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

Journals >Acta Photonica Sinica >Volume 51 >Issue 4 >Page 0410005 > Article

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

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

Shaohua ZENG^1、2、*, Bingyu ZHAO^1、2, Shuai WANG³, Yanan CHEN⁴, and Deli ZHU^1、2

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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DOI: 10.3788/gzxb20225104.0410005 Cite this Article

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 Copy Citation Text

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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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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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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 0. [in Chinese]

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

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

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

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

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

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

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

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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

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

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