# A Nonuniformity Correction Method Based on 1D Guided Filtering and Linear Fitting for High-Resolution Infrared Scan Images

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## Abstract

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## 1. Introduction

## 2. Proposed Approach

#### 2.1. Nonuniformity Correction Model Based on 1D Guided Image Filtering

#### 2.2. Linear Fitting Correction Model Based on Guided Filtering

#### 2.3. Proposed Workflow of the Proposed Method for Strip Nonuniformity Correction

- A portion of the raw infrared scan image is intercepted and used to calculate the linear correction coefficients. After the experiments (see Section 3.2), the linear correction coefficients are calculated using the 1500 image columns chosen for this work.
- The selected image is used to eliminate the horizontal strip caused by nonuniformity with the guided filtering model proposed in Section 2.1.
- We use the linear fitting model based on guided filtering proposed in Section 2.2 to calculate the linear correction coefficients $a(i),b(i)$.
- The whole frame of the infrared image is corrected using linear coefficients as shown in the Formula (12).

## 3. Experiments and Comparison

#### 3.1. Noise Modeling Analysis

#### 3.2. Image Correction Effect of Image Size Used in Linear Fitting Model

#### 3.3. Image Correction Effect of Noise

#### 3.4. Qualitative Analysis of the Correction Effect of the Algorithms

**Figure 8.**Nonuniformity correction effect of Cao [16], Wang [17], Wang [18], and our proposed algorithm. In order to better show the nonuniformity correction effect of each algorithm, this figure selects local magnified images of building, bus, and stairs to compare the effect of each algorithm. The parts in the red circle in the images are the parts where the non-uniform correction results of the contrast algorithm are not good.

#### 3.5. Quantitative Analysis of the Nonuniformity Correction Effect of the Algorithms

#### 3.6. Computational Time

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Schulz, M.; Caldwell, L. Nonuniformity correction and correctability of infrared focal plane arrays. Infrared Phys. Technol.
**1995**, 36, 763–777. [Google Scholar] [CrossRef] - Riou, O.; Berrebi, S.; Bremond, P. Nonuniformity correction and thermal drift compensation of thermal infrared camera. In Defense and Security, International Society for Optics and Photonics; SPIE: Bellingham, WA, USA, 2004; pp. 294–302. [Google Scholar]
- Song, S.; Zhai, X. Research on non-uniformity correction based on blackbody calibration. In Proceedings of the 2020 IEEE 4th Information Technology, Networking, Electronic and Automation Control Conference (ITNEC), Chongqing, China, 12–14 June 2020; Volume 1, pp. 2146–2150. [Google Scholar]
- Vollmer, M.; Klaus-Peter, M.A. Infrared Thermal Imaging: Fundamentals, Research and Applications; Wiley-VCH: Hoboken, NJ, USA, 2017. [Google Scholar]
- Teena, M.; Manickavasagan, A. Thermal infrared imaging. In Imaging with Electromagnetic Spectrum; Springer: Berlin/Heidelberg, Germany, 2014; pp. 147–173. [Google Scholar]
- Scribner, D.A.; Kruer, M.R.; Gridley, J.C.; Sarkady, K. Physical Limitations to Nonuniformity Correction in Focal Plane Arrays. SPIE
**1988**, 865, 185–201. [Google Scholar] - Kim, S. Two-point correction and minimum filter-based nonuniformity correction for scan-based aerial infrared cameras. Opt. Eng.
**2012**, 51, 106401. [Google Scholar] [CrossRef] - Hu, X. Study on nonuniformity and calibration method of infrared focal plane detector. Infrared Laser Eng.
**1999**, 28, 9–12. [Google Scholar] - Shi, Y.; Zhang, T.; Cao, Z. A New Piecewise Approach for Nonuniformity Correction in IRFPA. Int. J. Infrared Millim. Waves
**2004**, 25, 959–972. [Google Scholar] [CrossRef] - Boutemedjet, A.; Deng, C.; Zhao, B. Robust Approach for Nonuniformity Correction in Infrared Focal Plane Array. Sensors
**2016**, 16, 1890. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Sheng, M.; Xie, J.; Fu, Z. Calibration-based NUC Method in Real-time Based on IRFPA. Phys. Procedia
**2011**, 22, 372–380. [Google Scholar] [CrossRef] [Green Version] - Zhu, R.; Wang, C.; Wei, Q.; Jia, H.; Zhou, W. Development of nonuniformity correction system for infrared detector. Infrared Laser Eng.
**2013**, 42, 1669–1673. [Google Scholar] - Tendero, Y.; Landeau, S.; Gilles, J. Non-uniformity Correction of Infrared Images by Midway Equalization. Image Process. Line
**2012**, 2012, 134–146. Available online: http://demo.ipol.im/demo/glmtmire/ (accessed on 12 July 2012). [CrossRef] [Green Version] - He, K.; Sun, J.; Tang, X. Guided image filtering. IEEE Trans. Pattern Anal. Mach. Intell.
**2012**, 35, 1397–1409. [Google Scholar] [CrossRef] - Cao, Y.; Yang, M.Y.; Tisse, C.-L. Effective Strip Noise Removal for Low-Textured Infrared Images Based on 1-D Guided Filtering. IEEE Trans. Circuits Syst. Video Technol.
**2016**, 26, 2176–2188. [Google Scholar] [CrossRef] - Cao, Y.; He, Z.; Yang, J.; Ye, X.; Cao, Y. A multi-scale non-uniformity correction method based on wavelet decomposition and guided filtering for uncooled long wave infrared camera. Signal Process. Image Commun.
**2018**, 60, 13–21. [Google Scholar] [CrossRef] - Wang, E.; Jiang, P.; Hou, X.; Zhu, Y.; Peng, L. Infrared stripe correction algorithm based on wavelet analysis and gradient equalization. Appl. Sci.
**2019**, 9, 1993. [Google Scholar] [CrossRef] [Green Version] - Wang, E.; Jiang, P.; Li, X.; Cao, H. Infrared stripe correction algorithm based on wavelet decomposition and total variation-guided filtering. J. Eur. Opt.-Soc.-Rapid Publ.
**2020**, 16, 1–12. [Google Scholar] [CrossRef] [Green Version] - Hardie, R.C.; Hayat, M.M.; Armstrong, E.; Yasuda, B. Scene-based nonuniformity correction with video sequences and registration. Appl. Opt.
**2000**, 39, 1241–1250. [Google Scholar] [CrossRef] - Ratliff, B.M.; Hayat, M.M.; Hardie, R.C. An algebraic algorithm for nonuniformity correction in focal-plane arrays. J. Opt. Soc. Am. Opt. Image Sci. Vis.
**2002**, 19, 1737–1747. [Google Scholar] [CrossRef] - Zuo, C.; Chen, Q.; Gu, G.; Sui, X.; Ren, J. Improved interframe registration based nonuniformity correction for focal plane arrays. Infrared Phys. Technol.
**2012**, 55, 263–269. [Google Scholar] [CrossRef] - Abbass, M.Y.; Sadic, N.; Ashiba, H.I.; Hassan, E.S.; El-Dolil, S.; Soliman, N.F.; Algarni, A.D.; Alabdulkreem, E.A.; Algarni, F.; El-Banby, G.M.; et al. An Efficient Technique for Non-Uniformity Correction of Infrared Video Sequences with Histogram Matching. J. Electr. Eng. Technol.
**2022**, 17, 2971–2983. [Google Scholar] [CrossRef] - Ashiba, H.I.; Sadic, N.; Hassan, E.S.; El-Dolil, S.; Abd El-Samie, F.E. New Proposed Algorithms for Infrared Video Sequences Non-uniformity Correction. Wirel. Pers. Commun.
**2022**, 126, 1051–1073. [Google Scholar] [CrossRef] - Zhang, X.; Li, H.; Hou, J.; Zhao, D.; Zhou, H.; Zhang, J.; Zhang, Z.; Cheng, K. Non-uniformity correction algorithm based on improved neural network. Seventh Symp. Nov. Photoelectron. Detect. Technol. Appl. Spie
**2021**, 11763, 717–726. [Google Scholar] - Li, Y.; Liu, N.; Xu, J. Infrared scene-based non-uniformity correction based on deep learning model. Optik
**2021**, 227, 165899. [Google Scholar] [CrossRef] - Guan, J.; Lai, R.; Xiong, A.; Liu, Z.; Gu, L. Fixed pattern noise reduction for infrared images based on cascade residual attention CNN. Neurocomputing
**2020**, 377, 301–313. [Google Scholar] [CrossRef] [Green Version] - Luo, Q.; Gao, B.; Woo, W.L.; Yang, Y. Temporal and spatial deep learning network for infrared thermal defect detection. NDT Int.
**2019**, 108, 102164. [Google Scholar] [CrossRef] - Tomasi, C.; Manduchi, R. Bilateral filtering for gray and color images. In Proceedings of the Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271), Bombay, India, 7 January 1998; pp. 839–846. [Google Scholar]
- Lu, C.H. Stripe non-uniformity correction of infrared images using parameter estimation. Infrared Phys. Technol.
**2020**, 107, 103313. [Google Scholar] [CrossRef]

**Figure 1.**Non-uniform correction effect of real infrared scanning image. (

**a**) Raw infrared scanning image. (

**b**) Non-uniform correction results of our proposed algorithm.

**Figure 4.**Infrared scan image with the addition of Gaussian noise. Due to the very high resolution of the infrared column scan image (3053 × 55,000), only a portion of the scanned image (3053 × 8192) is displayed in this figure. The image within the red border is the image utilized for the linear fitting model in Section 2.1, with a resolution of 3053 × 1500 pixels.

**Figure 6.**Image after adding analog stripes (

**a2**) stairs (

**b2**) people (

**c2**) hands (

**d2**) bus (

**e2**) buildings.

**Figure 7.**Nonuniformity correction effect of Cao [16], Wang [17], and Wang [18] with respect to distinct wavelet bases. The wavelet bases include “haar”, “db4”, and “sym8” wavelets. The image “bus” is added with stimulated nonuniformity noise. In order to highlight the correction effect of the algorithm on horizontal stripes and the fuzzy degree of the algorithm on image texture details, the images within the red border are enlarged.

**Figure 9.**Real infrared focal plane linear array non-uniform correction of Cao [16], Wang [17], Wang [18], and our proposed algorithm. The resolution of the presented image is 1024 × 4096 due to the high resolution of the scanned image, as shown in this figure, in order to more accurately compare the denoising effect.

**Figure 10.**PSNR results of Cao [16], Wang [17], Wang [18], and our method. In order to verify the universality of the nonuniformity correction effect of the algorithm in this paper, 50 images are selected at random from the FLIRADAS dataset, and Gaussian cross-stripe noise with different variance $\sigma $ is added as shown in Equation (15). The mean PSNR values of the corrected images are calculated using various algorithms to create a relationship curve, as depicted in this figure.

Images\Colums | 500 | 1000 | 1500 | 2000 | 2500 |

PSNR | 39.79 | 40.33 | 40.76 | 40.78 | 40.74 |

Variance | 25 | 36 | 49 | 64 | 81 | 100 | 121 | 144 | 169 | 196 | 225 |

PSNR | 43.90 | 44.02 | 44.14 | 44.12 | 44.17 | 44.12 | 43.79 | 43.93 | 44.03 | 43.55 | 43.41 |

Sequence\Method | Cao [16] | Wang [17] | Wang [18] | Proposed Method |
---|---|---|---|---|

bus | 40.16 | 41.18 | 31.90 | 46.24 |

people | 40.80 | 42.72 | 36.19 | 45.30 |

building | 42.35 | 43.48 | 39.17 | 47.20 |

hand | 38.49 | 44.48 | 43.21 | 46.65 |

stairs | 34.78 | 38.19 | 29.77 | 38.98 |

dataset | 39.85 | 42.84 | 34.79 | 45.74 |

Sequence\Method | Original | Cao [16] | Wang [17] | Wang [18] | Proposed Method |
---|---|---|---|---|---|

bus | 0.0741 | 0.0765 | 0.0787 | 0.0652 | 0.0740 |

people | 0.0942 | 0.0962 | 0.0975 | 0.0863 | 0.0943 |

building | 0.0621 | 0.0646 | 0.0662 | 0.0591 | 0.0623 |

hand | 0.0877 | 0.0939 | 0.0936 | 0.0868 | 0.0891 |

stairs | 0.0977 | 0.1009 | 0.1045 | 0.0939 | 0.0984 |

dataset | 0.0834 | 0.0851 | 0.0876 | 0.0786 | 0.0841 |

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**MDPI and ACS Style**

Li, B.; Chen, W.; Zhang, Y.
A Nonuniformity Correction Method Based on 1D Guided Filtering and Linear Fitting for High-Resolution Infrared Scan Images. *Appl. Sci.* **2023**, *13*, 3890.
https://doi.org/10.3390/app13063890

**AMA Style**

Li B, Chen W, Zhang Y.
A Nonuniformity Correction Method Based on 1D Guided Filtering and Linear Fitting for High-Resolution Infrared Scan Images. *Applied Sciences*. 2023; 13(6):3890.
https://doi.org/10.3390/app13063890

**Chicago/Turabian Style**

Li, Bohan, Weicong Chen, and Yong Zhang.
2023. "A Nonuniformity Correction Method Based on 1D Guided Filtering and Linear Fitting for High-Resolution Infrared Scan Images" *Applied Sciences* 13, no. 6: 3890.
https://doi.org/10.3390/app13063890