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

^{1}

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## Abstract

**:**

^{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.

## 1. Introduction

## 2. Study Area and Imagery Set

## 3. Methodology

#### 3.1. Estimation of Water Fractions

#### 3.1.1. Semi-Simulated Fractions

#### 3.1.2. Real Fractions

_{h}) and a low-reflective band (b

_{l}) for which different pairs of bands can be employed for the computation of NDWI according to the following equation:

_{i}and b

_{j}for an n-band image that subscripts i and j can be assigned to different bands of an image considering the specified ranges in the equation. This provides a full search among all the possible options for choosing a pair of spectral bands which is also common in other applications such as bathymetry from optical imagery [37]. The total number of possible pairs of spectral bands would be $n\text{\hspace{0.17em}}!/((n-2)!\times 2\text{\hspace{0.17em}}!)$ for an n-band image, which means 28 pairs for a WV-3 image. After identification of the optimal combination of bands to be used for calculation of NDWI, the corresponding regression model is used to predict the water fractions of the image pixels. The regression-based approaches are previously used for estimation of fractional vegetation coverage using vegetation indices [38,39,40] but have not been explored yet for the estimation of water fractions based on water indices. Figure 5 illustrates the step-by-step procedure for estimation of water fractions based on the proposed OBA-NDWI.

#### 3.2. Super Resolution Mapping (SRM)

#### 3.2.1. Pixel Swapping (PS)

^{2}gives the number of sub-pixels for the non-water class.

^{k}denotes the attractiveness of a sub-pixel with respect to the class k, ${F}_{i}^{k}$ is the fraction of class k in the i-th neighbor pixel. The number of neighbor pixels is n, and d

_{i}is the distance of the i-th neighbor pixel from the sub-pixel for which the attractiveness is computed.

#### 3.2.2. Proposed Modified Binary Pixel Swapping (MBPS)

^{k}locations with the highest attractiveness values toward that class. The remaining sub-pixel locations are then directly assigned to the other class (non-water). The proposed modified binary PS (MBPS) method is applied on the same example discussed in Figure 6. In this case, the resultant sub-pixel map is the same as that of the original PS algorithm (Figure 7).

#### 3.2.3. Interpolation-Based SRM

## 4. Implementations and Results

#### 4.1. Estimation of Water Fractions

^{2}). Consideration of all the possible pair of bands is a systematic approach to identify the optimal structure of the NDWI that the results are in line with the assumption of Xie et al. [8] regarding the use of a relatively high-reflective band and a low-reflective band for calculation of the NDWI. As illustrated in Figure 12, coastal-blue (CB), blue (B), and green (G) bands can be considered as optimal high-reflective bands (b

_{h}), while the portion of the spectrum covering red-edge (RE), NIR1, and NIR2 could be effective as low-reflective bands (b

_{l}) using the WV-3 image. In particular, CB and RE bands provide the strongest relation with an R

^{2}on the order of 0.97 and an RMSE of 2%. This is while the original NDWI with the (G, NIR1) band combination provides significantly less accuracy (R

^{2}of 0.85 and RMSE of 12%). Blue and NIR are the optimal pair of bands for the GeoEye image. Their corresponding NDWI yields an R

^{2}value of 0.92 and an RMSE value of 7% through a quadratic relation with water fractions (Figure 13).

^{2}= 0.9, RMSE = 7% for the WV-3 image and R

^{2}= 0.87, RMSE = 9% for the GeoEye image) is observed between the estimated fractions of the proposed OBA-NDWI method and the SPU algorithm.

#### 4.2. Super Resolution Mapping (SRM)

## 5. Discussion

## 6. Conclusions and Suggestions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**True color composites of (

**a**) WV-3 image of Sarca River and (

**b**) the GeoEye image of Noce River; the river channels are highlighted by blue lines.

**Figure 2.**The procedure considered for the mapping and assessment of river boundaries at the sub-pixel resolution using both real and semi-simulated fractions; ZF represents the zoom factor.

**Figure 3.**(

**a**) Reference high resolution map, (

**b**) semi-simulated fractions with ZF = 5, (

**c**) hard classified map, and (

**d**) a possible random sub-pixel map.

**Figure 4.**The scheme for linear spectral mixture of three dominant endmembers of the land surface (i.e., water, vegetation, and soil). Each point inside the triangle represents a possible combination of fractions; adapted from Ji et al. [31].

**Figure 5.**The step-by-step procedure for implementation of the proposed optimal band analysis for the normalized difference water index (OBA-NDWI) for the estimation of water fractions.

**Figure 6.**Water fractions and the pixel swapping (PS) process for spatial allocation of sub-pixels for a given pixel; (

**a**) water fractions, (

**b**) random allocation of sub-pixels, and (

**c**,

**d**,

**e**) swaps (candidate sub-pixels for swapping are highlighted by dash-lines). Values of sub-pixels represent their attractiveness toward the water class.

**Figure 7.**Water fractions and the proposed modified binary pixel swapping (MBPS) for spatial allocation of sub-pixels for a given pixel; (

**a**) water fractions, (

**b**) identification of sub-pixel locations with highest attractiveness, highlighted by dash-lines, and (

**c**) allocation of water and non-water sub-pixels. The values of sub-pixels represent their attractiveness toward the water class.

**Figure 8.**An example of bilinear interpolation of water fractions; (

**a**) water fractions at the pixel level, and (

**b**) interpolated water fractions at the sub-pixel level with ZF = 5.

**Figure 9.**The regressions of normalized difference water index (NDWI) values with different band combinations obtained from synthetic WV-3 spectra against known water fractions; the pair of bands used for calculation of NDWI is indicated on each graph (CB and RE stand for coastal-blue and red-edge bands, respectively); zero-threshold and Otsu’s threshold are illustrated respectively with blue (dashed) and red (dot-dashed) lines.

**Figure 10.**The regressions of NDWI values with different band combinations obtained from synthetic GeoEye spectra against known water fractions; the pair of bands used for the calculation of NDWI is indicated on each graph; zero-threshold and Otsu’s threshold are illustrated, respectively, with blue (dashed) and red (dot-dashed) lines.

**Figure 11.**Minimum water fractions corresponding to zero-threshold and Otsu’s threshold for several NDWIs using synthetic WV-3 and GeoEye spectra; CB and RE stand, respectively, for coastal-blue and red-edge bands.

**Figure 12.**OBA-NDWI for the synthetic WV-3 spectra; all possible combinations of spectral bands are considered in the structure of NDWI to perform a second-order regression against water fractions. Values of (

**a**) R

^{2}and (

**b**) RMSE are represented by color bars.

**Figure 13.**OBA-NDWI for the synthetic GeoEye spectra; all possible combinations of spectral bands are considered in the structure of NDWI to perform a second order regression against water fractions. Values of (

**a**) R

^{2}and (

**b**) RMSE are represented by the color bars.

**Figure 14.**Water fractions of the WV-3 image obtained from (

**a**) the proposed OBA-NDWI method and (

**b**) the SPU algorithm.

**Figure 15.**Sub-pixel maps resultant from different super-resolution mapping (SRM) algorithms using semi-simulated water fractions: (

**a**) reference map, (

**b**) semi-simulated water fractions (ZF = 5), (

**c**) hard classified map, sub-pixel maps of (

**d**) PS, (

**e**) bilinear, (

**f**) bicubic, and (

**g**) lanczos3 algorithms; reference river boundaries are represented by red lines on each map.

**Figure 16.**Interpolation-based SRM using semi-simulated water fractions: (

**a**) reference map, (

**b**) semi-simulated water fractions (ZF = 5), (

**c**) hard classifed map, (

**d**) bicubic interpolation of water fractions, and (

**e**) sub-pixel map; reference river boundaries are represented by red lines on each map.

**Figure 17.**User and producer accuracies of hard classification and SRM algorithms using semi-simulated water fractions across a range of ZF for Sarca River; (HC: hard classification, PS: pixel swapping, MBPS: modified binary PS, BL: bilinear, BC: bicubic, L3: lanczos3).

**Figure 18.**User and producer accuracies of hard classification and SRM algorithms using semi-simulated water fractions across a range of ZF for Noce River; (HC: hard classification, PS: pixel swapping, MBPS: modified binary PS, BL: bilinear, BC: bicubic, L3: lanczos3).

**Figure 19.**Error maps of (

**a**) hard classification and (

**b**) sub-pixel map obtained from MBPS for a segment of the Sarca River using the WV-3 image with ZF = 6; red and blue pixels show erroneously committed and omitted water pixels, respectively.

**Figure 20.**Sub-pixel maps obtained from real water fractions based on OBA-NDWI algorithm for Sarca River: (

**a**) reference map, sub-pixel maps of (

**b**) PS, (

**c**) MBPS, (

**d**) bilinear, (

**e**) bicubic, and (

**f**) lanczos3 algorithms, ZF = 5.

**Figure 21.**Sub-pixel maps obtained from real water fractions based on OBA-NDWI algorithm for Noce River: (

**a**) reference map, (

**b**) real water fractions based on OBA-NDWI algorithm; sub-pixel maps of (

**c**) PS, (

**d**) MBPS, (

**e**) majority filter applied on MBPS, (

**f**) bilinear, (

**g**) bicubic, and (

**h**) lanczos3 algorithms, ZF = 5.

**Figure 22.**User and producer accuracies of SRM algorithms using real water fractions of: (

**a**,

**b**) the SPU algorthom, and (

**c**,

**d**) the OBA-NDWI algorithm across a range of ZF for Sarca River; (PS: pixel swapping, MBPS: modified binary PS, BL: bilinear, BC: bicubic, L3: lanczos3).

**Figure 23.**User and producer accuracies of SRM algorithms using real water fractions of: (

**a**,

**b**) the SPU algorithm, and (

**c**,

**d**) the OBA-NDWI algorithm across a range of ZF for Noce River; (PS: pixel swapping, MBPS: modified binary PS, BL: bilinear, BC: bicubic, L3: lanczos3).

**Figure 24.**Sub-pixel maps derived from OBA-NDWI using (

**a**) optimal pair of bands (CB and RE) against (

**b**) original pair of bands (NIR1, G) for the WV-3 image.

**Table 1.**Multispectral bands of GeoEye and WV-3 sensors and list of the sensors providing same/similar spectral resolutions.

Sensor | Multispectral Bands | High Resolution Sensors with Same/Similar Spectral and Radiometric Resolutions |
---|---|---|

GeoEye | Blue: 450–510 nm Green: 510–580 nm Red: 655–690 nm NIR: 780–920 nm | WV-4, IKONOS, QuickBird, KOMPSAT-3A, KOMPSAT-3, KOMPSAT-2, GaoFen-2, |

WV-3 | Coastal: 397–454 nm, Red: 626–696 nm Blue: 445–517 nm, Red Edge: 698–749 nm Green: 507–586 nm, NIR-1: 765–899 nm Yellow: 580–629 nm, NIR-2: 857–1039 nm | WV-2 |

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**MDPI and ACS Style**

Niroumand-Jadidi, M.; Vitti, A.
Reconstruction of River Boundaries at Sub-Pixel Resolution: Estimation and Spatial Allocation of Water Fractions. *ISPRS Int. J. Geo-Inf.* **2017**, *6*, 383.
https://doi.org/10.3390/ijgi6120383

**AMA Style**

Niroumand-Jadidi M, Vitti A.
Reconstruction of River Boundaries at Sub-Pixel Resolution: Estimation and Spatial Allocation of Water Fractions. *ISPRS International Journal of Geo-Information*. 2017; 6(12):383.
https://doi.org/10.3390/ijgi6120383

**Chicago/Turabian Style**

Niroumand-Jadidi, Milad, and Alfonso Vitti.
2017. "Reconstruction of River Boundaries at Sub-Pixel Resolution: Estimation and Spatial Allocation of Water Fractions" *ISPRS International Journal of Geo-Information* 6, no. 12: 383.
https://doi.org/10.3390/ijgi6120383