Combining Pixel Swapping and Simulated Annealing for Land Cover Mapping
<p>Spatial correlations of the subpixels in the pixel-swapping algorithm (PSA) (<span class="html-italic">S</span> = 4). (<b>a</b>) Mixed pixels, (<b>b</b>) high-resolution image, (<b>c</b>) subpixels in <span class="html-italic">P</span><sub><span class="html-italic">a</span>,<span class="html-italic">b</span></sub>.</p> "> Figure 2
<p>Interpretation of the PSA_MSA algorithm. (<b>a</b>) Original image, (<b>b</b>) randomly selected subpixels for swapping, (<b>c</b>) Swapping result 1, (<b>d</b>) Swapping result 2.</p> "> Figure 3
<p>Flow chart of the modified simulated annealing algorithm.</p> "> Figure 4
<p>Different mixed pixel selection methods: (<b>a</b>) Sequential and (<b>b</b>) Stochastic.</p> "> Figure 5
<p>Comparison of the results from different SPM models for artificial shapes at a reconstruction scale of 10: (<b>a</b>) the reference image, (<b>b</b>) the PSA results, (<b>c</b>) the PSA_SA algorithm results, (<b>d</b>) the DSAM algorithm results, (<b>e</b>) the PSA_MSA1 algorithm results, and (<b>f</b>) the PSA_MSA2 algorithm results.</p> "> Figure 6
<p>Proportional images of four classes with a scale of 12. (<b>a</b>) Reference image, (<b>b</b>) class 1, (<b>c</b>) class 2, (<b>d</b>) class 3, (<b>e</b>) class 4.</p> "> Figure 7
<p>Comparison results of different SPM models for an artificial land image with a scale of 12. (<b>a</b>) PSA result, (<b>b</b>) PSA_SA result, (<b>c</b>) DSAM result, (<b>d</b>) PSA_MSA1 result, (<b>e</b>) PSA_MSA2 result.</p> "> Figure 8
<p>The improved PCC′ values (%) of different algorithms for the synthetic data set. (<b>a</b>) <span class="html-italic">S</span> = 8, (<b>b</b>) <span class="html-italic">S</span> = 10, (<b>c</b>) <span class="html-italic">S</span> = 12.</p> "> Figure 9
<p>The improved Kappa′ values (%) of different algorithms for the synthetic data set. (<b>a</b>) <span class="html-italic">S</span> = 8, (<b>b</b>) <span class="html-italic">S</span> = 10, (<b>c</b>) <span class="html-italic">S</span> = 12.</p> "> Figure 10
<p>Proportional images of three classes with a scale of 8. (<b>a</b>) Reference image, (<b>b</b>) water, (<b>c</b>) vegetation, (<b>d</b>) soil.</p> "> Figure 11
<p>Comparison of the results from different SPM models for a real land image at a reconstruction scale of 8: (<b>a</b>) the reference image, (<b>b</b>) the PSA results, (<b>c</b>) the PSA_SA results, (<b>d</b>) the DSAM algorithm results, (<b>e</b>) the PSA_MSA1 algorithm results, (<b>f</b>) the PSA_MSA2 algorithm results, (<b>g</b>) the local details in the reference image, (<b>h</b>) the local details in the PSA results, (<b>i</b>) the local details in the PSA_SA results, (<b>j</b>) the local details in the DSAM algorithm results, (<b>k</b>) the local details in the PSA_MSA1 algorithm results, and (<b>l</b>) the local details in the PSA_MSA2 algorithm results.</p> "> Figure 12
<p>Proportion images of three classes with a scale of 8. (<b>a</b>) Reference image, (<b>b</b>) water, (<b>c</b>) vegetation, (<b>d</b>) soil.</p> "> Figure 13
<p>Comparison of the results of different SPM models for an artificial land image with a scale of 8. (<b>a</b>) PSA result, (<b>b</b>) PSA_SA result, (<b>c</b>) DSAM result, (<b>d</b>) PSA_MSA1 result, (<b>e</b>) PSA_MSA2 result.</p> "> Figure 14
<p>Proportional images of three classes with a 10% error in the proportional image (<span class="html-italic">S</span> = 8). (<b>a</b>) Water, (<b>b</b>) vegetation, (<b>c</b>) soil.</p> "> Figure 15
<p>Comparison results of different SPM models for real land image1 with a 10% error in the proportional image (<span class="html-italic">S</span> = 10). (<b>a</b>) PSA result, (<b>b</b>) PSA_SA result, (<b>c</b>) DSAM result, (<b>d</b>) PSA_MSA1 result, (<b>e</b>) PSA_MSA2 result.</p> "> Figure 16
<p>Accuracies of the PSA_MSA1 algorithm under different low attractiveness ranges. (<b>a</b>) PCC′ and (<b>b</b>) Kappa′.</p> "> Figure 17
<p>Accuracy of the PSA_MSA2 algorithm under different ranges of low attractiveness. (<b>a</b>) PCC′ and (<b>b</b>) Kappa′.</p> ">
Abstract
:1. Introduction
2. Materials and Methods
2.1. Principles of the PSA
2.2. PSA with Simulated Annealing (SA)
2.3. PSA Based on the Modified Simulated Annealing Algorithm (PSA_MSA)
3. Experiments and Analysis
3.1. Artificial Shapes
3.2. Artificial Land Images
3.3. Real land Image
3.4. Influence of Errors on the Process of Proportion Acquisition in the SPM_MSA Algorithm
3.5. Stochastic Optimization of Mixed Pixels in the PSA_MSA Algorithm
4. Discussion
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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PCC | Kappa | Improved PCC′ | Improved Kappa′ | ||
---|---|---|---|---|---|
Circle | PSA | 99.56 | 98.91 | 90.65 | 81.25 |
PSA_SA algorithm | 99.52 | 98.82 | 89.80 | 79.55 | |
DSAM | 99.72 | 99.31 | 94.07 | 88.11 | |
PSA_MSA1 algorithm | 99.91 | 99.77 | 98.03 | 96.05 | |
PSA_MSA2 algorithm | 99.90 | 99.75 | 97.88 | 95.75 | |
Star | PSA | 99.33 | 98.01 | 89.13 | 77.91 |
PSA_SA algorithm | 99.20 | 97.64 | 87.10 | 73.83 | |
DSAM | 99.65 | 98.96 | 94.29 | 88.41 | |
PSA_MSA1 algorithm | 99.88 | 99.63 | 97.98 | 95.91 | |
PSA_MSA2 algorithm | 99.85 | 99.56 | 97.56 | 95.06 | |
Letters | PSA | 98.44 | 87.66 | 88.25 | 76.51 |
PSA_SA algorithm | 98.10 | 84.91 | 85.64 | 71.29 | |
DSAM | 99.20 | 93.69 | 93.95 | 87.89 | |
PSA_MSA1 algorithm | 99.73 | 97.86 | 97.94 | 95.88 | |
PSA_MSA2 algorithm | 99.75 | 98.00 | 98.08 | 96.15 |
PCC | Kappa | Improved PCC′ | Improved Kappa′ | ||
---|---|---|---|---|---|
S = 8 | PSA | 97.64 | 96.80 | 91.21 | 88.15 |
PSA_SA algorithm | 97.36 | 96.43 | 90.17 | 86.75 | |
DSAM | 98.44 | 97.89 | 94.19 | 92.17 | |
PSA_MSA1 algorithm | 99.10 | 98.78 | 96.64 | 95.48 | |
PSA_MSA2 algorithm | 99.09 | 98.76 | 96.59 | 95.41 | |
S = 10 | PSA | 96.40 | 95.12 | 89.32 | 85.55 |
PSA_SA algorithm | 95.61 | 94.06 | 87.00 | 82.42 | |
DSAM | 97.77 | 96.89 | 93.38 | 91.05 | |
PSA_MSA1 algorithm | 98.85 | 98.44 | 96.58 | 95.38 | |
PSA_MSA2 algorithm | 98.80 | 98.38 | 96.46 | 95.21 | |
S = 12 | PSA | 95.15 | 93.43 | 88.14 | 84.02 |
PSA_SA algorithm | 93.46 | 91.14 | 84.00 | 78.45 | |
DSAM | 97.08 | 96.05 | 92.86 | 90.38 | |
PSA_MSA1 algorithm | 98.41 | 97.85 | 96.12 | 94.77 | |
PSA_MSA2 algorithm | 98.48 | 97.94 | 96.28 | 94.99 |
Algorithm1 | Algorithm2 | S = 8 | S = 10 | S = 12 |
---|---|---|---|---|
PSA_MSA1 | PSA | 7.54 | 9.04 | 10.21 |
PSA_SA | 11.01 | 14.12 | 16.23 | |
DSAM | 0.45 | 0.67 | 1.24 | |
PSA_MSA2 | PSA | 7.21 | 8.99 | 10.14 |
PSA_SA | 10.68 | 14.07 | 16.15 | |
DSAM | 0.15 | 0.63 | 1.17 |
Algorithm1 | Algorithm2 | S = 8 | S = 10 | S = 12 |
---|---|---|---|---|
PSA_MSA1 | PSA | 12.14 | 14.82 | 17.00 |
PSA_SA | 18.14 | 23.87 | 28.14 | |
DSAM | 0.72 | 1.07 | 1.95 | |
PSA_MSA2 | PSA | 11.61 | 14.73 | 16.86 |
PSA_SA | 17.58 | 23.78 | 27.98 | |
DSAM | 0.24 | 0.99 | 1.83 |
PCC | Kappa | Improved PCC′ | Improved Kappa′ | ||
---|---|---|---|---|---|
S = 8 | PSA | 89.56 | 84.33 | 81.38 | 70.45 |
PSA_SA algorithm | 87.61 | 81.41 | 77.91 | 65.00 | |
DSAM | 90.77 | 86.15 | 83.55 | 73.88 | |
PSA_MSA1 algorithm | 91.66 | 87.49 | 85.14 | 76.46 | |
PSA_MSA2 algorithm | 92.03 | 88.05 | 85.80 | 77.49 | |
S = 10 | PSA | 85.59 | 78.38 | 77.37 | 64.18 |
PSA_SA algorithm | 84.01 | 76.01 | 74.89 | 60.23 | |
DSAM | 87.26 | 80.89 | 79.99 | 68.32 | |
PSA_MSA1 algorithm | 88.51 | 82.76 | 81.95 | 71.42 | |
PSA_MSA2 algorithm | 88.50 | 82.75 | 81.95 | 71.44 |
S = 8 | PSA | PSA_SA | DSAM | PSA_MSA1 | PSA_MSA2 |
---|---|---|---|---|---|
Water | 84.85 | 82.06 | 86.61 | 90.02 | 90.60 |
Vegetation | 79.80 | 75.78 | 82.55 | 83.75 | 84.24 |
Soil | 81.25 | 77.95 | 83.11 | 84.29 | 85.11 |
S = 10 | PSA | PSA_SA | DSAM | PSA_MSA1 | PSA_MSA2 |
Water | 82.60 | 78.89 | 84.48 | 87.31 | 87.68 |
Vegetation | 75.91 | 73.97 | 78.90 | 80.17 | 80.40 |
Soil | 76.50 | 74.05 | 78.94 | 81.29 | 80.94 |
PCC | Kappa | Improved PCC′ | Improved Kappa′ | ||
---|---|---|---|---|---|
S = 8 | PSA | 85.90 | 58.06 | 79.64 | 49.94 |
PSA_SA algorithm | 86.21 | 53.66 | 79.77 | 49.83 | |
DSAM | 87.15 | 62.12 | 81.53 | 54.35 | |
PSA_MSA1 algorithm | 87.25 | 62.26 | 81.59 | 54.94 | |
PSA_MSA2 algorithm | 87.14 | 61.81 | 81.43 | 54.40 | |
S = 10 | PSA | 85.08 | 55.17 | 80.96 | 49.47 |
PSA_SA algorithm | 85.05 | 49.10 | 80.40 | 47.24 | |
DSAM | 85.58 | 56.69 | 81.59 | 50.90 | |
PSA_MSA1 algorithm | 85.38 | 56.40 | 81.33 | 50.86 | |
PSA_MSA2 algorithm | 85.66 | 56.95 | 81.69 | 51.47 |
S = 8 | PSA | PSA_SA | DSAM | PSA_MSA1 | PSA_MSA2 |
---|---|---|---|---|---|
Water | 44.23 | 37.41 | 50.38 | 49.87 | 48.80 |
Vegetation | 90.02 | 90.43 | 90.20 | 90.91 | 90.94 |
Soil | 55.91 | 56.00 | 58.73 | 60.28 | 59.73 |
S = 10 | PSA | PSA_SA | DSAM | PSA_MSA1 | PSA_MSA2 |
Water | 36.51 | 30.12 | 39.72 | 40.23 | 40.39 |
Vegetation | 91.23 | 91.60 | 90.57 | 91.22 | 91.64 |
Soil | 54.49 | 51.71 | 57.36 | 55.73 | 55.90 |
PSA | PSA_SA | DSAM | PSA_MSA1 | PSA_MSA2 | ||
---|---|---|---|---|---|---|
S = 8 | 0 | 89.56 | 87.61 | 90.74 | 91.66 | 92.03 |
5% | 88.23 | 86.45 | 89.50 | 89.81 | 89.94 | |
10% | 86.22 | 84.77 | 88.12 | 87.82 | 87.80 | |
S = 10 | 0 | 85.59 | 84.01 | 87.26 | 88.51 | 88.50 |
5% | 84.42 | 82.88 | 85.89 | 86.10 | 86.63 | |
10% | 82.55 | 81.35 | 84.04 | 84.09 | 84.57 |
PSA | PSA_SA | DSAM | PSA_MSA1 | PSA_MSA2 | ||
---|---|---|---|---|---|---|
S = 8 | 0 | 84.33 | 81.41 | 86.11 | 87.49 | 88.05 |
5% | 82.35 | 79.67 | 84.24 | 84.71 | 84.90 | |
10% | 79.32 | 77.15 | 82.18 | 81.72 | 81.69 | |
S = 10 | 0 | 78.38 | 76.01 | 80.89 | 82.76 | 82.75 |
5% | 76.63 | 74.31 | 78.83 | 79.14 | 79.94 | |
10% | 73.83 | 72.01 | 76.05 | 76.12 | 76.85 |
Circle | Star | ||||
---|---|---|---|---|---|
Improved PCC′ | Improved Kappa′ | Improved PCC′ | Improved Kappa′ | ||
S = 8 | Sequential | 97.63 | 95.25 | 96.70 | 93.15 |
Stochastic | 97.93 | 95.86 | 97.79 | 95.42 | |
S = 10 | Sequential | 97.89 | 95.77 | 97.85 | 95.64 |
Stochastic | 98.03 | 96.05 | 97.98 | 95.91 |
Circle | Star | ||||
---|---|---|---|---|---|
Improved PCC′ | Improved Kappa′ | Improved PCC′ | Improved Kappa′ | ||
S = 8 | Sequential | 97.59 | 95.17 | 97.27 | 94.32 |
Stochastic | 97.75 | 95.50 | 97.31 | 94.41 | |
S = 10 | Sequential | 97.51 | 94.99 | 97.20 | 94.32 |
Stochastic | 97.88 | 95.75 | 97.56 | 95.06 |
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Su, L.; Xu, Y.; Yuan, Y.; Yang, J. Combining Pixel Swapping and Simulated Annealing for Land Cover Mapping. Sensors 2020, 20, 1503. https://doi.org/10.3390/s20051503
Su L, Xu Y, Yuan Y, Yang J. Combining Pixel Swapping and Simulated Annealing for Land Cover Mapping. Sensors. 2020; 20(5):1503. https://doi.org/10.3390/s20051503
Chicago/Turabian StyleSu, Lijuan, Yue Xu, Yan Yuan, and Jingyi Yang. 2020. "Combining Pixel Swapping and Simulated Annealing for Land Cover Mapping" Sensors 20, no. 5: 1503. https://doi.org/10.3390/s20051503