# Image Enhancement for Inspection of Cable Images Based on Retinex Theory and Fuzzy Enhancement Method in Wavelet Domain

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## Abstract

**:**

## 1. Introduction

## 2. Inspection Image Acquisition and Spectrum Analysis

#### 2.1. Inspection Image Acquisition

#### 2.2. Spectrum Analysis

## 3. Inspection Image Enhancement Principal

#### 3.1. Discrete Wavelet Transformation (DWT)

#### 3.2. Low Frequency Component Enhancement Based on Improved MSR

#### 3.2.1. Basic Principal of Image Enhancement Based on Retinex Model

_{k}is the kth scale surrounding function and W

_{k}is the corresponding weight factor. The excellent enhancement performance can be achieved by adopting MSR with three different scales (K = 3) according to work of Xue, Gao et al. [29,30].

#### 3.2.2. Implementation of the Low Frequency Component Enhancement Algorithm Based on Improved MSR

#### 3.3. High Frequency Components Enhancement Based on Fuzzy Enhancement

#### 3.3.1. Noise Reduction

#### 3.3.2. Implementation of Local Contrast Enhancement in the High Frequency Components Based on Fuzzy Enhancement

## 4. Experimental Results and Analysis

#### 4.1. Parameters Selection

#### 4.1.1. The Parameters for Improved MSR

#### 4.1.2. The Parameters for Fuzzy Enhancement

#### 4.2. Validation of the Effectiveness of the Proposed Method

#### 4.2.1. Visual Analysis

#### 4.2.2. Image Quality Analysis

_{Befor}and Q

_{After}represent the pre-enhancement and post-enhancement image quality scores under the same image quality assessment method, respectively. The results are shown in the following figures.

#### 4.3. Comparison with Other Methods

#### 4.3.1. Visual Comparison

#### 4.3.2. Quantitative Comparison

- (a)
- Average intensity value represents the overall brightness of the image:$$\mu =\frac{1}{M\times N}{\displaystyle \sum _{x=1}^{M}{\displaystyle \sum _{y=1}^{N}f\left(x,y\right)}}$$
- (b)
- Standard deviation represents the overall contrast of the given image. Higher standard deviation value means more contrast information in the image:$$\sigma =\sqrt{\frac{1}{M\times N}{\displaystyle \sum _{x=1}^{M}{{\displaystyle \sum _{y=1}^{N}\left[f\left(x,y\right)-\mu \right]}}^{2}}}\text{}$$
- (c)
- Mean square error (MSE) and peak signal ratio (PSNR) represent the de-noising performance of the method:$$\begin{array}{l}\mathrm{MSE}=\frac{1}{M\times N}{\displaystyle \sum _{i=0}^{M-1}{\displaystyle \sum _{j=0}^{N-1}{\left(I\left(i,j\right)-K\left(i,j\right)\right)}^{2}}},\\ \mathrm{PSNR}=10\times {\mathrm{log}}_{10}\left({\mathrm{MAX}}_{I}^{2}/\mathrm{MSE}\right)\end{array}$$
- (d)
- Image entropy is an important factor that represents the richness of the information of an image. Higher entropy value means more details in the image, and the entropy of the enhanced image should be larger than that of given image:$$E=-{\displaystyle \sum _{i}^{K}{P}_{i}\times {\mathrm{log}}_{2}{P}_{i}}$$
- (e)
- Average gradient represents the local contrast of the details by considering the intensity difference of pixels. The larger the average gradient value is, the higher the local contrast among the details in the image will be:$$\mathrm{AG}=\frac{1}{\left(M-1\right)\left(N-1\right)}{\displaystyle \sum _{x=1}^{M-1}{\displaystyle \sum _{y=1}^{N-1}\sqrt{\frac{{\left[f\left(x+1,y\right)-f\left(x,y\right)\right]}^{2}+{\left[f\left(x,y+1\right)-f\left(x,y\right)\right]}^{2}}{2}}}}$$

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The cameras and the captured inspection image under uneven illumination. (

**a**) Cameras installation; (

**b**) Inspection image under uneven illumination.

**Figure 2.**(

**a**–

**d**) Sample inspection images under different illumination heterogeneity in the same scene; and (

**e**–

**h**) corresponding spectrum maps to images in (

**a**–

**d**).

**Figure 6.**Gray-scale histogram of: (

**a**) horizontal; (

**b**) vertical; and (

**c**) diagonal wavelet components in high frequency.

**Figure 8.**(

**a**) The original inputl (

**b**) narrow surround σ = 25l (

**c**) medium surround σ = 80; (

**d**) wide surround σ = 100; and (

**e**) MSR output with W

_{k}= 1/3, k = 1, 2, 3. The narrow-surround acts as a high-pass filter to obtain the edge details, but some brightness information is lost. The wide-surround captures the right brightness information, but some detailed information is lost. The MSR is the average of the three renditions.

**Figure 10.**The local contrast enhancement effects under different β: (

**a**) the original image and the output image of proposed method with different parameters; and (

**b**) the enlarged images corresponding to the regions with red box in (

**a**).

**Figure 12.**Overhead ground wire (OGW) images under different illumination condition and its corresponding enhancement results: (

**a**) low light; (

**b**) uneven light and OGW is in the dark area; (

**c**) uneven light and OGW is in the bright area; and (

**d**–

**f**) the enhancement results corresponding to (

**a**–

**c**).

**Figure 13.**Tower head and suspension clamp image under different lighting condition and its corresponding enhancement result: (

**a**) uneven illumination caused by backlighting; (

**b**) backlighting; (

**c**) uniform light; and (

**d**–

**f**) enhancement results corresponding to (

**a**–

**c**).

**Figure 14.**Spacer images and enhancement results: (

**a**–

**c**) three spacer images under cloudy condition; and (

**d**–

**f**) enhancement results corresponding to (

**a**–

**c**).

**Figure 15.**Insulator images under different lighting condition and its corresponding enhancement results: (

**a**) cloudy condition; (

**b**) high light condition; and (

**c**) low contrast with noise. (

**d**–

**f**) enhancement results corresponding to (

**a**–

**c**)

**Figure 16.**Image quality assessment based on two methods: (

**a**) OGW; (

**b**) tower head; (

**c**) spacer; and (

**d**) insulator.

**Figure 17.**The OGW and its enhancement results corresponding to the proposed method and seven other methods.

**Figure 18.**Tower head image and its enhancement results corresponding to the proposed method and seven other methods.

**Figure 19.**Spacer image and its enhancement results corresponding to the proposed method and seven other methods.

**Figure 20.**The insulator image and its enhancement results corresponding to the proposed method and seven other methods.

**Figure 21.**Box plots on the evaluation results in Table 1.

**Table 1.**Performance comparison between the proposed method and seven other methods (the best and the next best results are marked in bold for clarity).

Images | Metrics | Original | HE | CLAHE | SSR | MSR | BFR | HF | UIC | Proposed |
---|---|---|---|---|---|---|---|---|---|---|

A | μ | 29.1978 | 127.9185 | 59.9373 | 109.7300 | 109.2672 | 52.2943 | 41.2363 | 85.3292 | 78.5231 |

σ | 45.6244 | 73.4726 | 62.7341 | 70.0999 | 72.858 | 61.6117 | 33.4113 | 72.4624 | 72.6589 | |

PSNR | 0 | 7.3783 | 16.1613 | 9.1124 | 9.0593 | 18.5812 | 19.7599 | 16.5293 | 17.3363 | |

E | 5.5765 | 7.1255 | 6.8520 | 7.2563 | 7.1274 | 6.7632 | 5.9347 | 7.3687 | 8.52 | |

AG | 11.2459 | 25.6000 | 19.4770 | 24.4279 | 24.7139 | 17.71889 | 10.3822 | 23.5873 | 24.9759 | |

B | μ | 114.2131 | 127.2792 | 118.5694 | 217.3490 | 217.3276 | 173.2557 | 89.3493 | 170.9758 | 170.0026 |

σ | 35.5155 | 75.0662 | 44.8043 | 27.2032 | 27.2031 | 39.5885 | 28.8699 | 48.2586 | 50.2931 | |

PSNR | 0 | 14.8789 | 17.1565 | 7.8022 | 7.8040 | 12.4479 | 17.2273 | 16.7657 | 17.5285 | |

E | 6.79104 | 7.8054 | 7.4964 | 5.9883 | 5.98528 | 6.5478 | 6.7040 | 7.5647 | 7.9810 | |

AG | 3.0168 | 6.5515 | 4.3512 | 2.5193 | 2.5117 | 3.2190 | 3.2947 | 5.4863 | 5.6898 | |

C | μ | 95.9608 | 126.6853 | 114.8822 | 204.8801 | 204.6748 | 166.8592 | 81.0755 | 175.3968 | 164.3482 |

σ | 16.9639 | 76.2246 | 37.6639 | 14.3400 | 14.3057 | 23.0463 | 21.9640 | 36.3856 | 38.5258 | |

PSNR | 0 | 11.1655 | 18.2749 | 7.3770 | 7.3933 | 10.9895 | 21.1130 | 17.1076 | 18.3802 | |

E | 5.6879 | 7.9420 | 7.2475 | 4.9972 | 4.9958 | 5.5791 | 6.21321 | 6.7278 | 8.8295 | |

AG | 5.7872 | 23.8295 | 18.1844 | 4.1298 | 4.1102 | 4.5419 | 6.3697 | 16.7515 | 19.5665 | |

D | μ | 71.4139 | 127.0236 | 107.1109 | 194.9818 | 195.0240 | 143.9296 | 76.5124 | 157.2113 | 148.1063 |

σ | 16.2501 | 75.7446 | 42.4883 | 26.4332 | 26.4856 | 26.7658 | 22.2173 | 44.8245 | 45.2240 | |

PSNR | 0 | 9.6807 | 14.7705 | 6.2544 | 6.2511 | 10.7697 | 24.4966 | 14.4342 | 15.3605 | |

E | 5.7003 | 7.9541 | 7.4366 | 5.9742 | 5.9773 | 5.8995 | 6.3785 | 7.8035 | 8.3831 | |

AG | 6.7750 | 39.9595 | 23.0930 | 8.8554 | 8.8670 | 5.2698 | 8.7855 | 23.0940 | 25.1184 |

Algorithm | HE | CLAHE | SSR | MSR | BFR | HF | UIC | Proposed |
---|---|---|---|---|---|---|---|---|

Time 1 (s) | 0.015 | 0.052 | 0.032 | 0.092 | 0.061 | 0.122 | 0.150 | 0.132 |

Time 2 (s) | 0.120 | 0.424 | 0.220 | 0.842 | 0.660 | 1.241 | 1.526 | 1.250 |

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## Share and Cite

**MDPI and ACS Style**

Ye, X.; Wu, G.; Huang, L.; Fan, F.; Zhang, Y.
Image Enhancement for Inspection of Cable Images Based on Retinex Theory and Fuzzy Enhancement Method in Wavelet Domain. *Symmetry* **2018**, *10*, 570.
https://doi.org/10.3390/sym10110570

**AMA Style**

Ye X, Wu G, Huang L, Fan F, Zhang Y.
Image Enhancement for Inspection of Cable Images Based on Retinex Theory and Fuzzy Enhancement Method in Wavelet Domain. *Symmetry*. 2018; 10(11):570.
https://doi.org/10.3390/sym10110570

**Chicago/Turabian Style**

Ye, Xuhui, Gongping Wu, Le Huang, Fei Fan, and Yongxiang Zhang.
2018. "Image Enhancement for Inspection of Cable Images Based on Retinex Theory and Fuzzy Enhancement Method in Wavelet Domain" *Symmetry* 10, no. 11: 570.
https://doi.org/10.3390/sym10110570