# Entropy and Contrast Enhancement of Infrared Thermal Images Using the Multiscale Top-Hat Transform

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## Abstract

**:**

## 1. Introduction

## 2. Entropy and Contrast in Digital Images

## 3. Enhancement of Thermal Infrared Images

#### 3.1. Classic Top-Hat Transform

#### 3.2. Modified Top-Hat Transform

#### 3.3. How Entropy is Changed by Top-Hat Transform

- The old value g was unique in the region, with a count of 1, hence it disappears from the region and is replaced by value h. No change in entropy occurs because in the old g bin of the histogram the count of 1 becomes 0, and in the new h bin the count of 0 becomes 1; or
- The old value g existed in k > 1 pixels in the region. In this case the count in the g bin decreases to $k-1$, and the count in the h bin increases to 1. The following Lemma shows that this change in the histogram increases the region’s entropy.

**Lemma**

**1.**

**Proof.**

#### 3.4. Proposed Method Using Multiscale Top-Hat Transform

Algorithm 1 Proposed method for TII Enhancement |

Input:I, G, ${G}^{\prime}$, n, $\omega $Output:${I}_{E}$(Enhanced image)Initialization: G, ${G}^{\prime}$ 1: for$i=1$ to n do2: Calculation of top-hat transform. $M{B}_{i}=I-((I\ominus {G}_{i})\oplus {G}_{i}^{\prime})$ (Equation (11)) $M{D}_{i}=((I\oplus {G}_{i})\ominus {G}_{i}^{\prime})-I$ (Equation (12)) 3: Calculation of subtractions from neighboring scales, obtained through the top-hat transform. The top-hat is subtracted with the previous difference, from the first subtraction of the first neighboring top-hat.
$$SNB{S}_{i-1}=\left\{\begin{array}{c}M{B}_{i}-M{B}_{i-1},\phantom{\rule{4.pt}{0ex}}\mathrm{to}\phantom{\rule{4.pt}{0ex}}i=2\\ M{B}_{i}-SNB{S}_{i-2},\phantom{\rule{4.pt}{0ex}}\mathrm{to}\phantom{\rule{4.pt}{0ex}}i>2\end{array}\right.\phantom{\rule{4.pt}{0ex}}(\mathrm{Equation}\phantom{\rule{4.pt}{0ex}}(13))$$
$$SND{S}_{i-1}=\left\{\begin{array}{c}M{D}_{i}-M{D}_{i-1},\phantom{\rule{4.pt}{0ex}}\mathrm{to}\phantom{\rule{4.pt}{0ex}}i=2\\ M{D}_{i}-SND{S}_{i-2},\phantom{\rule{4.pt}{0ex}}\mathrm{to}\phantom{\rule{4.pt}{0ex}}i>2\end{array}\right.\phantom{\rule{4.pt}{0ex}}(\mathrm{Equation}\phantom{\rule{4.pt}{0ex}}(14))$$
4: end for5: Calculation of the maximum values of all the multiple scales obtained. $SMB={\sum}_{i=1}^{n}M{B}_{i}$ (Equation (15)) $SMD={\sum}_{i=1}^{n}M{D}_{i}$ (Equation (16)) $SSNBS={\sum}_{i=1}^{n-1}SNB{S}_{i-1}$ (Equation (17)) $SSNDS={\sum}_{i=1}^{n-1}SND{S}_{i-1}$ (Equation (18)) 6: TII enhancement calculation.The contrast enhancement calculation consists of adding the results of the multiple bright scales to the original image and subtracting the results of the multiple dark scales. ${I}_{E}=I+\omega \times (SMB+SSNBS)-\omega \times (SND+SSNDS)$ (Equation (19)) 7: return ${I}_{E}$ |

## 4. Results and Discussion

- In the first part (Section 4.1) we perform a parameter adjustment to find good parameter values that maximize the entropy of the output image after applying the proposed method.
- Then, in the second part (Section 4.2) we analyze the proposed method per iteration and compare its performance with Multiscale Morphological Infrared Image Enhancement (MMIIE) (mathematical morphology-based multiscale approach) [4].
- Finally, in the last part (Section 4.3), we apply the proposed method and compare the results achieved with the proposed techniques with the following competitive methods from the literature: HE, Contrast Limited Adaptive Histogram Equalization (CLAHE) [51], the method of Kun Liang et al. [6] called IRHE2PL for infrared images, and the MMIIE method for infrared images.

#### 4.1. Parameter Tuning

#### 4.2. Performance of Proposed Method per Iteration

- The Standard Deviation (SD), which quantifies the global contrast of the infrared images, is defined as [16]:$$SD\left(I\right)=\sqrt{\sum _{k=0}^{L-1}{(k-A\left(I\right))}^{2}\times p\left(k\right)},$$
- The metric adopted to measure the signal-to-noise ratio of an image is the PSNR.Given the original infrared image I and the infrared image with enhancement ${I}_{EN}$ where the size of the images is $M\times N$, the PSNR between I and ${I}_{EN}$ is given by [30]:$$PSNR(I,{I}_{E})=10\times lo{g}_{10}{\displaystyle \frac{{(L-1)}^{2}}{MSE(I,{I}_{E})}}.$$The Mean Squared Error (MSE) is defined as:$$MSE(I,{I}_{E})={\displaystyle \frac{1}{M\times N}}\sum _{u=0}^{M-1}\sum _{v=0}^{N-1}{(I(u,v)-{I}_{EN}(u,v))}^{2}.$$
- The Absolute Mean Brightness Error (AMBE) [11], which quantifies the conservation of the mean brightness of the processed image, is given by:$$AMBE(I,{I}_{E})=|A\left(I\right)-A\left({I}_{E}\right)|,$$
- The linear blur index $\gamma $ [4] is used to measure the performance of the infrared image enhancement. It is defined as follows:$$\gamma \left(I\right)={\displaystyle \frac{2}{M\times N}}\sum _{u=1}^{M}\sum _{v=1}^{N}min\{{p}_{uv},(1-{p}_{uv})\},$$$${p}_{uv}=sin[{\displaystyle \frac{\pi}{2}}\times (1-{\displaystyle \frac{I(u,v)}{L-1}})].$$

#### 4.3. Comparison of the Performance of the Proposed Method with State of the Art Methods

#### 4.3.1. Analysis of Methods by Scenes

- E metric: The CLAHE method and the proposed method are the methods that have the best performance in terms of entropy for scenes 1 to 8. However, in scene 9 the CLAHE and MMIIE methods have the best results.
- SD metric: The HE, CLAHE, IRHE2PL methods and the proposed method enhance the contrast of the TII in the 9 scenes. The MMIIE method did not enhance the contrast of scenes 2, 4, 7, 8, and 9. The HE method is the best performing method for all scenes and the proposed method is in second place.
- PSNR metric: The methods that produce the less distortion to TII are the IRHE2PL, the proposed method, and CLAHE.
- AMBE metric: For all scenes, the best method in regards to maintaining the average brightness is the proposed method.
- $\gamma $ metric: The MMIIE method and the proposed method present the best results in terms of blurring.

#### 4.3.2. General Analysis of Methods

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Havens, K.J.; Sharp, E.J. Thermal Imaging Techniques to Survey and Monitor Animals in the Wild: A Methodology; Elsevier: Amsterdam, The Netherlands, 2016. [Google Scholar] [CrossRef]
- Portmann, J.; Lynen, S.; Chli, M.; Siegwart, R. People detection and tracking from aerial thermal views. In Proceedings of the 2014 IEEE International Conference on Robotics and Automation (ICRA), Hong Kong, China, 31 May–7 June 2014; pp. 1794–1800. [Google Scholar]
- Krapels, C.K.; Driggers, C.R.G.; Garcia, C.J.F. Performance of infrared systems in swimmer detection for maritime security. Opt. Express
**2007**, 15, 12296–12305. [Google Scholar] [CrossRef] [PubMed] - Bai, X. Morphological infrared image enhancement based on multi-scale sequential toggle operator using opening and closing as primitives. Infrared Phys. Technol.
**2015**, 68, 143–151. [Google Scholar] [CrossRef] - Bai, X.; Zhou, F.; Xue, B. Infrared image enhancement through contrast enhancement by using multiscale new top-hat transform. Infrared Phys. Technol.
**2011**, 54, 61–69. [Google Scholar] [CrossRef] - Liang, K.; Ma, Y.; Xie, Y.; Zhou, B.; Wang, R. A new adaptive contrast enhancement algorithm for infrared images based on double plateaus histogram equalization. Infrared Phys. Technol.
**2012**, 55, 309–315. [Google Scholar] [CrossRef] - Lin, C.L. An approach to adaptive infrared image enhancement for long-range surveillance. Infrared Phys. Technol.
**2011**, 54, 84–91. [Google Scholar] [CrossRef] - Lai, R.; Yang, Y.T.; Wang, B.J.; Zhou, H.X. A quantitative measure based infrared image enhancement algorithm using plateau histogram. Opt. Commun.
**2010**, 283, 4283–4288. [Google Scholar] [CrossRef] - Li, Y.; Zhang, Y.; Geng, A.; Cao, L.; Chen, J. Infrared image enhancement based on atmospheric scattering model and histogram equalization. Opt. Laser Technol.
**2016**, 83, 99–107. [Google Scholar] [CrossRef] - Yoo, J.H.; Ohm, S.Y.; Chung, M.G. Brightness Preservation and Image Enhancement Based on Maximum Entropy Distribution. In Convergence and Hybrid Information Technology; Springer: Berlin/Heidelberg, Germany, 2012; pp. 365–372. [Google Scholar]
- Aquino-Morínigo, P.B.; Lugo-Solís, F.R.; Pinto-Roa, D.P.; Ayala, H.L.; Noguera, J.L.V. Bi-histogram equalization using two plateau limits. Signal Image Video Process.
**2017**, 11, 857–864. [Google Scholar] [CrossRef] - Kim, Y.T. Contrast enhancement using brightness preserving bi-histogram equalization. IEEE Trans. Consum. Electron.
**1997**, 43, 1–8. [Google Scholar] [CrossRef] - Ooi, C.H.; Kong, N.S.P.; Ibrahim, H. Bi-histogram equalization with a plateau limit for digital image enhancement. IEEE Trans. Consum. Electron.
**2009**, 55, 2072–2080. [Google Scholar] [CrossRef] - Lim, S.H.; Isa, N.A.M.; Ooi, C.H.; Toh, K.K.V. A new histogram equalization method for digital image enhancement and brightness preservation. Signal Image Video Process.
**2013**, 9, 675–689. [Google Scholar] [CrossRef] - Pineda, I.A.B.; Caballero, R.D.M.; Silva, J.J.C.; Román, J.C.M.; Noguera, J.L.V. Quadri-histogram equalization using cutoff limits based on the size of each histogram with preservation of average brightness. Signal Image Video Process.
**2019**. [Google Scholar] [CrossRef] - Román, J.C.M.; Ayala, H.L.; Noguera, J.L.V. Top-Hat transform for enhancement of aerial thermal images. In Proceedings of the 2017 30th SIBGRAPI Conference on Graphics, Patterns and Images (SIBGRAPI), Niteroi, Brazil, 17–20 October 2017; pp. 277–284. [Google Scholar]
- Sun, K.; Sang, N. Enhancement of vascular angiogram by multiscale morphology. In Proceedings of the 1st International Conference on Bioinformatics and Biomedical Engineering (ICBBE 2007), Wuhan, China, 6–8 July 2007; pp. 1311–1313. [Google Scholar]
- Bai, X. Microscopy mineral image enhancement through center operator construction. Appl. Opt.
**2015**, 54, 4678–4688. [Google Scholar] [CrossRef] [PubMed] - Bai, X.; Zhou, F.; Xue, B. Noise-suppressed image enhancement using multiscale top-hat selection transform through region extraction. Appl. Opt.
**2012**, 51, 338–347. [Google Scholar] [CrossRef] [PubMed] - Bai, X.; Liu, H. Edge enhanced morphology for infrared image analysis. Infrared Phys. Technol.
**2017**, 80, 44–57. [Google Scholar] [CrossRef] - Bai, X.; Zhou, F. Analysis of new top-hat transformation and the application for infrared dim small target detection. Pattern Recognit.
**2010**, 43, 2145–2156. [Google Scholar] [CrossRef] - Bai, X.; Zhou, F.; Xue, B. Infrared dim small target enhancement using toggle contrast operator. Infrared Phys. Technol.
**2012**, 55, 177–182. [Google Scholar] [CrossRef] - Bai, X.; Zhou, F. Analysis of different modified top-hat transformations based on structuring element construction. Signal Process.
**2010**, 90, 2999–3003. [Google Scholar] [CrossRef] - Bai, X.; Zhou, F.; Xue, B. Toggle and top-hat based morphological contrast operators. Comput. Electr. Eng.
**2012**, 38, 1196–1204. [Google Scholar] [CrossRef] - Bai, X.; Zhou, F.; Xue, B. Multi-scale toggle operator for constructing image sharpness measure. Opt. Laser Technol.
**2012**, 44, 2004–2014. [Google Scholar] [CrossRef] - Mukhopadhyay, S.; Chanda, B. A multiscale morphological approach to local contrast enhancement. Signal Process.
**2000**, 80, 685–696. [Google Scholar] [CrossRef] [Green Version] - Gonzalez, R.C.; Woods, R.E.; Eddins, S.L. Digital Image Processing Using MATLAB; Pearson-Prentice-Hall: Upper Saddle River, NJ, USA, 2004; Volume 624. [Google Scholar]
- Soille, P. Morphological Image Analysis: Principles and Applications; Springer: Berlin, Germany, 2004. [Google Scholar] [CrossRef]
- Bai, X.; Zhou, F. A unified form of multi-scale top-hat transform based algorithms for image processing. Optik
**2013**, 124, 1614–1619. [Google Scholar] [CrossRef] - Bai, X.; Zhou, F.; Xue, B. Image enhancement using multi scale image features extracted by top-hat transform. Opt. Laser Technol.
**2012**, 44, 328–336. [Google Scholar] [CrossRef] - Liao, M.; Zhao, Y.Q.; Wang, X.H.; Dai, P.S. Retinal vessel enhancement based on multi-scale top-hat transformation and histogram fitting stretching. Opt. Laser Technol.
**2014**, 58, 56–62. [Google Scholar] [CrossRef] - Peng, B.; Wang, Y.; Yang, X. A multiscale morphological approach to local contrast enhancement for ultrasound images. In Proceedings of the 2010 International Conference on Computational and Information Sciences, Chengdu, China, 17–19 December 2010; pp. 1142–1145. [Google Scholar]
- Bai, X. Image enhancement through contrast enlargement using the image regions extracted by multiscale top-hat by reconstruction. Optik
**2013**, 124, 4421–4424. [Google Scholar] [CrossRef] - Bai, X.; Zhou, F.; Xue, B. Image fusion through local feature extraction by using multi-scale top-hat by reconstruction operators. Optik
**2013**, 124, 3198–3203. [Google Scholar] [CrossRef] - Zhao, J.; Zhou, Q.; Chen, Y.; Feng, H.; Xu, Z.; Li, Q. Fusion of visible and infrared images using saliency analysis and detail preserving based image decomposition. Infrared Phys. Technol.
**2013**, 56, 93–99. [Google Scholar] [CrossRef] - Zhu, P.; Ding, L.; Ma, X.; Huang, Z. Fusion of infrared polarization and intensity images based on improved toggle operator. Opt. Laser Technol.
**2018**, 98, 139–151. [Google Scholar] [CrossRef] - Mukhopadhyay, S.; Chanda, B. Multiscale morphological segmentation of gray-scale images. IEEE Trans. Image Process.
**2003**, 12, 533–549. [Google Scholar] [CrossRef] [PubMed] - Ye, B.; Peng, J.x. Small target detection method based on morphology top-hat operator. J. Image Graph.
**2002**, 7, 638–642. [Google Scholar] - Tsai, D.Y.; Lee, Y.; Matsuyama, E. Information entropy measure for evaluation of image quality. J. Dig. Imaging
**2008**, 21, 338–347. [Google Scholar] [CrossRef] [PubMed] - Singh, K.; Kapoor, R. Image enhancement using exposure based sub image histogram equalization. Pattern Recognit. Lett.
**2014**, 36, 10–14. [Google Scholar] [CrossRef] - Ye, Z.; Mohamadian, H.; Pang, S.S.; Iyengar, S. Image contrast enhancement and quantitative measuring of information flow. In Proceedings of the 6th WSEAS International Conference on Information Security and Privacy, Tenerife, Spain, 14–16 December 2007; pp. 172–177. [Google Scholar]
- More, L.G.; Brizuela, M.A.; Ayala, H.L.; Pinto-Roa, D.P.; Noguera, J.L.V. Parameter tuning of CLAHE based on multi-objective optimization to achieve different contrast levels in medical images. In Proceedings of the 2015 IEEE International Conference on Image Processing (ICIP), Quebec City, QC, Canada, 27–30 September 2015; pp. 4644–4648. [Google Scholar]
- Khellaf, A.; Beghdadi, A.; Dupoisot, H. Entropic contrast enhancement. IEEE Trans. Med. Imaging
**1991**, 10, 589–592. [Google Scholar] [CrossRef] [PubMed] - Wang, S.H.; Cheng, H.; Phillips, P.; Zhang, Y.D. Multiple Sclerosis Identification Based on Fractional Fourier Entropy and a Modified Jaya Algorithm. Entropy
**2018**, 20, 254. [Google Scholar] [CrossRef] - Zhang, Y.; Wu, X.; Lu, S.; Wang, H.; Phillips, P.; Wang, S. Smart detection on abnormal breasts in digital mammography based on contrast-limited adaptive histogram equalization and chaotic adaptive real-coded biogeography-based optimization. Simulation
**2016**, 92, 873–885. [Google Scholar] [CrossRef] - Lee, K.; Lee, S. A new framework for measuring 2D and 3D visual information in terms of entropy. IEEE Trans. Circuits Syst. Video Technol.
**2016**, 26, 2015–2027. [Google Scholar] [CrossRef] - Shannon, C.E. A mathematical theory of communication. Bell Syst. Tech. J.
**1948**, 27, 379–423. [Google Scholar] [CrossRef] - Niu, Y.; Wu, X.; Shi, G. Image enhancement by entropy maximization and quantization resolution upconversion. IEEE Trans. Image Process.
**2016**, 25, 4815–4828. [Google Scholar] [CrossRef] - Burger, W.; Burge, M.J. Digital Image Processing: An Algorithmic Introduction Using Java; Springer: London, UK, 2016. [Google Scholar] [CrossRef]
- Dataset. Thermal Infrared Dataset. 2014. Available online: https://projects.asl.ethz.ch/datasets/doku.php?id=ir:iricra2014 (accessed on 1 December 2018).
- Zuiderveld, K. Contrast limited adaptive histogram equalization. In Graphics Gems; Elsevier: Amsterdam, The Netherlands, 1994; pp. 474–485. [Google Scholar] [CrossRef]

**Figure 3.**Loss of information with enhanced contrast. (

**a**) TII enhanced with HE; (

**b**) Histogram of the TII enhanced with HE.

**Figure 5.**Visual results obtained with the proposed method and the configuration of $\omega $ and n. (

**a**) Original TII with $E=6.7893$; (

**b**) TII enhancement with proposed method with $\omega =0.35$, $n=8$ and $E=7.4696$; (

**c**) TII enhancement with proposed method with $\omega =0.45$, $n=7$ and $E=7.4467$.

**Figure 6.**Example of a thermal infrared imaging (TII) to compare the proposed method and Multiscale Morphological Infrared Image Enhancement (MMIIE) method. (

**a**) Original TII with $E=6.8387$ and $SD=31.8204$; (

**b**) Histogram of the original image; (

**c**) TII enhanced with the MMIIE method with $E=6.8619$, $SD=42.5731$, and $AMBE=24.1018$; (

**d**) Histogram of the image enhanced with MMIIE; (

**e**) TII enhanced with the proposed method with $E=7.3629$, $SD=58.8730$, and $AMBE=2.1848$; (

**f**) Histogram of the image enhanced with the proposed method.

**Figure 7.**(

**a**) Original TII 449.png, $E=7.2210$, $SD=53.1827$; (

**b**) TII enhanced with IRHE2PL method, $E=7.2058$, $SD=53.3164$, and $PSNR=48.0940$ and (

**c**) TII enhanced with the proposed method, $E=7.2411$, $SD=62.8887$, and $PSNR=20.6578$.

**Figure 8.**An example of comparison of a TII with a dark background. (

**a**) Original TII, (

**b**) TII enhanced with HE method, (

**c**) TII enhanced with Contrast Limited Adaptive Histogram Equalization (CLAHE) method, (

**d**) TII enhanced with IRHE2PL method, (

**e**) TII enhanced with MMIIE method, and (

**f**) TII enhanced with the proposed method.

**Figure 9.**This example shows a TII with a dark background and semi-bright objectives. (

**a**) original TII, (

**b**) TII enhanced with HE, (

**c**) TII enhanced with CLAHE, (

**d**) TII enhanced with IRHE2PL, (

**e**) TII enhanced with MMIIE, and (

**f**) TII enhanced with the proposed method.

**Figure 10.**TII with improved contrast and detail, (

**a**) the Original TII with $E=6.9334$ and $SD=58.24$ and (

**b**) the TII enhanced with the proposed method with $E=7.5783$ and $SD=70.7615$

Parameter | Value(s) |
---|---|

n | $[2,10]$ |

$\omega $ | $[0,1]$ |

G | $3\times 3$ |

${G}^{\prime}$ | $15\times 15$ |

**Table 2.**Entropy values of the enhanced thermal infrared imaging (TII) obtained by the proposed method with parameters $\omega $ and n.

$\mathit{\omega}$ | n | ||||||||
---|---|---|---|---|---|---|---|---|---|

2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |

0.05 | 6.5931 | 6.5962 | 6.6041 | 6.6188 | 6.6396 | 6.6656 | 6.6950 | 6.7271 | 6.7607 |

0.10 | 6.5971 | 6.6120 | 6.6394 | 6.6777 | 6.7224 | 6.7696 | 6.8174 | 6.8658 | 6.9129 |

0.15 | 6.6037 | 6.6315 | 6.6756 | 6.7326 | 6.7900 | 6.8502 | 6.9100 | 6.9653 | 7.0099 |

0.20 | 6.6145 | 6.6577 | 6.7190 | 6.7861 | 6.8548 | 6.9228 | 6.9848 | 7.0326 | 7.0593 |

0.25 | 6.6242 | 6.6821 | 6.7540 | 6.8316 | 6.9081 | 6.9788 | 7.0349 | 7.0661 | 7.0648 |

0.30 | 6.6293 | 6.6970 | 6.7790 | 6.8678 | 6.9498 | 7.0185 | 7.0633 | 7.0702 | 7.0348 |

0.35 | 6.6430 | 6.7217 | 6.8089 | 6.9025 | 6.9851 | 7.0475 | 7.0740 | 7.0519 | 6.9828 |

0.40 | 6.6518 | 6.7420 | 6.8398 | 6.9380 | 7.0181 | 7.0673 | 7.0688 | 7.0161 | 6.9169 |

0.45 | 6.6568 | 6.7545 | 6.8607 | 6.9637 | 7.0394 | 7.0735 | 7.0505 | 6.9706 | 6.8448 |

0.50 | 6.6806 | 6.7872 | 6.8957 | 6.9957 | 7.0596 | 7.0726 | 7.0225 | 6.9165 | 6.7668 |

0.55 | 6.6824 | 6.7928 | 6.9068 | 7.0085 | 7.0647 | 7.0610 | 6.9900 | 6.8619 | 6.6915 |

0.60 | 6.6914 | 6.8113 | 6.9314 | 7.0295 | 7.0702 | 7.0450 | 6.9516 | 6.8011 | 6.6111 |

0.65 | 6.6945 | 6.8201 | 6.9451 | 7.0404 | 7.0682 | 7.0249 | 6.9112 | 6.7406 | 6.5330 |

0.70 | 6.7066 | 6.8408 | 6.9655 | 7.0516 | 7.0631 | 7.0010 | 6.8676 | 6.6786 | 6.4556 |

0.75 | 6.7161 | 6.8588 | 6.9835 | 7.0602 | 7.0550 | 6.9745 | 6.8216 | 6.6152 | 6.3778 |

0.80 | 6.7221 | 6.8707 | 6.9979 | 7.0639 | 7.0433 | 6.9462 | 6.7747 | 6.5531 | 6.3032 |

0.85 | 6.7259 | 6.8791 | 7.0077 | 7.0650 | 7.0303 | 6.9167 | 6.7289 | 6.4929 | 6.2319 |

0.90 | 6.7309 | 6.8906 | 7.0183 | 7.0641 | 7.0140 | 6.8843 | 6.6802 | 6.4311 | 6.1612 |

0.95 | 6.7326 | 6.8959 | 7.0235 | 7.0604 | 6.9973 | 6.8515 | 6.6320 | 6.3702 | 6.0927 |

1.00 | 6.7791 | 6.9368 | 7.0460 | 7.0610 | 6.9780 | 6.8134 | 6.5783 | 6.3055 | 6.0210 |

**Table 3.**Results achieved with the proposed method and Multiscale Morphological Infrared Image Enhancement (MMIIE) method.

n | Proposed Method | MMIIE | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

E | SD | PSNR | AMBE | $\mathit{\gamma}$ | Time (ms) | E | SD | PSNR | AMBE | $\mathit{\gamma}$ | Time (ms) | |

2 | 6.643 | 40.835 | 40.417 | 0.129 | 0.332 | 2328 | 6.324 | 30.247 | 16.236 | 38.072 | 0.194 | 454 |

3 | 6.722 | 41.969 | 33.564 | 0.286 | 0.320 | 3752 | 6.447 | 32.069 | 16.176 | 37.775 | 0.193 | 902 |

4 | 6.809 | 43.632 | 29.256 | 0.466 | 0.311 | 6719 | 6.441 | 33.016 | 16.211 | 37.528 | 0.192 | 1605 |

5 | 6.902 | 45.854 | 26.023 | 0.714 | 0.301 | 10,629 | 6.519 | 34.438 | 16.204 | 37.193 | 0.193 | 2759 |

6 | 6.985 | 48.556 | 23.509 | 1.107 | 0.293 | 11,947 | 6.515 | 35.486 | 16.216 | 36.902 | 0.194 | 4770 |

7 | 7.047 | 51.749 | 21.434 | 1.636 | 0.286 | 16,429 | 6.570 | 36.798 | 16.177 | 36.580 | 0.195 | 7187 |

8 | 7.074 | 55.353 | 19.693 | 2.299 | 0.281 | 19,979 | 6.565 | 37.558 | 16.194 | 36.318 | 0.196 | 9255 |

9 | 7.052 | 59.216 | 18.219 | 3.034 | 0.275 | 20,176 | 6.612 | 38.453 | 16.178 | 36.093 | 0.197 | 18,318 |

10 | 6.983 | 63.111 | 16.980 | 3.830 | 0.268 | 21,527 | 6.604 | 39.017 | 16.201 | 35.884 | 0.197 | 20,003 |

Methods | Percentage of Images Improved (%) |
---|---|

HE | 98.89% |

CLAHE | 82.67% |

IRHE2PL | 90.22% |

MMIIE | 47.56% |

Proposed method | 100% |

Methods | E | SD | PSNR | AMBE | $\mathit{\gamma}$ | |
---|---|---|---|---|---|---|

Scene 1 | I | 6.814 | 32.336 | - | - | 0.284 |

HE | 6.596 | 73.420 | 11.543 | 48.519 | 0.406 | |

CLAHE | 7.557 | 50.808 | 15.984 | 24.259 | 0.401 | |

IRHE2PL | 6.814 | 36.776 | 29.603 | 7.065 | 0.293 | |

MMIIE | 6.910 | 43.573 | 17.005 | 25.392 | 0.164 | |

Proposed method | 7.418 | 60.136 | 16.767 | 1.887 | 0.273 | |

Scene 2 | I | 7.039 | 55.330 | - | - | 0.454 |

HE | 6.844 | 73.364 | 20.479 | 3.101 | 0.400 | |

CLAHE | 7.500 | 53.721 | 21.237 | 1.657 | 0.488 | |

IRHE2PL | 7.036 | 58.604 | 33.310 | 6.802 | 0.453 | |

MMIIE | 7.038 | 45.486 | 13.085 | 48.345 | 0.273 | |

Proposed method | 7.601 | 69.425 | 18.215 | 1.534 | 0.419 | |

Scene 3 | I | 5.945 | 18.269 | - | - | 0.477 |

HE | 5.881 | 73.063 | 10.789 | 47.807 | 0.408 | |

CLAHE | 6.970 | 32.154 | 19.839 | 18.275 | 0.485 | |

IRHE2PL | 5.945 | 42.197 | 20.011 | 13.270 | 0.326 | |

MMIIE | 6.133 | 20.900 | 17.288 | 32.819 | 0.127 | |

Proposed method | 6.826 | 30.332 | 23.205 | 0.136 | 0.273 | |

Scene 4 | I | 6.808 | 41.521 | - | - | 0.342 |

HE | 6.642 | 73.148 | 12.977 | 41.972 | 0.407 | |

CLAHE | 7.482 | 48.135 | 18.560 | 19.816 | 0.422 | |

IRHE2PL | 6.808 | 56.144 | 22.617 | 11.306 | 0.313 | |

MMIIE | 6.848 | 35.941 | 16.106 | 33.095 | 0.149 | |

Proposed method | 7.566 | 56.723 | 19.019 | 1.328 | 0.312 | |

Scene 5 | I | 7.052 | 40.839 | - | - | 0.356 |

HE | 6.901 | 73.319 | 14.793 | 32.298 | 0.404 | |

CLAHE | 7.620 | 50.630 | 17.786 | 15.352 | 0.433 | |

IRHE2PL | 7.048 | 45.807 | 32.631 | 11.444 | 0.307 | |

MMIIE | 7.025 | 44.123 | 15.660 | 34.956 | 0.173 | |

Proposed method | 7.505 | 61.669 | 17.599 | 2.584 | 0.317 | |

Scene 6 | I | 6.272 | 24.626 | - | - | 0.152 |

HE | 6.158 | 72.882 | 8.091 | 86.636 | 0.408 | |

CLAHE | 7.200 | 42.379 | 16.477 | 31.714 | 0.263 | |

IRHE2PL | 6.272 | 37.308 | 21.316 | 17.733 | 0.179 | |

MMIIE | 6.035 | 28.802 | 21.602 | 15.389 | 0.048 | |

Proposed method | 6.702 | 40.545 | 20.893 | 2.284 | 0.114 | |

Scene 7 | I | 6.990 | 67.015 | - | - | 0.348 |

HE | 6.783 | 73.516 | 18.535 | 19.921 | 0.398 | |

CLAHE | 7.548 | 66.298 | 19.828 | 7.159 | 0.400 | |

IRHE2PL | 6.987 | 75.173 | 33.982 | 14.009 | 0.295 | |

MMIIE | 7.125 | 53.062 | 12.017 | 54.459 | 0.327 | |

Proposed method | 7.204 | 75.462 | 19.735 | 1.405 | 0.323 | |

Scene 8 | I | 6.219 | 28.522 | - | - | 0.237 |

HE | 6.131 | 72.805 | 8.042 | 89.033 | 0.409 | |

CLAHE | 7.134 | 41.543 | 16.828 | 31.090 | 0.309 | |

IRHE2PL | 6.219 | 62.031 | 11.319 | 60.173 | 0.334 | |

MMIIE | 5.952 | 23.883 | 21.792 | 14.567 | 0.077 | |

Proposed method | 6.589 | 37.486 | 23.014 | 2.426 | 0.118 | |

Scene 9 | I | 6.191 | 53.458 | - | - | 0.448 |

HE | 6.001 | 80.909 | 13.975 | 41.396 | 0.329 | |

CLAHE | 6.459 | 59.638 | 19.045 | 13.075 | 0.440 | |

IRHE2PL | 6.188 | 67.644 | 30.537 | 10.979 | 0.386 | |

MMIIE | 6.438 | 50.305 | 11.052 | 65.813 | 0.433 | |

Proposed method | 6.254 | 66.401 | 18.794 | 7.105 | 0.378 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mello Román, J.C.; Vázquez Noguera, J.L.; Legal-Ayala, H.; Pinto-Roa, D.P.; Gomez-Guerrero, S.; García Torres, M.
Entropy and Contrast Enhancement of Infrared Thermal Images Using the Multiscale Top-Hat Transform. *Entropy* **2019**, *21*, 244.
https://doi.org/10.3390/e21030244

**AMA Style**

Mello Román JC, Vázquez Noguera JL, Legal-Ayala H, Pinto-Roa DP, Gomez-Guerrero S, García Torres M.
Entropy and Contrast Enhancement of Infrared Thermal Images Using the Multiscale Top-Hat Transform. *Entropy*. 2019; 21(3):244.
https://doi.org/10.3390/e21030244

**Chicago/Turabian Style**

Mello Román, Julio César, José Luis Vázquez Noguera, Horacio Legal-Ayala, Diego P. Pinto-Roa, Santiago Gomez-Guerrero, and Miguel García Torres.
2019. "Entropy and Contrast Enhancement of Infrared Thermal Images Using the Multiscale Top-Hat Transform" *Entropy* 21, no. 3: 244.
https://doi.org/10.3390/e21030244