Robust Parameter Design of Derivative Optimization Methods for Image Acquisition Using a Color Mixer †
Abstract
:1. Introduction
2. Derivative Optimum for Image Quality
2.1. Index for Image Quality
2.2. Derivative Optimum Methods
3. Robust Parameter Design
3.1. System for Experiment
3.2. Taguchi Method
3.3. Experiment Design
4. Results
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
STD | Steepest descent method |
CJG | Conjugate gradient method |
LED | Light emitting diode |
RGB | Red, green and blue |
sRGB | Standard red, green and blue |
ESS | Equal step search |
TAE | Trial-and-error |
SN | Signal-to-noise |
Grey level of an image pixel | |
Brightness, average grey level of an image | |
k | Current iteration |
m | Horizontal pixel number of an image |
N | Number of voltage inputs for a color mixer |
n | Vertical pixel number of an image |
u | the performance index |
V | Vector of voltage inputs for a color mixer |
v | Individual voltage input for an LED |
w | the number of experiments |
x | Horizontal coordinate of an image |
y | Vertical coordinate of an image |
Convergence coefficient | |
Terminal condition | |
Convergence coefficient for limited range | |
Negative sharpness, cost function | |
Sharpness, image quality | |
Threshold | |
Index of update for conjugate gradient method |
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Factors | Code | Level | ||||
---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | ||
: Initial | A | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 |
: Initial | B | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 |
: Initial | C | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 |
: Threshold | D | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 |
: Convergence Constant | E | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 |
Run # | Control Factors | Pattern A | Pattern B | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A | B | C | D | E | |||||||||||
1 | 1 | 1 | 1 | 1 | 1 | 389.43 | 117 | 0.98 | 0.00 | 0.41 | 353.88 | 153 | 0.53 | 0.30 | 0.00 |
2 | 1 | 2 | 2 | 2 | 2 | 390.50 | 255 | 0.00 | 0.00 | 1.25 | - | - | - | - | - |
3 | 1 | 3 | 3 | 3 | 3 | - | - | - | - | - | 340.47 | 3 | 0.00 | 0.42 | 0.42 |
4 | 1 | 4 | 4 | 4 | 4 | 382.4 | 2 | 0.00 | 0.72 | 0.72 | - | - | - | - | - |
5 | 1 | 5 | 5 | 5 | 5 | 390.43 | 152 | 0.00 | 0.00 | 1.30 | 317.63 | 2 | 0.00 | 0.53 | 0.82 |
6 | 2 | 1 | 2 | 3 | 4 | 386.09 | 189 | 0.52 | 0.02 | 0.52 | 344.02 | 1 | 0.52 | 0.02 | 0.52 |
7 | 2 | 2 | 3 | 4 | 5 | 387.22 | 1 | 0.20 | 0.20 | 0.70 | 337.22 | 1 | 0.20 | 0.20 | 0.70 |
8 | 2 | 3 | 4 | 5 | 1 | 390.40 | 123 | 0.00 | 0.00 | 1.26 | 333.35 | 6 | 0.00 | 0.30 | 0.80 |
9 | 2 | 4 | 5 | 1 | 2 | 390.36 | 49 | 0.00 | 0.00 | 1.27 | 335.65 | 22 | 0.00 | 0.24 | 0.74 |
10 | 2 | 5 | 1 | 2 | 3 | 384.64 | 6 | 0.00 | 1.06 | 0.00 | 346.93 | 108 | 0.00 | 0.58 | 0.00 |
11 | 3 | 1 | 3 | 5 | 2 | 389.01 | 109 | 0.75 | 0.02 | 0.57 | - | - | - | - | - |
12 | 3 | 2 | 4 | 1 | 3 | 388.87 | 263 | 0.78 | 0.00 | 0.51 | 340.46 | 11 | 0.42 | 0.00 | 0.68 |
13 | 3 | 3 | 5 | 2 | 4 | 390.36 | 164 | 0.00 | 0.00 | 1.29 | 324.30 | 107 | 0.00 | 0.00 | 0.90 |
14 | 3 | 4 | 1 | 3 | 5 | 385.88 | 3 | 0.41 | 0.70 | 0.00 | 331.85 | 2 | 0.30 | 0.80 | 0.00 |
15 | 3 | 5 | 2 | 4 | 1 | 389.21 | 237 | 0.99 | 0.00 | 0.38 | 346.91 | 192 | 0.00 | 0.58 | 0.00 |
16 | 4 | 1 | 4 | 2 | 5 | 387.71 | 3 | 0.80 | 0.00 | 0.80 | 338.46 | 18 | 0.40 | 0.00 | 0.40 |
17 | 4 | 2 | 5 | 3 | 1 | 389.18 | 206 | 1.04 | 0.00 | 0.36 | 338.25 | 15 | 0.30 | 0.00 | 0.70 |
18 | 4 | 3 | 1 | 4 | 2 | - | - | - | - | - | 354.62 | 4 | 0.72 | 0.22 | 0.00 |
19 | 4 | 4 | 2 | 5 | 3 | 382.32 | 2 | 0.80 | 0.80 | 0.00 | 303.61 | 2 | 0.82 | 0.80 | 0.00 |
20 | 4 | 5 | 3 | 1 | 4 | 384.95 | 49 | 0.24 | 0.74 | 0.00 | 349.91 | 151 | 0.24 | 0.42 | 0.00 |
21 | 5 | 1 | 5 | 4 | 3 | 387.90 | 4 | 0.58 | 0.00 | 0.60 | 341.62 | 4 | 0.58 | 0.00 | 0.58 |
22 | 5 | 2 | 1 | 5 | 4 | 386.36 | 2 | 1.28 | 0.00 | 0.00 | 358.14 | 2 | 0.90 | 0.00 | 0.00 |
23 | 5 | 3 | 2 | 1 | 5 | 386.78 | 6 | 1.30 | 0.30 | 0.00 | 358.26 | 82 | 0.90 | 0.00 | 0.00 |
24 | 5 | 4 | 3 | 2 | 1 | 389.05 | 191 | 1.08 | 0.00 | 0.32 | 355.32 | 23 | 0.66 | 0.16 | 0.00 |
25 | 5 | 5 | 4 | 3 | 2 | 386.50 | 8 | 0.58 | 0.58 | 0.08 | 350.51 | 137 | 0.34 | 0.34 | 0.00 |
Run # | Control Factors | Pattern A | Pattern B | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A | B | C | D | E | |||||||||||
1 | 1 | 1 | 1 | 1 | 1 | 389.28 | 59 | 0.99 | 0.00 | 0.43 | 358.49 | 143 | 0.95 | 0.00 | 0.00 |
2 | 1 | 2 | 2 | 2 | 2 | 390.58 | 41 | 0.00 | 0.00 | 1.25 | 343.00 | 24 | 0.48 | 0.16 | 0.43 |
3 | 1 | 3 | 3 | 3 | 3 | 390.43 | 139 | 0.00 | 0.00 | 1.20 | 340.21 | 3 | 0.00 | 0.42 | 0.42 |
4 | 1 | 4 | 4 | 4 | 4 | 382.42 | 2 | 0.00 | 0.72 | 0.72 | 354.05 | 9 | 0.80 | 0.00 | 0.00 |
5 | 1 | 5 | 5 | 5 | 5 | 384.66 | 2 | 0.00 | 0.57 | 0.78 | 316.46 | 2 | 0.00 | 0.50 | 0.88 |
6 | 2 | 1 | 2 | 3 | 4 | 386.07 | 1 | 0.52 | 0.02 | 0.52 | 343.92 | 1 | 0.52 | 0.02 | 0.52 |
7 | 2 | 2 | 3 | 4 | 5 | 387.16 | 1 | 0.20 | 0.20 | 0.70 | 337.14 | 1 | 0.20 | 0.20 | 0.70 |
8 | 2 | 3 | 4 | 5 | 1 | 390.40 | 50 | 0.00 | 0.00 | 1.30 | 358.43 | 168 | 0.98 | 0.00 | 0.00 |
9 | 2 | 4 | 5 | 1 | 2 | 390.54 | 28 | 0.00 | 0.00 | 1.27 | 338.89 | 29 | 0.24 | 0.16 | 0.66 |
10 | 2 | 5 | 1 | 2 | 3 | 388.64 | 178 | 0.74 | 0.02 | 0.71 | 350.01 | 21 | 0.48 | 0.41 | 0.00 |
11 | 3 | 1 | 3 | 5 | 2 | 390.42 | 24 | 0.00 | 0.00 | 1.28 | 331.95 | 2 | 0.70 | 0.00 | 0.70 |
12 | 3 | 2 | 4 | 1 | 3 | 390.50 | 144 | 0.00 | 0.00 | 1.25 | 352.28 | 16 | 0.58 | 0.24 | 0.08 |
13 | 3 | 3 | 5 | 2 | 4 | 390.37 | 17 | 0.00 | 0.00 | 1.31 | 324.42 | 15 | 0.00 | 0.00 | 0.90 |
14 | 3 | 4 | 1 | 3 | 5 | 388.16 | 5 | 1.48 | 0.00 | 0.00 | 347.42 | 33 | 0.00 | 0.60 | 0.00 |
15 | 3 | 5 | 2 | 4 | 1 | 390.39 | 284 | 0.00 | 0.00 | 1.29 | 348.20 | 26 | 0.11 | 0.63 | 0.00 |
16 | 4 | 1 | 4 | 2 | 5 | 387.61 | 3 | 0.80 | 0.00 | 0.80 | 338.48 | 124 | 0.40 | 0.00 | 0.40 |
17 | 4 | 2 | 5 | 3 | 1 | 390.43 | 273 | 0.00 | 0.00 | 1.24 | 342.81 | 38 | 0.28 | 0.28 | 0.43 |
18 | 4 | 3 | 1 | 4 | 2 | 390.43 | 264 | 0.00 | 0.00 | 1.25 | 354.42 | 4 | 0.72 | 0.22 | 0.00 |
19 | 4 | 4 | 2 | 5 | 3 | 387.57 | 7 | 0.95 | 0.60 | 0.00 | 304.10 | 2 | 0.80 | 0.80 | 0.00 |
20 | 4 | 5 | 3 | 1 | 4 | 387.84 | 39 | .00 | 0.27 | 0.91 | 349.67 | 13 | 0.24 | 0.42 | 0.00 |
21 | 5 | 1 | 5 | 4 | 3 | 387.92 | 5 | 0.74 | 0.08 | 0.70 | 338.57 | 4 | 0.58 | 0.00 | 0.65 |
22 | 5 | 2 | 1 | 5 | 4 | 384.69 | 1 | 1.70 | 0.20 | 0.00 | 358.02 | 2 | 0.90 | 0.00 | 0.00 |
23 | 5 | 3 | 2 | 1 | 5 | 387.46 | 8 | 0.90 | 0.30 | 0.20 | 357.96 | 8 | 0.90 | 0.00 | 0.00 |
24 | 5 | 4 | 3 | 2 | 1 | 389.12 | 80 | 0.93 | 0.00 | 0.42 | 358.45 | 118 | 0.95 | 0.00 | 0.00 |
25 | 5 | 5 | 4 | 3 | 2 | 386.35 | 8 | 0.58 | 0.58 | 0.08 | 350.36 | 9 | 0.34 | 0.34 | 0.00 |
Control Factors | l | |||||||
---|---|---|---|---|---|---|---|---|
Source | Parameter | DF | SS | MS | Contribution (%) | SS | MS | Contribution (%) |
A | Initial | 4 | 19.548 | 4.887 | 14.2 | 71,168 | 17,792 | 24.5 |
B | Initial | 4 | 18.847 | 4.712 | 13.7 | 36,910 | 9228 | 12.7 |
C | Initial | 4 | 34.290 | 8.572 | 23.0 | 65,697 | 16,424 | 22.6 |
D | 4 | 17.188 | 4.297 | 12.5 | 43,406 | 10,851 | 14.9 | |
E | 4 | 41.656 | 10.414 | 30.3 | 71,069 | 17,767 | 24.5 | |
Error | 2 | 5.806 | 2.903 | 4.2 | 2171 | 1085 | 0.7 | |
Total | 22 | 137.335 | 290,421 |
Control Factors | l | |||||||
---|---|---|---|---|---|---|---|---|
Source | Parameter | DF | SS | MS | Contribution (%) | SS | MS | Contribution (%) |
A | Initial | 4 | 1094.64 | 273.66 | 24.0 | 4027 | 1007 | 4.5 |
B | Initial | 4 | 916.54 | 229.13 | 20.1 | 40,860 | 10,215 | 45.6 |
C | Initial | 4 | 1019.66 | 254.91 | 22.4 | 2807 | 702 | 3.1 |
D | 4 | 715.99 | 179 | 15.7 | 17,557 | 4389 | 19.6 | |
E | 4 | 516.07 | 129.02 | 11.3 | 10,919 | 2730 | 12.2 | |
Error | 4 | 291.90 | 72.97 | 6.4 | 13,524 | 3381 | 15.1 | |
Total | 24 | 4554.80 | 89,694 |
Control Factors | l | |||||||
---|---|---|---|---|---|---|---|---|
Source | Parameter | DF | SS | MS | Contribution (%) | SS | MS | Contribution (%) |
A | Initial | 4 | 24.802 | 6.2 | 18.5 | 30,195 | 7549 | 14.8 |
B | Initial | 4 | 23.749 | 5.937 | 17.7 | 34,288 | 8572 | 16.9 |
C | Initial | 4 | 8.295 | 2.074 | 6.2 | 9756 | 2439 | 4.8 |
D | 4 | 19.159 | 4.8 | 14.3 | 24,720 | 6180 | 12.1 | |
E | 4 | 51.27 | 12.818 | 38.2 | 72,863 | 18,216 | 35.8 | |
Error | 4 | 7.054 | 1.763 | 5.3 | 31,656 | 7914 | 15.6 | |
Total | 24 | 134.329 | 203,478 |
Control Factors | l | |||||||
---|---|---|---|---|---|---|---|---|
Source | Parameter | DF | SS | MS | Contribution (%) | SS | MS | Contribution (%) |
A | Initial | 4 | 637.8 | 159.5 | 14.3 | 1884.4 | 471.1 | 3.3 |
B | Initial | 4 | 161.4 | 40.3 | 3.6 | 5903.6 | 1475.9 | 10.3 |
C | Initial | 4 | 1491.5 | 372.9 | 33.4 | 8974.8 | 2243.7 | 15.6 |
D | 4 | 840.4 | 210.1 | 18.8 | 8401.6 | 2100.4 | 14.6 | |
E | 4 | 794.9 | 198.7 | 17.8 | 29,353.6 | 7338.4 | 51.1 | |
Error | 4 | 537.4 | 134.3 | 12.0 | 2888 | 722 | 5.0 | |
Total | 24 | 4463.4 | 57,406 |
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Kim, H.; Cho, K.; Kim, J.; Jin, K.; Kim, S. Robust Parameter Design of Derivative Optimization Methods for Image Acquisition Using a Color Mixer. J. Imaging 2017, 3, 31. https://doi.org/10.3390/jimaging3030031
Kim H, Cho K, Kim J, Jin K, Kim S. Robust Parameter Design of Derivative Optimization Methods for Image Acquisition Using a Color Mixer. Journal of Imaging. 2017; 3(3):31. https://doi.org/10.3390/jimaging3030031
Chicago/Turabian StyleKim, HyungTae, KyeongYong Cho, Jongseok Kim, KyungChan Jin, and SeungTaek Kim. 2017. "Robust Parameter Design of Derivative Optimization Methods for Image Acquisition Using a Color Mixer" Journal of Imaging 3, no. 3: 31. https://doi.org/10.3390/jimaging3030031