transformer [7, 8].
A picture with two dimensions representing individual/distinct features such as structure, shape, texture and colour etc. is termed as an image [911]. Digital images of transformer oil captured through digital camera are associated with different noise due to inadequate illumination levels as well as natural or forced convection movement of oil. There are numerous linear and nonlinear filters exists in the literature for denoising and edge preservation of the images. Shock filter is best suited for transformer oil images since it operates at different temperatures in addition to abrupt variation of temperature of oil. Firstly, the shock filter proposed by Kramer and Bruckner [12] based on dilation process near a maximum and erosion near minimum. The introduction of original shock filter in [13] is very sensible and cannot remove noise. Many authors proposed diffusion schemes in shock filter such as smoothed Laplacian [14], while Gilboa, et al. [15] normalize the shock in complex domain.
In this paper a novel improved complex shock filter is proposed and tested its performance with the synthetic in addition to real transformer oil images. The objective of this paper to enhance the transformer oil images captured at different temperatures through improved complex shock filter. The visual and numerical results of the proposed method is compared with other image filtering enhancement techniques such as median, wiener, shock along with complex shock filter. Numerical results are validated through image quality evaluation metrics such as MSE, PSNR and SSIM [1618].
This paper is organized as follows: section 2 introduces the shock filter along with complex diffusion shock filter, section 3 describes the proposed method, section 4 furnishes the comprehensive experimental results and discussions, and in section 5 the conclusion of the paper presented.
Original Shock Filters (OSF) are morphological image enhancement techniques which processes each pixel of an image using Partial Differential Equations (PDE). The term shock filtering introduced by Osher and Rudin [13] based on hyperbolic PDE. In general, 1D (onedimensional) shock filter described by PDEs:
$\mathrm{I}_{\mathrm{t}}=\frac{\partial I}{\partial t}=I x \mathrm{F}(\mathrm{I} x x)$ (1)
where, I represent the image. Ix and Ixx represent first and the second directional derivatives of the image I respectively. Function F must satisfy F (0) = 0, F(s) sign(s) ≥0. Equation (1) satisfies Neumann boundary conditions with initial conditions I ( x,0)=I_{0}(x). Choosing F(s) = sign(s) gives the shock filter equation in 1D as:
$\mathrm{I}_{\mathrm{t}}=\operatorname{sign}(\mathrm{I} x x)\mathrm{I} x$ (2)
In the 2D (twodimensional) case the shock filter equation is commonly generalized to:
$\mathrm{I}_{\mathrm{t}}=\operatorname{sign}(\eta \eta)\nabla I$ (3)
where, η is direction of gradient ∇I.
OSF used in image processing enhancement to remove blurs edges in the image. But they are exceptionally sensitive to noise signal that is any noise in the blurred signal will be enhanced. A blur edge steep input signal and its OSF output is as shown in Figure 1(a) – 1(b). Similarly, the noisy edge input signal along with OSF output is characterized in Figure 1(c) – 1(d) respectively. The output of OSF is not completely enhanced with noisy steep blur edge input signal but when the input signal is steep blur edge input an unambiguously enhancement can be observed Figure 1(a) – 1(d).
Figure 1. (a) Blur edge input signal b) OSF output for blur edge input signal (c) Noisy edge input signal (d) OSF output for noisy edge input signal
The noise in the blurred input signal is not completely removed using OSF. The advance in formulation of PDEs is developed to eliminate the difficulties in classical shock filter. Gilboa et al. [15] combined shock and diffusion in their work to form complex diffusion shock filter (CSF). The PDE equation for 2D image with nonlinear complex diffusion approach has of the form
$\mathrm{I}_{\mathrm{t}}=\frac{2}{\pi} \arctan \left(\mathrm{a} \operatorname{Im}\left(\frac{I}{\theta}\right)\right)\nabla \mathrm{I}+\lambda \operatorname{In} \eta+\tilde{\lambda} \operatorname{I}\varepsilon \varepsilon$ (4)
where, λ= re^{iɵ} is a complex scalar, $\tilde{\lambda}$ is a real scalar, $\theta \in\left(\frac{\pi}{2}, \frac{\pi}{2}\right)$ is the phase angle, Im represents imaginary and parameter a control the sharpness of the slope near zero. The gradient norm ∇I in equation (3) and (4) is computed using a slope limiter minmod function in order to minimize the sudden signal variations [19].
The transformer oil subjected to variation in temperature during the operation of in service transformer. Image captured at different temperatures are enhanced using different filters. Since the removal of undesirable information is not completely achieved by Classical filters as well as the OSF or CSF, the novel Improved CSF is proposed in this paper to enhance the digital transformer oil image obtained at different temperature. The CSF defined in eq. 4 is modified for the theoretical analysis by multiplying each term of this equation with real scalar correction constant C. The performance of this novel Improved Complex Shock Filter (ICSF) are validated by comparing the results obtained by ICSF with the results of median, wiener, OSF and CSF. Eq. (4) develop into three different cases as:
Case 1:
$\left.\mathrm{I}_{\mathrm{t}}=\frac{2}{\pi} \arctan \left(\mathrm{a} \operatorname{lm}\left(\frac{I}{\theta}\right)\right)\nabla \mathrm{I}+\lambda \operatorname{In} \eta+\mathcal{C} \tilde{\lambda} \operatorname{l\varepsilon} \varepsilon\right)$ (5)
Case 2:
$\mathrm{I}_{\mathrm{t}}=\frac{2}{\pi} \arctan \left(\operatorname{alm}\left(\frac{I}{\theta}\right)\right)\nabla \mathrm{I}+C(\lambda \operatorname{I\eta} \eta)+\tilde{\lambda} \operatorname{l\varepsilon} \varepsilon$ (6)
Case 3:
$\mathrm{I}_{\mathrm{t}}=C\left(\frac{2}{\pi} \arctan \left(\mathrm{a} \operatorname{Im}\left(\frac{I}{\theta}\right)\right)\nabla \mathrm{I}\right)+\lambda \operatorname{I\eta} \eta+\tilde{\lambda} \operatorname{Is} \varepsilon$ (7)
All three cases of the filter possess new variable C in addition to the all the variables of Eq. 4. In case 1, the quantity of diffusion in intensity set direction altered by multiplying C with the last term having λ Iεε. In case 2, C is multiplied with the middle term containing λ Iηη to adjust the complex diffusion term intended for removal of noise. In case 3, the false inflection points produced by noise are accustomed by multiplying C with first term having trigonometric tan function. The results of each case tabulated in table1 for the values of C=0.2, 0.4, 0.6 and 0.8. Figure 2 describes the flowchart of proposed method.
Figure 2. Flow chart of proposed ICSF
In this section, the experimental results of proposed method on both synthetic images and real transformer oil images, and compare experimental results of proposed method with other image enhancement methods. The performance of proposed method along with other image enhancement filtering techniques is evaluated using image quality metrics such as MSE, PSNR and SSIM.
4.1 Performance on synthetic images
In this part, the visual plus numerical results obtained on three classical synthetic images: Lena, baboon, peppers are established. Figure 3 presents the gray image, the denoised images obtained in all three cases of proposed ICSF method with real scalar correction constant C=0.2 in addition to other filtering methods like shock as well as complex shock filter. Further to enumerate the performance, the results obtained with proposed ICSF are compared with conventional median and wiener filtering methods in addition to OSF as well as CSF. The filtered images obtain with ICSF method with case2/C=0.2appear to be smoothed with a better edge and shape preservation compared with the other methods. Figure 4 shows the gray image, resultant synthetic images obtained from median, wiener, OSF, CSF and ICSF/case2/C=0.2 filtering methods. To quantify the denoising qualities, first three columns of Table 1 present the numerical results for classical synthetic images. The performance criterion used is MSE, PSNR and SSIM. It can be observed that the proposed ICSF method has low MSE, high PSNR & on the brink of unity SSIM.
Figure 3. Top to bottom gray images of Lena, baboon and peppers. Enhanced images using (b) OSF (c) CSF (d) ICSF/CASE1/C=0.2, (e) ICSF/CASE2/C=0.2, and (f) ICSF/CASE2/C=0.2
Figure 4. Top to bottom gray images of Lena, baboon and peppers. Enhanced images using (b) Median Filter, (c)wiener filter, (d) OSF, (e) CSF and (f) ICSF / CASE2 / C=0.2
Figure 5. Transformer oil (300C) Gray, OSF, CSF and ICSF images with case1, case2 and case3using C=0.2, 0.4, 0.6 & 0.8
Figure 5 shows the gray image along with OSF, CSF and ICSF (selecting C=0.2, 0.4, 0.6 and 0.8 in case1, case2, case3) filtered transformer oil images. It can be seen that for case2/C=0.2, the proposed ICSF filter relent improved smoothening of image compared to other filtering methods. The trivial variation of results accomplished in the other cases of ICSF for all the values of C along with increased values of C in the same case.
Figure 6. Top to bottom gray images of transformer oil at 30 ℃, 60 ℃, 90 ℃ and at 120 ℃ temperatures. Enhanced images using (b) Median Filter, (c) wiener filter, (d) OSF, (e) CSF, and (f) ICSF/CASE2/C=0.2
Figure 7. (a), (c) and (e) MSE, PSNR and SSIM for classical images (b), (d) and (f) MSE, PSNR and SSIM for transformer oil images
4.2 Performance on transformer oil images
Further, the performance of the proposed ICSF method tested on transformer oil images and comparison of results are made with the median, wiener, shock and complex shock filtering methods. To denoise, real scalar correction constant C introduced in proposed ICSF method whose values ranges between 0.10.8. In this paper, C values of 0.2, 0.4, 0.6 and 0.8 are considered in all the three cases (Eq. (5) to Eq. (7)).
Table 1. Summarizing image quality metrics (MSE, PSNR & SSIM) of different filters
Image Filtering Method 
Image Quality Assessment Metrics 
IMAGES 

Lena 
Baboon 
peppers 
Transformer oil (30^{0}C) 
Transformer oil (60^{0}C) 
Transformer oil (90^{0}C) 
Transformer oil (120^{0}C) 

Median Filter 
MSE 
45.96 
45.33 
9.45 
1.61 
1.94 
2.19 
2.04 


PSNR 
31.542 
31.603 
38.411 
46.106 
45.288 
44.762 
45.069 

SSIM 
0.93 
0.66 
0.95 
1.00 
1.00 
1.00 
1.00 

Weiner Filter 
MSE 
20.63 
44.04 
9.53 
0.26 
0.33 
0.23 
0.21 


PSNR 
35.020 
31.726 
38.372 
53.942 
53.046 
54.606 
54.960 

SSIM 
0.95 
0.79 
0.95 
1.00 
1.00 
1.00 
1.00 

Shock Filter 
MSE 
19.57 
27.61 
11.12 
0.03 
0.05 
0.03 
0.02 


PSNR 
35.250 
33.754 
37.705 
63.522 
61.453 
63.903 
65.970 

SSIM 
0.98 
0.98 
0.99 
1.00 
1.00 
1.00 
1.00 

Complex Shock Filter 
MSE 
3.33 
7.13 
2.47 
0.00334 
0.004 
0.0030 
0.0028 


PSNR 
42.93 
39.636 
44.236 
72.92 
72.06 
73.355 
73.660 

SSIM 
1.00 
0.99 
0.99 
1.00 
1.00 
1.00 
1.00 

Improved Complex Shock Filter (scalar correction constant C = 0.2) 
Case 1 
MSE 
8.12 
25.30 
18.68 
0.00042196 
0.00049685 
0.00035656 
0.00034390 
PSNR 
39.064 
34.131 
35.44 
81.9120 
81.2024 
82.6434 
82.8003 

SSIM 
0.99 
0.98 
0.99 
1.00 
1.00 
1.00 
1.00 

Case 2 
MSE 
2.46 
4.38 
2.16 
0.00003087 
0.00003691 
0.00002725 
0.00002573 

PSNR 
44.257 
41.749 
44.80 
93.26937 
92.4936 
93.8105 
94.0601 

SSIM 
1.00 
1.00 
1.00 
1.00 
1.00 
1.00 
1.00 

Case 3 
MSE 
6.821 
27.98 
19.332 
0.00046481 
0.00054842 
0.00039633 
0.00038066 

PSNR 
39.826 
33.694 
35.301 
81.4919 
80.7736 
82.1841 
82.3593 

SSIM 
0.99 
0.97 
0.99 
1.00 
1.00 
1.00 
1.00 

Improved Complex Shock Filter (scalar correction constant C = 0.4) 
Case 1 
MSE 
8.17 
25.84 
18.713 
0.00043209 
0.00050902 
0.00036596 
0.00035260 
PSNR 
39.04 
34.040 
35.443 
81.8089 
81.0974 
82.5303 
82.6919 

SSIM 
0.99 
0.98 
0.99 
1.00 
1.00 
1.00 
1.00 

Case 2 
MSE 
4.22 
9.094 
5.17 
0.00008989 
0.00010656 
0.00007782 
0.00007420 

PSNR 
41.90 
38.577 
41.02 
88.6275 
87.8886 
89.2537 
89.4606 

SSIM 
1.00 
0.99 
1.00 
1.00 
1.00 
1.00 
1.00 

Case 3 
MSE 
6.28 
26.688 
18.61 
0.00046481 
0.00054842 
0.00039633 
0.00038066 

PSNR 
40.180 
33.901 
35.466 
81.4919 
80.7736 
82.1841 
82.3593 

SSIM 
0.99 
0.97 
0.99 
1.00 
1.00 
1.00 
1.00 

Improved Complex Shock Filter (scalar correction constant C = 0.6) 
Case 1 
MSE 
8.22 
26.42 
18.75 
0.00044261 
0.00052166 
0.00037573 
0.00036163 
PSNR 
39.010 
33.94 
35.43 
81.7044 
80.9908 
82.4159 
82.5821 

SSIM 
0.99 
0.98 
0.99 
1.00 
1.00 
1.00 
1.00 

Case 2 
MSE 
5.54 
14.39 
9.01 
0.00018189 
0.00021503 
0.00015619 
0.00014951 

PSNR 
40.727 
36.583 
38.612 
85.5667 
84.8396 
86.2282 
86.4179 

SSIM 
1.00 
0.99 
1.00 
1.00 
1.00 
1.00 
1.00 

Case 3 
MSE 
6.42 
26.22 
18.338 
0.00046481 
0.00054842 
0.00039633 
0.00038066 

PSNR 
40.086 
33.977 
35.531 
81.4919 
80.7736 
82.1841 
82.3593 

SSIM 
0.99 
0.98 
0.99 
1.00 
1.00 
1.00 
1.00 

Improved Complex Shock Filter (scalar correction constant C = 0.8) 
Case 1 
MSE 
8.29 
27.003 
18.786 
0.00045352 
0.00053480 
0.00038585 
0.00037098 
PSNR 
39.003 
33.850 
35.42 
81.5987 
80.8828 
82.3005 
82.4712 

SSIM 
0.99 
0.98 
0.99 
1.00 
1.00 
1.00 
1.00 

Case 2 
MSE 
6.88 
20.552 
13.60 
0.00030686 
0.00036232 
0.00026236 
0.00025167 

PSNR 
39.784 
35.036 
36.828 
83.2952 
82.5738 
83.9757 
84.1564 

SSIM 
0.99 
0.98 
1.00 
1.00 
1.00 
1.00 
1.00 

Case 3 
MSE 
7.15 
26.575 
18.428 
0.00046481 
0.00054842 
0.00039633 
0.00038066 

PSNR 
39.622 
33.919 
35.509 
81.4919 
80.7736 
82.1841 
82.3593 

SSIM 
0.99 
0.98 
0.99 
1.00 
1.00 
1.00 
1.00 
This paper presents a novel ICSF method for transformer oil images which are captured at different temperatures. This method involves three different cases i.e., each term of CSF equation multiplied with real scalar constant to evolve three different cases of ICSF method. Experiments were performed on synthetic as well as real transformer oil images. The visual as well as numerical results of ICSF method of all three cases are checked for all the images. ICSF method furnish superior results for all the images in case2 with C=0.2. The results of all the images are validated using image performance quality metrics such as MSE, PSNR and SSIM. The visual as well as numerical results shows ICSF method provide better performance when compared with median, wiener, OSF in addition to CSF filter. Finally, this paper concludes the proposed filtering method performance is optimal compared to other classical state of the art filtering methods. Further this proposed filter can be used for segmentation, feature extraction of an image.
Figure 8. (a) Top to bottom one dimensional images (gray) of transformer oil at 30 ℃, 60 ℃, 90 ℃, 120 ℃. Enhanced images using (b) Median Filter, wiener filter, (d) OSF, (e) CSF, and (f) ICSF/CASE2/C=0.2
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