Controllable Brightness Enhancement of the Soil Image Based on Weighted Gaussian Subtraction Fitting

Shaohua ZENG; Bingyu ZHAO; Shuai WANG; Yanan CHEN; Deli ZHU

doi:10.3788/gzxb20225104.0410005

Acta Photonica Sinica, Volume. 51, Issue 4, 0410005(2022)

Controllable Brightness Enhancement of the Soil Image Based on Weighted Gaussian Subtraction Fitting

Shaohua ZENG1...2,*, Bingyu ZHAO1,2, Shuai WANG3, Yanan CHEN4, and Deli ZHU12 |Show fewer author(s)

Author Affiliations

¹College of Computer and Information Science，Chongqing Normal University，Chongqing 401331，China

²Chongqing Research Center on Engineer Technology of Digital Agricultural & Services，Chongqing 401331，China

³Chongqing Master Station of Agricultural Technology Promotion，Chongqing 400014，China

⁴Chongqing Wanzhou District Station of Soil Fertilizer and Agricultural Ecological Protection，Chongqing 404199，China

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Abstract Get PDF(in Chinese)

Figures & Tables(22)

Fig. 1. The histogram analysis of Y component（brightness）of soil image

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Fig. 2. Gaussian fitting of the left local region of soil image Y component histogram

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Fig. 3. The process of weighted Gaussian subtractive fittings of soil image Y component（brightness）histogram

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Fig. 4. Converting sub-images from low to high brightness on dataset 1（No.3 group）with different algorithms

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Fig. 5. Converting sub-images from high to low brightness on dataset 1（No.7 group）with different algorithms

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Fig. 6. Converting sub-images from low to high brightness in experiment 5（No.5 group）

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Fig. 7. Converting sub-images from low to high brightness in experiment 6（No.9 group）

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Fig. 8. Controllable brightness enhancement of soil image converted to high brightness in experiment 7（No.6 group）

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Fig. 9. Controllable brightness enhancement of soil image converted to low brightness in experiment 7（No.8 group）

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Fig. 10. The histogram of iterations of the weighted Gaussian subtraction fit

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Table 0. [in Chinese]

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Table 0. [in Chinese]

输入	加权高斯减法拟合曲线，土壤图像U、V分量
输出	增强RGB图像
过程	Step1：用式（17）和式（18）计算原始的亮度值 $μ_{o r g}$ ； Step2：用式（19）计算亮度差值 $Δ μ$ ； Step3：用式（20）和式（21）计算增强图像的期望概率密度 $P_{t a r} (y)$ ； Step4：用式（22）计算原始图像累积分布 $C_{o r g} (y)$ ； Step5：用式（23）和式（24）计算增强图像期望累积分布 $C_{t a r} (y)$ ； Step6：用式（25）计算新灰度级 $y^{'}$ ； Step7：用式（26）计算增强图像Y分量增强比例 $γ$ ； Step8：用式（27）和式（28），计算U、V分量的增强结果 $u_{n e w}$ 、 $v_{n e w}$ ，并进行RGB转化，获得增强RGB图像。

Table 0. [in Chinese]

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Table 0. [in Chinese]

输入	土壤图像Y分量
输出	加权高斯减法拟合曲线
过程	Step1：用式（1）计算土壤图像 $Y$ 分量各灰度级概率密度 $P_{o r g} (y)$ ； Step2：令 $P_{o r g} (y)$ 为剩余待拟合直方图 $h^{(0)} (y)$ ； Step3：repeat｛ Step3-1：根据式（7）和式（8）设置参数 $b^{(t)}$ 的搜索区间 $[b_{1}^{(t)}, b_{2}^{(t)}]$ ； Step3-2：根据式（9）和式（10）设置参数 $a^{(t)}$ 的搜索区间 $[a_{1}^{(t)}, a_{2}^{(t)}]$ ； Step3-3：根据式（11）和式（12）设置参数 $c^{(t)}$ 的搜索区间 $[c_{1}^{(t)}, c_{2}^{(t)}]$ ； Step3-4：依据式（5），循环搜索 $h^{(t)} (y)$ 左局部区域的高斯拟合优化解，获得本次高斯拟合参数 $a^{(t)}$ 、 $b^{(t)}$ 、 $c^{(t)}$ ； Step3-5：计算剩余待拟合直方图 $h^{(t + 1)} (y)$ ，并用式（13）计算拟合剩余差和 $s$ ；｝until（满足 $s \leq 0.01$ ） Step4：用式（16）计算式（14）加权高斯减法拟合曲线 $f (y)$ 。

Table 1. Accuracy of converting sub-images from low to high brightness on dataset 1（No.3 group）with different algorithms

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Table 1. Accuracy of converting sub-images from low to high brightness on dataset 1（No.3 group）with different algorithms

Sub-image

Algorithms

{\bar{d}}_{y}

D (d_{y})

{\bar{d}}_{r}

{\bar{d}}_{g}

{\bar{d}}_{b}

\frac{1}{3} {\bar{d}}_{c}

\frac{1}{3} D (d_{c})

No.3-1

1-D HS

2-D HS

Ours

11.645 1

11.429 7

10.405 9

14.350 5

14.352 6

13.301 7

12.216 8

11.966 9

11.045 4

11.541 0

11.366 8

10.361 6

11.941 0

11.621 2

10.306 6

11.899 6

11.651 6

10.571 2

14.257 2

14.279 0

13.264 8

No.3-2

1-D HS

2-D HS

Ours

12.214 8

12.147 7

10.868 4

15.602 8

15.515 2

13.551 7

12.107 8

11.983 9

10.519 8

12.335 3

12.280 7

11.055 4

12.755 8

12.760 5

11.581 7

12.399 6

12.341 7

11.052 3

15.649 3

15.561 9

13.633 8

No.3-3

1-D HS

2-D HS

Ours

12.873 8

12.796 7

11.445 7

16.330 7

16.229 5

14.607 8

13.680 9

13.543 0

12.681 7

12.983 8

12.932 9

11.800 3

13.046 9

13.001 7

11.683 6

13.237 2

13.159 2

12.055 2

16.346 8

16.247 8

14.609 7

Average

1-D HS

2-D HS

Ours

12.244 6

12.124 7

10.906 7

15.428 0

15.365 8

13.820 4

12.668 5

12.498 0

11.415 6

12.286 7

12.193 5

11.072 4

12.581 3

12.461 1

11.190 6

12.512 2

12.384 2

11.226 2

15.417 7

15.362 9

13.837 8

Table 2. Accuracy of converting sub-images from low to high brightness on dataset 1 with different algorithms

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Table 2. Accuracy of converting sub-images from low to high brightness on dataset 1 with different algorithms

1-D HS

2-D HS

Ours

13.468 3

13.343 1

11.682 1

16.575 2

16.530 4

14.827 3

13.922 3

13.772 1

12.264 1

13.412 8

13.306 6

11.642 5

13.536 9

13.396 5

11.611 5

13.624 0

13.491 7

11.839 4

16.535 3

16.494 9

14.803 2

1-D HS

2-D HS

Ours

14.021 4

13.8600

12.167 9

17.708 9

17.523 5

15.226 3

14.728 4

14.505 5

13.096 4

14.049 4

13.911 9

12.366 2

14.324 6

14.206 4

12.779 3

14.367 5

14.207 9

12.747 3

17.725 0

17.540 2

15.264 3

1-D HS

2-D HS

Ours

14.827 9

14.555 5

12.024 0

18.108 0

17.942 0

15.047 3

15.555 4

15.221 3

12.872 7

14.756 4

14.518 1

12.047 0

14.993 2

14.732 5

12.372 1

15.101 7

14.823 9

12.430 6

18.038 4

17.881 5

15.020 9

1-D HS

2-D HS

Ours

13.220 0

12.979 1

10.515 8

16.066 6

15.940 7

13.233 5

13.681 7

13.428 1

11.094 9

13.193 0

12.968 9

10.509 1

13.099 1

12.827 7

10.478 2

13.324 6

13.074 9

10.694 1

15.977 4

15.859 5

13.176 0

1-D HS

2-D HS

Ours

14.253 5

14.091 5

11.746 8

17.751 1

17.585 2

14.843 1

15.061 1

14.830 9

12.984 2

14.264 0

14.127 1

11.866 3

14.493 2

14.409 3

12.243 6

14.606 1

14.455 8

12.364 7

17.728 6

17.563 5

14.844 8

1-D HS

2-D HS

Ours

14.836 3

14.626 7

11.996 4

18.382 4

18.177 9

14.954 7

15.326 0

15.066 2

12.617 2

14.823 0

14.629 0

12.032 2

15.107 4

14.967 3

12.601 9

15.085 5

14.887 5

12.417 1

18.379 2

18.175 1

14.990 6

Average

1-D HS

2-D HS

Ours

13.787 3

13.613 1

11.617 7

17.161 6

17.015 4

14.600 2

14.415 7

14.183 8

12.437 7

13.793 8

13.644 7

11.719 4

14.021 1

13.887 7

12.034 5

14.076 9

13.905 4

12.063 9

17.137 3

16.994 6

14.602 5

Table 3. Accuracy of converting sub-images from high to low brightness on dataset 1（No.7 group）with different algorithms

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Table 3. Accuracy of converting sub-images from high to low brightness on dataset 1（No.7 group）with different algorithms

Sub-image

Algorithms

{\bar{d}}_{y}

D (d_{y})

{\bar{d}}_{r}

{\bar{d}}_{g}

{\bar{d}}_{b}

\frac{1}{3} {\bar{d}}_{c}

\frac{1}{3} D (d_{c})

No.7-1

1-D HS

2-D HS

Ours

15.479 8

15.394 3

13.005 5

19.433 9

19.323 8

16.392 5

15.997 6

15.943 3

13.676 8

15.367 7

15.276 0

12.872 2

15.524 1

15.374 1

12.771 5

15.629 8

15.531 2

13.106 8

19.444 2

19.331 8

16.383 4

No.7-2

1-D HS

2-D HS

Ours

12.023 3

11.605 9

10.954 0

14.682 1

14.529 6

13.967 4

12.517 8

12.179 7

11.789 1

12.057 2

11.589 8

10.861 6

11.779 7

11.450 2

10.915 8

12.118 2

11.739 9

11.188 8

14.756 5

14.580 3

13.987 0

No.7-3

1-D HS

2-D HS

Ours

15.482 5

15.315 4

10.619 1

19.402 0

19.309 0

13.257 4

15.049 5

14.907 7

11.756 6

15.860 0

15.686 4

10.998 5

17.235 7

17.081 1

13.589 5

16.048 4

15.891 7

12.114 8

19.462 7

19.369 8

13.367 2

Average

1-D HS

2-D HS

Ours

14.328 5

14.105 2

11.526 2

17.839 3

17.720 8

14.539 1

14.521 6

14.343 6

12.407 5

14.428 3

14.184 1

11.577 4

14.846 5

14.635 1

12.425 6

14.598 8

14.387 6

12.136 8

17.887 8

17.760 6

14.579 2

Table 4. Accuracy of converting sub-images from high to low brightness on dataset 1 with different algorithms

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Table 4. Accuracy of converting sub-images from high to low brightness on dataset 1 with different algorithms

1-D HS

2-D HS

Ours

15.127 1

14.961 8

11.719 6

18.884 6

18.758 6

14.607 9

15.043 9

14.882 7

12.414 3

15.270 5

15.106 1

11.808 1

15.853 7

15.684 5

12.699 2

15.389 4

15.224 4

12.307 2

18.908 1

18.781 8

14.651 4

Average

1-D HS

2-D HS

Ours

13.880 3

13.766 7

11.432 1

17.466 6

17.399 6

14.400 6

14.015 0

13.927 6

12.141 4

14.028 4

13.906 2

11.565 0

14.454 7

14.332 7

12.261 0

14.166 0

14.055 5

11.989 1

17.499 7

17.428 7

14.428 0

Table 5. Subjective evaluation score and effective range of converting sub-images from low to high brightness in experiment 5（No.5 group）

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Table 5. Subjective evaluation score and effective range of converting sub-images from low to high brightness in experiment 5（No.5 group）

Sub-image	Brightness base point	Base point +10	Base point +20	Base point +30	Base point +40	Base point +50	Effective range
No.5-1	81.042 9	1.000 0	1.000 0	0.800 0	0.400 0	0.400 0	［0，30］
No.5-2	80.919 3	1.000 0	1.000 0	0.800 0	0.400 0	0.200 0	［0，30］
No.5-3	68.878 3	1.000 0	1.000 0	1.000 0	0.600 0	0.400 0	［0，30］
No.5-4	107.712 9	1.000 0	1.000 0	0.800 0	0.800 0	0.400 0	［0，40］
No.5-5	119.603 7	1.000 0	1.000 0	0.800 0	0.600 0	0.200 0	［0，30］
No.5-6	116.963 9	1.000 0	1.000 0	1.000 0	0.800 0	0.200 0	［0，40］
No.5-7	150.225 4	1.000 0	1.000 0	1.000 0	0.800 0	0.200 0	［0，40］
No.5-8	146.443 3	1.000 0	1.000 0	0.800 0	0.600 0	0.200 0	［0，30］
No.5-9	146.570 0	1.000 0	1.000 0	1.000 0	0.600 0	0.400 0	［0，30］

Table 6. Subjective evaluation score and effective range of converting sub-images from high to low brightness in experiment 6（No.9 group）

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Table 6. Subjective evaluation score and effective range of converting sub-images from high to low brightness in experiment 6（No.9 group）

Sub-image	Brightness base point	Base point -10	Base point -20	Base point -30	Base point -40	Base point -50	Effective range
No.9-1	81.788 1	1.000 0	1.000 0	0.800 0	0.800 0	0.600 0	［-40，0］
No.9-2	82.425 3	1.000 0	1.000 0	0.800 0	0.600 0	0.400 0	［-30，0］
No.9-3	83.403 4	1.000 0	1.000 0	0.800 0	0.400 0	0.400 0	［-30，0］
No.9-4	128.258 3	1.000 0	1.000 0	0.800 0	0.400 0	0.400 0	［-30，0］
No.9-5	139.228 0	1.000 0	1.000 0	0.800 0	0.800 0	0.600 0	［-40，0］
No.9-6	124.559 0	1.000 0	1.000 0	1.000 0	0.600 0	0.200 0	［-30，0］
No.9-7	143.997 4	1.000 0	1.000 0	0.800 0	0.600 0	0.400 0	［-30，0］
No.9-8	147.375 6	1.000 0	1.000 0	0.800 0	0.600 0	0.400 0	［-30，0］
No.9-9	144.343 0	1.000 0	1.000 0	0.800 0	0.600 0	0.400 0	［-30，0］

Table 7. Accuracy of the controllable brightness enhancement of soil image converted to high brightness in experiment 7（No.6 group）

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Table 7. Accuracy of the controllable brightness enhancement of soil image converted to high brightness in experiment 7（No.6 group）

Sub-image	Brightness base point	Base point +10			Base point +20			Base point +30
Sub-image	Brightness base point	1-D HS	2-D HS	Ours	1-D HS	2-D HS	Ours	1-D HS	2-D HS	Ours
No.6-1	138.050 8	2.841 0	2.472 2	0.721 4	4.266 3	3.886 9	1.161 2	6.000 4	5.693 3	1.689 3
No.6-2	127.270 9	1.960 6	0.939 5	0.481 8	2.055 6	1.939 6	1.080 7	3.213 4	3.063 8	1.492 7
No.6-3	63.996 2	0.805 0	2.151 9	0.527 4	1.754 2	3.106 0	0.592 4	2.490 2	3.860 5	0.603 7
Average	—	1.565 4	1.715 0	0.558 1	2.671 6	2.848 1	0.896 7	3.887 0	4.081 9	1.188 9

Table 8. Accuracy of the controllable brightness enhancement of soil image converted to high brightness in experiment 7（dataset 2）

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Table 8. Accuracy of the controllable brightness enhancement of soil image converted to high brightness in experiment 7（dataset 2）

Group	Base point +10			Base point +20			Base point +30
Group	1-D HS	2-D HS	Ours	1-D HS	2-D HS	Ours	1-D HS	2-D HS	Ours
1	1.937 8	1.803 2	0.824 1	3.292 2	3.211 2	1.197 2	4.742 7	4.715 1	1.584 4
2	1.480 9	1.939 2	0.707 6	2.311 6	3.269 4	0.894 2	3.536 5	4.536 4	0.989 8
3	1.827 9	1.830 1	0.833 8	3.203 4	3.186 9	1.149 5	4.662 0	4.655 9	1.426 3
4	0.868 7	1.269 4	0.485 5	1.103 1	3.309 7	0.602 4	2.450 9	4.756 8	0.614 3
5	1.425 1	1.296 3	0.501 6	2.610 1	2.459 7	0.752 7	3.844 0	3.710 1	0.969 7
6	1.565 4	1.715 0	0.558 1	2.671 6	2.848 1	0.896 7	3.887 0	4.081 9	1.188 9
7	2.668 2	1.811 1	0.737 9	2.908 9	2.941 5	1.136 7	4.121 5	4.708 4	1.413 9
8	2.014 3	1.734 8	0.954 3	3.123 9	2.956 5	1.474 7	4.560 8	4.407 5	1.921 0
9	2.440 1	2.204 0	0.779 9	3.764 5	3.529 1	1.257 5	5.384 5	5.216 6	1.638 3
10	1.137 3	1.502 7	0.342 6	2.345 0	2.738 2	0.470 0	3.426 2	3.881 5	0.513 1
Average	1.736 6	1.710 6	0.672 6	2.733 4	3.045 0	0.983 2	4.061 6	4.467 0	1.226 0

Table 9. Accuracy of the controllable brightness enhancement of soil image converted to low brightness in experiment 7（No.8 group）

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Table 9. Accuracy of the controllable brightness enhancement of soil image converted to low brightness in experiment 7（No.8 group）

Sub-image	Brightness base point	Base point -10			Base point -20			Base point -30
Sub-image	Brightness base point	1-D HS	2-D HS	Ours	1-D HS	2-D HS	Ours	1-D HS	2-D HS	Ours
No.8-1	126.067 0	0.365 0	0.697 0	0.155 3	0.900 0	1.203 6	0.669 0	1.625 8	1.983 7	1.535 8
No.8-2	127.363 1	0.343 8	0.502 5	0.319 4	0.904 2	1.077 7	0.178 9	1.685 0	1.953 0	1.054 6
No.8-3	121.752 3	0.548 9	0.742 2	0.151 8	1.190 9	1.386 1	0.435 4	2.162 5	2.414 1	1.243 2
Average	—	0.419 2	0.647 2	0.208 9	0.998 4	1.222 5	0.427 8	1.824 4	2.117 0	1.277 9

Table 10. Accuracy of the controllable brightness enhancement of soil image converted to low brightness in experiment 7（dataset 2）

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Table 10. Accuracy of the controllable brightness enhancement of soil image converted to low brightness in experiment 7（dataset 2）

Group	Base point -10			Base point-20			Base point -30
Group	1-D HS	2-D HS	Ours	1-D HS	2-D HS	Ours	1-D HS	2-D HS	Ours
1	0.385 1	0.715 0	0.315 9	0.951 8	1.252 0	0.473 7	1.750 8	2.003 8	1.369 6
2	0.557 3	0.779 5	0.301 4	1.210 5	1.448 2	0.297 8	2.211 8	2.453 1	1.189 8
3	0.584 1	0.904 0	0.257 6	1.243 3	1.567 6	0.297 7	2.213 6	2.522 5	1.208 0
4	0.643 2	0.901 8	0.270 5	1.367 4	1.632 7	0.218 4	2.419 3	2.660 0	1.125 8
5	0.516 4	0.751 4	0.332 6	1.177 0	1.442 9	0.158 8	2.182 4	2.405 6	1.057 6
6	0.558 1	0.978 5	0.244 6	1.179 4	1.587 9	0.255 4	2.112 0	2.479 6	1.220 1
7	0.346 2	0.604 6	0.182 3	0.956 3	1.225 0	0.467 1	1.794 7	2.077 2	1.317 0
8	0.419 2	0.647 2	0.208 9	0.998 4	1.222 5	0.427 8	1.824 4	2.117 0	1.277 9
9	0.604 8	0.886 4	0.207 2	1.253 6	1.543 5	0.392 8	2.202 7	2.532 9	1.209 9
10	0.700 2	1.044 9	0.425 3	1.415 5	1.728 4	0.187 5	2.404 6	2.741 9	1.120 6
Average	0.531 5	0.821 3	0.274 6	1.175 3	1.465 1	0.317 7	2.111 6	2.399 4	1.209 6

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Shaohua ZENG, Bingyu ZHAO, Shuai WANG, Yanan CHEN, Deli ZHU. Controllable Brightness Enhancement of the Soil Image Based on Weighted Gaussian Subtraction Fitting[J]. Acta Photonica Sinica, 2022, 51(4): 0410005

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Paper Information

Category:

Received: Oct. 18, 2021

Accepted: Nov. 17, 2021

Published Online: May. 18, 2022

The Author Email: ZENG Shaohua (zsh_cqu@126.com)

DOI:10.3788/gzxb20225104.0410005

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 0. [in Chinese]

Table 0. [in Chinese]

Table 0. [in Chinese]

Table 0. [in Chinese]

Table 1. Accuracy of converting sub-images from low to high brightness on dataset 1（No.3 group）with different algorithms

Table 1. Accuracy of converting sub-images from low to high brightness on dataset 1（No.3 group）with different algorithms

Table 2. Accuracy of converting sub-images from low to high brightness on dataset 1 with different algorithms

Table 2. Accuracy of converting sub-images from low to high brightness on dataset 1 with different algorithms

Table 3. Accuracy of converting sub-images from high to low brightness on dataset 1（No.7 group）with different algorithms

Table 3. Accuracy of converting sub-images from high to low brightness on dataset 1（No.7 group）with different algorithms

Table 4. Accuracy of converting sub-images from high to low brightness on dataset 1 with different algorithms

Table 4. Accuracy of converting sub-images from high to low brightness on dataset 1 with different algorithms

Table 5. Subjective evaluation score and effective range of converting sub-images from low to high brightness in experiment 5（No.5 group）

Table 5. Subjective evaluation score and effective range of converting sub-images from low to high brightness in experiment 5（No.5 group）

Table 6. Subjective evaluation score and effective range of converting sub-images from high to low brightness in experiment 6（No.9 group）

Table 6. Subjective evaluation score and effective range of converting sub-images from high to low brightness in experiment 6（No.9 group）

Table 7. Accuracy of the controllable brightness enhancement of soil image converted to high brightness in experiment 7（No.6 group）

Table 7. Accuracy of the controllable brightness enhancement of soil image converted to high brightness in experiment 7（No.6 group）

Table 8. Accuracy of the controllable brightness enhancement of soil image converted to high brightness in experiment 7（dataset 2）

Table 8. Accuracy of the controllable brightness enhancement of soil image converted to high brightness in experiment 7（dataset 2）

Table 9. Accuracy of the controllable brightness enhancement of soil image converted to low brightness in experiment 7（No.8 group）

Table 9. Accuracy of the controllable brightness enhancement of soil image converted to low brightness in experiment 7（No.8 group）

Table 10. Accuracy of the controllable brightness enhancement of soil image converted to low brightness in experiment 7（dataset 2）

Table 10. Accuracy of the controllable brightness enhancement of soil image converted to low brightness in experiment 7（dataset 2）

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