Comparing Fuzzy Sets and Random Sets to Model the Uncertainty of Fuzzy Shorelines

Abstract

This paper addresses uncertainty modelling of shorelines by comparing fuzzy sets and random sets. Both methods quantify extensional uncertainty of shorelines extracted from remote sensing images. Two datasets were tested: pan-sharpened Pleiades with four bands (Pleiades) and pan-sharpened Pleiades stacked with elevation data as the fifth band (Pleiades + DTM). Both fuzzy sets and random sets model the spatial extent of shoreline including its uncertainty. Fuzzy sets represent shorelines as a margin determined by upper and lower thresholds and their uncertainty as confusion indices. They do not consider randomness. Random sets fit the mixed Gaussian model to the image histogram. It represents shorelines as a transition zone between water and non-water. Their extensional uncertainty is assessed by the covering function. The results show that fuzzy sets and random sets resulted in shorelines that were closely similar. Kappa (κ) values were slightly different and McNemar's test showed high p-values indicating a similar accuracy. Inclusion of the DTM (digital terrain model) improved the classification results, especially for roofs, inundated houses and inundated land. The shoreline model using Pleiades + DTM performed better than that of using Pleiades only, when using either fuzzy sets or random sets. It achieved κ values above 80%.

Integrating Multisource of Bathymetry Data for Updating Basepoint and Baseline Positions of Maritime Boundary

“…The coastline can also be built based on tidecoordinated coastline, for example, by referring to the mean high water line whose information is obtained, for example using LIDAR data or field measurements (Liu, 2008;Kim, Lee and Min, 2017). Furthermore, the coastline can also be generated by classifying beach features using remote sensing images, namely by extracting water and non-water pixels, for example from multispectral, radar and hyperspectral images (Al Fugura, Billa and Pradhan, 2011;Dewi, Bijker and Stein, 2017).…”

Transferability and Upscaling of Fuzzy Classification for Shoreline Change over 30 Years

“…The second category consisted of image-based methods, which extracted instantaneous shoreline data from images whose acquisition time was correlated with tidal data-for instance, shoreline mapping from digital photogrammetry [13] and remote sensing imagery [14]. Since remotely sensed images record a shoreline at a particular instant, modelling shoreline with remote sensing images should include estimation of its uncertainty [15,16]. The uncertainty in shoreline modelling can arise, due to an inherent variability in nature, such as variation of a shoreline over time and the presence of gradual transitions between land and water [17,18].…”