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%.
Highlights
Remote sensing offers a practical and economical means for coastal research
We focused on the similarity of fuzzy sets and random sets in modelling the uncertainty in shoreline locations
This paper demonstrates that fuzzy sets and random sets produced comparable results for modelling the uncertainty of fuzzy shorelines
Summary
Remote sensing offers a practical and economical means for coastal research. A series of remote sensing images can be used, for example, for mapping the dynamics of wet grassland and vegetation patches [1], mapping depth and water quality [2], coastal erosion [3], and in particular shoreline mapping [4,5,6]. Several methods have been proposed, for example, using manual digitization [7], spectral indices extraction such as water and vegetation indices [8], active contour segmentation [6], band ratios [9], and image classification [10,11]. Most of these methods are based on hard classifications, and only a few considered soft classifications in the context of shoreline mapping [4,5,12]. This first type of uncertainty is classified as errors [14]
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