# Reconstruction of River Boundaries at Sub-Pixel Resolution: Estimation and Spatial Allocation of Water Fractions

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Department of Civil, Environmental, and Mechanical Engineering, University of Trento, Via Mesiano, 77, 38123 Trento, Italy

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Department of Biology, Chemistry, and Pharmacy, Freie Universität Berlin, Altensteinstraße 6, 14195 Berlin, Germany

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Leibniz-Institute of Freshwater Ecology and Inland Fisheries, Müggelseedamm 310, 12587 Berlin, Germany

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Author to whom correspondence should be addressed.

Received: 4 October 2017 / Revised: 7 November 2017 / Accepted: 20 November 2017 / Published: 24 November 2017

(This article belongs to the Special Issue Geographic Information Science and Spatial Analysis in Water Resources)

Boundary pixels of rivers are subject to a spectral mixture that limits the accuracy of river areas extraction using conventional hard classifiers. To address this problem, unmixing and super-resolution mapping (SRM) are conducted in two steps, respectively, for estimation and then spatial allocation of water fractions within the mixed pixels. Optimal band analysis for the normalized difference water index (OBA-NDWI) is proposed for identifying the pair of bands for which the NDWI values yield the highest correlation with water fractions. The OBA-NDWI then incorporates the optimal NDWI as predictor of water fractions through a regression model. Water fractions obtained from the OBA-NDWI method are benchmarked against the results of simplex projection unmixing (SPU) algorithm. The pixel swapping (PS) algorithm and interpolation-based algorithms are also applied on water fractions for SRM. In addition, a simple modified binary PS (MBPS) algorithm is proposed to reduce the computational time of the original PS method. Water fractions obtained from the proposed OBA-NDWI method are demonstrated to be in good agreement with those of SPU algorithm (R

^{2}= 0.9, RMSE = 7% for eight-band WorldView-3 (WV-3) image and R^{2}= 0.87, RMSE = 9% for GeoEye image). The spectral bands of WV-3 provide a wealth of choices through the proposed OBA-NDWI to estimate water fractions. The interpolation-based and MBPS methods lead to sub-pixel maps comparable with those obtained using the PS algorithm, while they are computationally more effective. SRM algorithms improve user/producer accuracies of river areas by about 10% with respect to conventional hard classification.*Keywords:*river boundaries; NDWI; unmixing; super resolution mapping; pixel swapping; interpolation