A Fractal Approach to the Classification of Land Cover in Radar imagery
Results:
Table 1 shows the averaged values for the fractal and first-order statistical measures computed for the original dataset. Urban areas, mainly because of the presence of corner reflectors such as buildings and houses, registered the highest average radar backscatter, while bay areas, owing to the presence of specular reflectors such as calm sea surface and oil spills, registered the lowest average radar backscatter. The dielectric properties of the land cover show promience in the SAR intensity image as shown by the fact the "wet" classes such as bay areas, river areas and wetlands have low backscatter values while "dry" classes such as mountainous terrain and urban areas have high backscatter values.
Urban areas have the highest Fract3D and CapDim values while forested areas have the highest InfDim and CorrDim values. On the other hand, bay areas have the lowest Fract3D and CapDim values while urban areas have the lowest InfDim and CorrDim values.
Table 1: Summary of Fractal and Statistical Measure for the Original Dataset.
| |
Mean |
SD |
Fract3D |
CapDim |
InfDim |
CurrDim |
| Bay |
103.14 |
31.78 |
2.35844 |
2.21692 |
2.53970 |
2.56609 |
| Forest |
146.79 |
44.87 |
2.39759 |
2.31883 |
2.62425 |
2.63461 |
| Mountain |
153.29 |
52.72 |
2.38655 |
2.31784 |
2.57592 |
2.53493 |
| Rice |
138.56 |
45.00 |
2.38733 |
2.28655 |
2.58937 |
2.60590 |
| River |
146.02 |
46.15 |
2.38209 |
2.30249 |
2.59268 |
2.59480 |
| Urban |
196.13 |
49.17 |
2.43025 |
2.43996 |
2.50514 |
2.43740 |
| Wetland |
130.62 |
47.07 |
2.37199 |
2.27743 |
2.54952 |
2.55889 |
A stepwise entry method for the four fractal and two-first order statistical measures into the multiple discriminant analysis showed that the all six measures significantly separate the land cover types under study. Table II shows the coefficients of the discriminant functions as well as their eigenvalues and discriminating power (in%).
Table II. Coefficient of Discriminant Functions
| |
Func 1 |
Func 2 |
Func 3 |
Func 4 |
Func 5 |
Func 6 |
| Mean |
0.52605 |
0.09352 |
-0.42143 |
0.60039 |
1.11546 |
-0.45859 |
| StDev |
-0.09889 |
1.03309 |
-0.17043 |
0.57872 |
-0.09337 |
0.26626 |
| Fract3D |
0.32973 |
-0.26088 |
0.67790 |
-0.47630 |
0.29160 |
0.54774 |
| CapDim |
0.69605 |
-0.12868 |
0.41142 |
0.18981 |
-0.97482 |
-0.15351 |
| InfDim |
0.02065 |
1.27824 |
-0.97654 |
-2.83297 |
-0.29363 |
-0.00875 |
| CorrDim |
-0.96785 |
-0.42771 |
1.54715 |
2.37210 |
0.14065 |
-0.15488 |
| Eigenval |
7.61760 |
0.95890 |
0.43070 |
0.16390 |
0.01260 |
0.00900 |
| DiscPower |
82.87 |
10.43 |
4.68 |
1.78 |
0.14 |
0.10 |
The first three discriminant functions already account for 98% of the discriminating power between classes. The first discriminant function is dominated by the mean, Fract3D, CapDim, and CorrDim. The second discriminant function is dominated by the standard deviation, InfDim, and CorrDim. The third discriminant function is dominant by the mean, Fract3D, InfDim, and CorrDim.
Land cover classification can be done based on these discriminant functions. Table III above shows the accuracy matrix for the classification of the original SAR images. The observed accuracy is 70.95% while the kappa coefficient is equal to 0.66. Bay areas, forested areas, mountainous terrain, and urban areas registered classification accuracy rates of over 75%. Twenty SAR image subsets, on the other hands, were erroneously labeled as "rice fields".
Table III . Classification Accuracy Table
| |
Bay |
Forest |
Mountain |
Rice |
River |
Urban |
Wetland |
|
| Bay |
24 |
0 |
0 |
1 |
4 |
0 |
1 |
30 |
| Forest |
0 |
23 |
1 |
4 |
1 |
0 |
1 |
30 |
| Mountain |
0 |
2 |
27 |
1 |
0 |
0 |
0 |
30 |
| Rice |
1 |
4 |
0 |
18 |
6 |
0 |
1 |
30 |
| River |
2 |
4 |
2 |
4 |
17 |
0 |
1 |
30 |
| Urban |
0 |
0 |
0 |
0 |
0 |
30 |
0 |
30 |
| Wetland |
1 |
2 |
0 |
10 |
7 |
0 |
10 |
30 |
| |
28 |
35 |
30 |
38 |
35 |
30 |
14 |
210 |
Student's t-test revealed that speckle filtering generated a set of SAR images satistically different from the original Speckle filtering resulted in a decrease in the computed values for the six parameters. This is due to the smoothening effect of the filter. Table IV gives the statistical summary of computed fractal and first-order statistical measures for the filtered set of images. Urban areas and mountainous terrain remained to be the "brightest" land cover while bay areas and wetlands remained to be the "darkest" features. Wetlands have the lower average CapDim, InfDim, and CorrDim values. Urban areas and mountainous terrain continued to have high fractal dimensions.
Table IV : Summary of Fractal and Statistical Measures for the Filtered Dataset
| |
Mean |
SD |
Fract3D |
CapDim |
InfDim CorrDim |
|
| Bay |
97.32 |
24.44 |
2.21061 |
2.21111 |
2.41131 |
2.39354 |
| Forest |
142.91 |
34.12 |
2.24125 |
2.20987 |
2.49377 |
2.53643 |
| Mountain |
152.37 |
38.88 |
2.27388 |
2.26826 |
2.48999 |
2.49033 |
| Rice |
134.81 |
36.53 |
2.24070 |
2.22692 |
2.41507 |
2.43872 |
| River |
142.02 |
38.49 |
2.24840 |
2.21636 |
2.40033 |
2.42013 |
| Urban |
190.53 |
45.49 |
2.21456 |
2.24969 |
2.49954 |
2.49142 |
| Wetland |
126.91 |
39.35 |
2.23532 |
2.20642 |
2.35461 |
2.63273 |
