Unmixing Results Research Articles

Curvelet Transform Domain-Based Sparse Nonnegative Matrix Factorization for Hyperspectral Unmixing

Hyperspectral unmixing (HU) is an efficient way to extract component information from mixed pixels in remotely sensed imagery. Nonnegative matrix factorization (NMF) based unmixing methods have been widely used due to their ability to extract endmembers (pure spectral signatures) and their corresponding fractional abundances in simultaneous fashion. In this article, we propose a new sparse-constrained NMF method for HU purposes. Unlike most sparse regularizers, imposed on abundances (vectors or matrix) directly, our method imposes sparse constraints on a transformed abundance domain. It is based on the assumption that sparsity, when applied on a well-designed transform domain, leads to sparser representations than those in the corresponding source domain (e.g., natural images are approximately sparse in a wavelet domain). In this regard, we specifically explore sparsity on a curvelet transformed domain of abundances. Moreover, we consider the Chambolle–Pock algorithm to solve the involved optimization model, so as to obtain a fast and stable solution. Our experiments, carried out on both synthetic and real hyperspectral datasets, reveal that our newly proposed transform domain-based sparse NMF unmixing method (hereinafter named as “TS-NMF”) obtains better unmixing results than those achieved by other state-of-the-art NMF-based unmixing methods, with less parameter tuning and better robustness to noise.

Nonlinear Endmember Identification for Hyperspectral Imagery via Hyperpath-Based Simplex Growing and Fuzzy Assessment

Nonlinear geometric manifold of hyperspectral data usually makes great trouble for accurate endmember extraction in literature. To address this issue, we propose a novel nonlinear endmember extraction algorithm by building a hypergraph and a fuzzy assessment strategy. The global change of nonlinear data manifold is first measured in a hypergraph whose hyperedges correspond to different local pixel subgroups. In contrast to edges in a simple graph, every hyperpath connected by multiple hyperedges instead of individual pixels effectively facilitates the determination of the simplex spanned by endmembers on complex data manifolds interfered by noises and outliers. Furthermore, in the hypergraph-based manifold system, a reliable fuzzy assessment mechanism for extracting the final endmembers is established by combining the classic simplex volume maximization rule with the inherent properties of hyperspectral data and hypergraph. In this procedure, the impact of outliers and the complex geometric structures of data can be further effectively reduced, leading to better unmixing results. Experimental results of various types of simulated data and real hyperspectral imagery demonstrate that the proposed algorithm (hypergraph and fuzzy-assessment-based nonlinear endmember extraction) can extract more accurate endmembers from complex data manifolds, and it is more robust to noises and outliers compared with state-of-the-art algorithms.

Improving Spectral-Based Endmember Finding by Exploring Spatial Context for Hyperspectral Unmixing

Hyperspectral unmixing, which intends to decompose mixed pixels into a collection of endmembers weighted by their corresponding fraction abundances, has been widely utilized for remote sensing image exploitation. Recent studies have revealed that spatial context of pixels is important complemental information for hyperspectral image processing. However, many well-known endmember finding (EF) algorithms identify spectrally pure spectra from hyperspectral images according to spectral information only, resulting in limited accuracy of hyperspectral unmixing application since they ignore spatial distribution or structure information in the image. Therefore, in this article, several novel spatial exploiting (SE) strategies are proposed to improve the performance of the well-known spectral-based EF (sEF) algorithms by integrating spatial information. Three different spatial exploiting strategies are designed to use pixel spatial context, by which the spectral variation of pixels can be alleviated to improve the performance of hyperspectral unmixing. Specifically, in pixel domain, the pixels are linearly reconstructed using their neighbors in which the spatially derived factor to weight the importance of the spectral information is generated using local linear representation and local sparse representation, while in the feature domain, pixels are revised using dominated features of neighboring pixels in singular value decomposition. The proposed spatial exploiting strategies can not only be used as a preprocessing stage to revise pixels for sEF algorithms, but also be used as a postprocessing step to revise endmembers found via sEF algorithms. Finally, experimental results on both synthetic and real hyperspectral datasets demonstrate that the proposed SE strategies can certainly improve the performance of several well-known sEF algorithms, and obtain more accurate unmixing results than several state-of-the-art spatial preprocessing methods.

Illumination invariant hyperspectral image unmixing based on a digital surface model.

Although many spectral unmixing models have been developed to address spectral variability caused by variable incident illuminations, the mechanism of the spectral variability is still unclear. This paper proposes an unmixing model, named illumination invariant spectral unmixing (IISU). IISU makes the first attempt to use the radiance hyperspectral data and a LiDAR-derived digital surface model (DSM) in order to physically explain variable illuminations and shadows in the unmixing framework. Incident angles, sky factors, visibility from the sun derived from the LiDAR-derived DSM support the explicit explanation of endmember variability in the unmixing process from radiance perspective. The proposed model was efficiently solved by a straightforward optimization procedure. The unmixing results showed that the other state-of-the-art unmixing models did not work well especially in the shaded pixels. On the other hand, the proposed model estimated more accurate abundances and shadow compensated reflectance than the existing models.

Decomposition of mixed pixels in MODIS data using Bernstein basis functions

The decomposition of mixed pixels in Moderate Resolution Imaging Spectroradiometer (MODIS) images is essential for the application of MODIS data in many fields. Many existing methods for unmixing mixed pixels use principal component analysis to reduce the dimensionality of the image data and require the extraction of endmember spectra. We propose the pixel spectral unmixing index (PSUI) method for unmixing mixed pixels in MODIS images. In this method, a set of third-order Bernstein basis functions is applied to reduce the dimensionality of the image data and characterize the spectral curves of the mixed pixels in a MODIS image, and then the derived PSUIs (i.e., the coefficients of the basis functions) are calibrated by means of the abundance values of the ground features from the Landsat Enhanced Thematic Mapper Plus (ETM+)/Operational Land Imager (OLI) classification images corresponding to the date and region of the MODIS image. The proposed method was tested on MODIS and ETM+/OLI images, and it obtained satisfying unmixing results. We compared the PSUI method with conventional methods, including the pixel purity index, the N-finder algorithm, the sequential maximum angle convex cone, and vertex component analysis and found that the PSUI method outperformed the other four methods.

Spatial Patterns of Chemical Weathering at the Basal Tertiary Nonconformity in California from Multispectral and Hyperspectral Optical Remote Sensing

Visible through shortwave (VSWIR) spectral reflectance of the geologic units across the basal Tertiary nonconformity (BTN) is characterized at three spatially disparate locations in California. At two of these sites, location-specific spectral endmembers are obtained from AVIRIS imaging spectroscopy and linear spectral mixture models are used to visualize spatial patterns in chemical weathering associated with the BTN. Weathering patterns are found to match well with traditional geologic maps of the BTN at each site, but results show more spatially detailed quantitative geologic information about the spatial variability of chemical weathering near the nonconformity than is possible in a traditional geologic map. Spectral endmembers and unmixing results are also compared across locations. At the two locations with AVIRIS coverage, strong absorptions centered near 2200 nm are observed, consistent with previous geologic publications reporting intense chemical weathering at the BTN. Information loss associated with multispectral sampling of the reflectance continuum is also examined by resampling endmembers from the Maniobra location to mimic the spectral response functions of the WorldView 3, Sentinel-2 and Landsat 8 sensors. Simulated WorldView 3 data most closely approximate the full information content of the AVIRIS observations, resulting in nearly unbiased unmixing results for both endmembers. Mean fraction differences are −0.02 and +0.03 for weathered and unweathered endmembers, respectively. Sentinel-2 and Landsat 8 are unable to distinguish narrow, deep SWIR absorptions from changes in the overall amplitude of the SWIR spectral continuum, resulting in information loss and biased unmixing results. Finally, we characterize a third location using Sentinel-2 observations only. At this site we also find spectrally distinct features associated with several lithologies, providing new information relevant to the mapping of geologic contacts which is neither present in high spatial resolution visible imagery, nor in published geologic mapping. Despite these limitations, the spatial pattern of the Sentinel-2 and Landsat 8 fraction estimates is sufficiently similar to that of the WorldView 3 and AVIRIS fraction estimates to be useful for mapping purposes in cases where hyperspectral data are unavailable.

Mineralogical and lithological unmixing with radiative transfer modelling in the open-pit context of Mine Canadian Malartic

In this study, Hapke's radiative transfer model is used to verify the feasibility of retrieving the composition and grain-size of the ground in an open-pit mine, seen as a regolith. Such a tool could be useful for dust surveys and thus preventing potential environmental risks such as acid mine drainage. As the true compositional endmembers of the medium are not retrieved but rather chosen from spectral libraries and the range of grain sizes (a few to hundreds of micrometers) and porosities (0.22 to 0.52 for the filling factor) vary greatly in an open-pit mine, we show that the mineralogical unmixing results are not reliable. Too many combinations of different relative abundances, grain sizes and porosities lead to fits between modelled and measured spectra under 0.3% in reflectance. To tackle this issue, we explore a lithological unmixing approach. Considering lithologies as endmembers, as opposed to considering minerals, reduces the variability in the solutions as fewer endmembers are used. The results show that the studied samples with multi-component grains behave spectrally as expected for mono-mineral grains. With no root mean square errors higher than 5%, the relative abundances retrieved are sufficiently precise to consider mapping lithologies with this method.

Joint Local Block Grouping with Noise-Adjusted Principal Component Analysis for Hyperspectral Remote-Sensing Imagery Sparse Unmixing

Spatial regularized sparse unmixing has been proved as an effective spectral unmixing technique, combining spatial information and standard spectral signatures known in advance into the traditional spectral unmixing model in the form of sparse regression. In a spatial regularized sparse unmixing model, spatial consideration acts as an important role and develops from local neighborhood pixels to global structures. However, incorporating spatial relationships will increase the computational complexity, and it is inevitable that some negative influences obtained by inaccurate estimated abundances’ spatial correlations will reduce the accuracy of the algorithms. To obtain a more reliable and efficient spatial regularized sparse unmixing results, a joint local block grouping with noise-adjusted principal component analysis for hyperspectral remote-sensing imagery sparse unmixing is proposed in this paper. In this work, local block grouping is first utilized to gather and classify abundant spatial information in local blocks, and noise-adjusted principal component analysis is used to compress these series of classified local blocks and select the most significant ones. Then the representative spatial correlations are drawn and replace the traditional spatial regularization in the spatial regularized sparse unmixing method. Compared with total variation-based and non-local means-based sparse unmixing algorithms, the proposed approach can yield comparable experimental results with three simulated hyperspectral data cubes and two real hyperspectral remote-sensing images.

Superpixel-based local collaborative sparse unmixing for hyperspectral image

Hyperspectral sparse unmixing aims to identify the best subset of endmembers provided in previously available libraries (which may be very large) and their corresponding proportions (fractional abundance). A sparse unmixing method, local collaborative sparse unmixing (LCSU), including spatial information in standard collaborative formulations, has produced better unmixing results. However, the local window size taken in this method can always have an effect on unmixing result. In detail, LCSU tends to be affected by the distribution of ground objects as well as collaborative sparse unmixing. To address this limitation, we introduce a robust strategy to enforce the local collaborative property in homogeneous areas. The proposed method first divides the denoised image into superpixels according to the quarternion theory, which involves spatial information, and then implements collaborative sparse unmixing in each superpixel. Compared with the most advanced sparse unmixing methods, experiments on two different synthetic datasets and a real hyperspectral dataset effectively verify the advantages of our proposed method.

Endmember extraction from hyperspectral imagery based on QR factorisation using givens rotations

Hyperspectral images are mixtures of spectra of materials in a scene. Accurate analysis of hyperspectral image requires spectral unmixing. The result of spectral unmixing is the material spectral signatures and their corresponding fractions. The materials are called endmembers. Endmember extraction equals to acquire spectral signatures of the materials. In this study, the authors propose a new hyperspectral endmember extraction algorithm for hyperspectral image based on QR factorisation using Givens rotations (EEGR). Evaluation of the algorithm is demonstrated by comparing its performance with two popular endmember extraction methods, which are vertex component analysis (VCA) and maximum volume by householder transformation (MVHT). Both simulated mixtures and real hyperspectral image are applied to the three algorithms, and the quantitative analysis of them is presented. EEGR exhibits better performance than VCA and MVHT. Moreover, EEGR algorithm is convenient to implement parallel computing for real-time applications based on the hardware features of Givens rotations.

Reweighted local collaborative sparse regression for hyperspectral unmixing

Sparse unmixing is based on the assumption that each mixed pixel in the hyperspectral image can be expressed in the form of linear combinations of known pure signatures in the spectral library. Collaborative sparse regression improves the unmixing results by solving a joint sparse regression problem, where the sparsity is simultaneously imposed to all pixels in the data set. However, hyperspectral images exhibit rich spatial correlation that can be exploited to better estimate endmember abundances. The work, based on the iterative reweighted algorithm and local collaborative sparse unmixing, utilized a reweighted local collaborative sparse unmixing (RLCSU). The simultaneous utilization of iterative reweighted minimization and local collaborative sparse unmixing (including spectral information and spatial information in the formulation, respectively) significantly improved the sparse unmixing performance. The optimization problem was simply solved by the variable splitting and augmented Lagrangian algorithm. Our experimental results were obtained by using both simulated and real hyperspectral data sets. The proposed RLCSU algorithm obtain better signal-to-reconstruction error (SRE, measured in dB) results than LCSU and CLSUnSAL algorithms in all considered signal-to-noise ratio (SNR) levels, especially in the case of low noise values. The RLCSU algorithm obtains a better SRE(dB) result (30.01) than LCSU (20.08) and CLSUnSAL (17.28) algorithms for the simulated data 1 with SNR = 50 dB. It demonstrated that the proposed method is an effective and accurate spectral unmixing algorithm.

Phase Functions of Typical Lunar Surface Minerals Derived for the Hapke Model and Implications for Visible to Near‐Infrared Spectral Unmixing

AbstractLaboratory spectrophotometric measurements of minerals common on the lunar surface (olivine, pyroxene, plagioclase, and ilmenite) are measured over a wavelength range of 0.4 to 2.5 μm to better understand the effects of the particle phase function (PF; P[g]) on the application of Hapke's radiative transfer model to reflectance spectra of lunar materials. One objective of this work is to determine if accounting for wavelength‐dependent photometric effects can improve spectral estimates of mineral abundance in lunar materials, particularly that of ilmenite. We also discuss a two‐step calibration method to correct for the non‐Lambertian behavior and wavelength dependence of the common reference standard Spectralon. Both a two‐term Legendre polynomial representation of the PF and the Henyey‐Greenstein PF are examined. We use our results to apply the Hapke radiative transfer model to reflectance spectra of lab mixtures and test the effects of different PF characteristics and assumptions. Laboratory spectra indicate that ilmenite exhibits more backward scattering behavior compared with silicate minerals, which are more forward scattering. We find that the variations in PF can affect derived single‐scattering albedo values and thus spectral unmixing results. Because single‐scattering contribution dominates the reflectance properties of dark minerals such as ilmenite, large uncertainties in derived single‐scattering albedo values can be introduced by small changes in PFs. However, it is observed that the use of a wavelength‐dependent PF does not produce significant differences in spectral unmixing results for binary and ternary silicate mixtures.

Examining the effectiveness of weighted spectral mixture analysis (WSMA) in urban environments

ABSTRACTSpectral mixture analysis (SMA) has been widely applied for estimating fractional land-cover types from remote sensing pixels. SMA typically assumes each spectral band has equal contribution to the unmixing results, which has attracted debates on whether a different weight should be given to each band. Subsequently, a number of weighted SMA (WSMA) approaches have been developed and applied to different research fields. The necessity and applicability of WSMA, however, have not been adequately addressed, especially when applied to urban environments. This paper, therefore, aims to answer two research questions, including 1) whether significantly different results would be generated through applying a WSMA, and 2) which WSMA approach performs better in an urban environment. Specifically, five existing schemes: Shannon Entropy-weighted method (Entropy), reflected energy fixed-weighted vector (REFWV), InStability Index-based weighting method (ISIb), combined weighting vector (WV), and within-class variance (VW), and five potential schemes: between-class variance (VB), total-class variance (VT), inversed Optimum Index Factor (IOIF), mean (Mean), and standard deviation (SD), were employed to construct WSMAs. We tested each weighting scheme 100 times with different endmember classes’ spectra. Performance of each WSMA was evaluated using the mean absolute error (MAE). Paired-samples t-test was applied to indicate if there is a significant difference between the mean of MAEs. Results illustrated that only REFWV, ISIb, and WV in All samples (samples included vegetation, high albedo impervious surface area, and low albedo impervious surface area) outperformed the unweighted scheme significantly. Other weighting schemes, such as IOIF, VB, VT, and SD illustrated unstable performance in different study areas. The rest of weighting schemes weakened the performance compared to the unweighted scheme. We concluded that REFWV, ISIb, and WV in All samples can be applied in analysing urban environments with three-endmember (vegetation – high albedo impervious surface area – low albedo impervious surface area) model to improve the performance of SMA. The construction of future weighting schemes would be better to consider the class variance.

Spatial Discontinuity-Weighted Sparse Unmixing of Hyperspectral Images

Spectral unmixing is an important technique for remotely sensed hyperspectral image interpretation, of which the goal is to decompose the image into a set of pure spectral components (endmembers) and their abundance fractions in each pixel of the scene. Sparse-representation-based approaches have been widely studied for remotely sensed hyperspectral unmixing. A recent trend is to incorporate the spatial information to improve the spectral unmixing results. Those methods generally assume that the abundances of the pixels are piecewise smooth and fall into a homogeneous region occupied by the same endmembers and their corresponding fractional abundances. However, in real scenarios, abundances may vary abruptly from pixel to pixel. Therefore, the former assumption in most spatial models does not hold. To address this limitation, we propose a new strategy to preserve the spatial details in the abundance maps via a spatial discontinuity weight. Our experimental results, conducted with both simulated and real hyperspectral data sets, illustrate the good potential of our discontinuity-preserving strategy for sparse unmixing, which can greatly improve the abundance estimation results.

Spatially adaptive hyperspectral unmixing through endmembers analytical localization based on sums of anisotropic 2D Gaussians

Spectral unmixing provides, for each pixel in the image, an estimated vector of fractional abundances that correspond to pure signatures, known as endmembers (EMs). Standard unmixing techniques rely only on spectral information and each pixel is solved as an individual entity. Recent studies show that incorporating the image's spatial information enhances accuracy of the unmixing results. Spatial information may allow better selection of relevant EMs, for each pixel, rather than utilizing all potential EMs in solving the spectral mixing problem. To implement this approach, we developed a new method for spatially adaptive spectral unmixing called Gaussian-based spatially adaptive unmixing (GBSAU). GBSAU fits for each EM, a surface by a series of spatial anisotropic 2D Gaussians whose sum represents the EM's fraction distribution over the whole image. These analytical surfaces facilitate a sparse solution for the unmixing process by spatial localization of EMs, which is then used to determine an adaptive subset of actual EMs for each pixel. The performance of our novel method was compared with that of the state-of-art spatially adaptive unimximg method, sparse unmixing via variable splitting augmented Lagrangian and total variation (SUnSAL-TV) as well as with two ordinary non-spatial methods, sparse unmixing by variable splitting and augmented Lagrangian (SUnSAL) and vectorized code projected gradient descent unmixing (VPGDU). The comparison was carried out on both simulated and real hyperspectral images. The results obtained with GBSAU indicated a significant improvement in the overall accuracy of the unmixing process compared with both spatially adaptive and ordinary methods. Quantitatively, GBSAU reduces the average mean absolute error (MAE) of the results by ∼15%, for cases with SNR = 30 db and 20 db, and by ∼30% for cases with SNR = 10 db and 5 db.

A Hierarchical Sparsity Unmixing Method to Address Endmember Variability in Hyperspectral Image

With a low spectral resolution hyperspectral sensor, the signal recorded from a given pixel against the complex background is a mixture of spectral contents. To improve the accuracy of classification and subpixel object detection, hyperspectral unmixing (HU) is under research in the field of remote sensing. Two factors affect the accuracy of unmixing results including the search of global rather than local optimum in the HU procedure and the spectral variability. With that in mind, this paper proposes a hierarchical weighted sparsity unmixing (HWSU) method to improve the separation of similar interclass endmembers. The hierarchical strategy with abundance sparsity representation in each layer aims to obtain the global optimal solution. In addition, considering the significance of different bands, a weighted matrix of spectra is used to decrease the variability of intra-class endmembers. Both simulations and experiments with real hyperspectral data show that the proposed method can correctly obtain distinct signatures, accurate abundance estimation, and outperforms previous methods. Additionally, the test data shows that the mean spectral angle distance is less than 0.12 and the root mean square error is superior to 0.01.

Group Low-Rank Nonnegative Matrix Factorization With Semantic Regularizer for Hyperspectral Unmixing

In this paper, the low rank prior of abundances of hyperspectral data is explored and combined with semantic information to develop a new Group Low-rank constrained Nonnegative Matrix Factorization (GLrNMF) method for linear hyperspectral unmixing. First, hyperspectral image pixels are divided into several groups of superpixels, and then low-rank constraints are cast on them to explore the semantic geometry in both spatial and spectral domains. By incorporating semantic information into the NMF, we can recover more accurate endmembers and abundances in the linear unmixing model. Some experiments are taken on several synthetic and real hyperspectral data to investigate the performance of GLrNMF, and the results show that it can outperform some state-of-the-art unmixing results.

Hyperspectral Unmixing via Low-Rank Representation with Space Consistency Constraint and Spectral Library Pruning

Spectral unmixing is a popular technique for hyperspectral data interpretation. It focuses on estimating the abundance of pure spectral signature (called as endmembers) in each observed image signature. However, the identification of the endmembers in the original hyperspectral data becomes a challenge due to the lack of pure pixels in the scenes and the difficulty in estimating the number of endmembers in a given scene. To deal with these problems, the sparsity-based unmixing algorithms, which regard a large standard spectral library as endmembers, have recently been proposed. However, the high mutual coherence of spectral libraries always affects the performance of sparse unmixing. In addition, the hyperspectral image has the special characteristics of space. In this paper, a new unmixing algorithm via low-rank representation (LRR) based on space consistency constraint and spectral library pruning is proposed. The algorithm includes the spatial information on the LRR model by means of the spatial consistency regularizer which is based on the assumption that: it is very likely that two neighbouring pixels have similar fractional abundances for the same endmembers. The pruning strategy is based on the assumption that, if the abundance map of one material does not contain any large values, it is not a real endmember and will be removed from the spectral library. The algorithm not only can better capture the spatial structure of data but also can identify a subset of the spectral library. Thus, the algorithm can achieve a better unmixing result and improve the spectral unmixing accuracy significantly. Experimental results on both simulated and real hyperspectral datasets demonstrate the effectiveness of the proposed algorithm.

Sparsity-Constrained NMF Algorithm Based on Evolution Strategy for Hyperspectral Unmixing

As a powerful and explainable blind separation tool, non-negative matrix factorization (NMF) is attracting increasing attention in Hyperspectral Unmixing(HU). By effectively utilizing the sparsity priori of data, sparsity-constrained NMF has become a representative method to improve the precision of unmixing. However, the optimization technique based on simple multiplicative update rules makes its unmixing results easy to fall into local minimum and lack of robustness. To solve these problems, this paper proposes a new hybrid algorithm for sparsity constrained NMF by intergrating evolutionary computing and multiplicative update rules (MURs). To find the superior solution in each iteration,the proposed algorithm effectively combines the MURs based on alternate optimization technique, the coefficient matrix selection strategy with sparsity measure, as well as the global optimization technique for basis matrix via the differential evolution algorithm .The effectiveness of the proposed method is demonstrated via the experimental results on real data and comparison with representative algorithms.

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

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 (R2 = 0.9, RMSE = 7% for eight-band WorldView-3 (WV-3) image and R2 = 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.