Comparing Fuzzy Sets and Random Sets to Model the Uncertainty of Fuzzy Shorelines
Abstract
:1. Introduction
2. Methodology
2.1. Study Area
2.2. Dataset
2.3. Pre-Processing
- is a mix of settlements and vegetation. This group consists of six subsets. They have a similar land orientation, stretching from northwest to southeast direction indicating rural settlements with a strip land surrounded by inundated fishponds. Rivers with various widths divide each island into two sides and small roads are found on either sides of the river. Rural settlements are mostly concentrated alongside the roads with sparse vegetation coverage.
- is a mix of settlement and vegetation with more complex composition. Small rivers are clearly seen in and . Fishponds with irregular shapes are visible at the northern part of and .
- is dominated by vegetation coverage. Rural settlements are visible in along the river side and a wide muddy area can be found in the northern part of the subset close to the mangrove area.
- shows rural settlements surrounded by inundated fishponds. The settlements are protected by concrete embankment.
2.4. Modelling Shoreline Using Fuzzy Sets
2.4.1. FCM Classification
2.4.2. Image Segmentation
2.4.3. Uncertainty Estimation
2.5. Modelling Shoreline by Random Sets
2.5.1. Parameter Estimation of Random Sets
2.5.2. Modelling the Extent of Shoreline by Random Sets
2.6. Validation and Comparing Classification Performance
3. Results
3.1. Modelling Shoreline Using Fuzzy Sets
3.1.1. Parameter Estimation of FCM Classification
3.1.2. Hardened FCM and Accuracy Comparison
3.1.3. Fuzzy Shoreline and Uncertainty Estimation
3.2. Modelling Shoreline by Random Sets
3.2.1. Parameter Estimation Results
3.2.2. Uncertainty Modelling of Shoreline Objects
3.2.3. Accuracy Assessment of Random Sets Results
3.3. Comparing Classification Performance
4. Discussion
5. Conclusions
Supplementary Materials
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Acquisition Date | 27 February 2013 |
Acquisition time | 03:04 UTC |
Incidence angle (deg) | 13.66 |
Sun elevation (deg) | 62.51 |
Resolution (m) | 0.5 (pan-sharpened product) |
Bands (μm) | blue (0.43–0.55), green (0.50–0.62), red (0.59–0.71), NIR (0.74–0.94) |
Map projection | UTM WGS84 |
Definition | Equations |
---|---|
The -level set: to describe the spatial distribution of the varying sizes of | |
The core set: to describe the certain part of | |
The median set: to describe the 0.5-level set | |
The support set: to describe the possible part of | |
The mean area of | |
The mean set of | |
The set-theoretic variance | |
The sum of variance SV | |
The coefficient of variation CV |
Subset | Pleiades | Pleaides + DTM |
---|---|---|
0.77 | 0.86 | |
0.62 | 0.86 | |
0.76 | 0.88 | |
0.48 | 0.84 | |
0.56 | 0.87 | |
0.74 | 0.88 | |
0.74 | 0.91 | |
0.74 | 0.87 | |
0.78 | 0.87 | |
0.50 | 0.82 | |
0.74 | 0.89 | |
0.65 | 0.88 | |
0.67 | 0.81 |
Subset | SV | CV |
---|---|---|
657 | 0.007 | |
811 | 0.009 | |
915 | 0.010 | |
901 | 0.010 | |
466 | 0.005 | |
574 | 0.008 | |
953 | 0.009 | |
1525 | 0.032 | |
1710 | 0.017 | |
1490 | 0.025 | |
883 | 0.014 | |
441 | 0.005 | |
580 | 0.006 |
Subset | Pleiades | Pleiades + DTM |
---|---|---|
0.76 | 0.89 | |
0.58 | 0.86 | |
0.76 | 0.88 | |
0.48 | 0.84 | |
0.56 | 0.87 | |
0.74 | 0.88 | |
0.75 | 0.87 | |
0.74 | 0.87 | |
0.79 | 0.81 | |
0.56 | 0.90 | |
0.77 | 0.90 | |
0.66 | 0.88 | |
0.67 | 0.81 |
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Dewi, R.S.; Bijker, W.; Stein, A. Comparing Fuzzy Sets and Random Sets to Model the Uncertainty of Fuzzy Shorelines. Remote Sens. 2017, 9, 885. https://doi.org/10.3390/rs9090885
Dewi RS, Bijker W, Stein A. Comparing Fuzzy Sets and Random Sets to Model the Uncertainty of Fuzzy Shorelines. Remote Sensing. 2017; 9(9):885. https://doi.org/10.3390/rs9090885
Chicago/Turabian StyleDewi, Ratna Sari, Wietske Bijker, and Alfred Stein. 2017. "Comparing Fuzzy Sets and Random Sets to Model the Uncertainty of Fuzzy Shorelines" Remote Sensing 9, no. 9: 885. https://doi.org/10.3390/rs9090885