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Hyperspectral Unmixing: Ground Truth Labeling, Datasets, Benchmark Performances and Survey

Feiyun Zhu

arXiv:1708.05125v2cs.CV

TL;DR

HU research is constrained by limited commonly used datasets and generally unavailable ground truths, while unsupervised HU must estimate both endmembers and abundances. The paper proposes a general HU labeling method and HyC-dataset transformation, labels real images, implements synthetic-image generation, and reviews and implements benchmark HU algorithms. The paper labeled up to 15 hyperspectral images and compared five benchmark HU algorithms on the 15 hyperspectral images.

  • Problem

    HU research is constrained by limited commonly used datasets and generally unavailable ground truths, while unsupervised HU must estimate both endmembers and abundances.

    Source: §I · p. 1

  • Method

    The paper proposes a general HU labeling method and HyC-dataset transformation, labels real images, implements synthetic-image generation, and reviews and implements benchmark HU algorithms.

    Source: §I · p. 1

  • Results

    The paper labeled up to 15 hyperspectral images and compared five benchmark HU algorithms on the 15 hyperspectral images.

    Source: §VIII · pp. 11–12

  • Takeaways & Limitations

    The benchmark comparisons may provide a valid baseline for evaluating new HU algorithms.

    Source: §VIII · p. 12

Abstract

from arXiv · show

Hyperspectral unmixing (HU) is a very useful and increasingly popular preprocessing step for a wide range of hyperspectral applications. However, the HU research has been constrained a lot by three factors: (a) the number of hyperspectral images (especially the ones with ground truths) are very limited; (b) the ground truths of most hyperspectral images are not shared on the web, which may cause lots of unnecessary troubles for researchers to evaluate their algorithms; (c) the codes of most state-of-the-art methods are not shared, which may also delay the testing of new methods. Accordingly, this paper deals with the above issues from the following three perspectives: (1) as a profound contribution, we provide a general labeling method for the HU. With it, we labeled up to 15 hyperspectral images, providing 18 versions of ground truths. To the best of our knowledge, this is the first paper to summarize and share up to 15 hyperspectral images and their 18 versions of ground truths for the HU. Observing that the hyperspectral classification (HyC) has much more standard datasets (whose ground truths are generally publicly shared) than the HU, we propose an interesting method to transform the HyC datasets for the HU research. (2) To further facilitate the evaluation of HU methods under different conditions, we reviewed and implemented the algorithm to generate a complex synthetic hyperspectral image. By tuning the hyper-parameters in the code, we may verify the HU methods from four perspectives. The code would also be shared on the web. (3) To provide a standard comparison, we reviewed up to 10 state-of-the-art HU algorithms, then selected the 5 most benchmark HU algorithms, and compared them on the 15 real hyperspectral datasets. The experiment results are surely reproducible; the implemented codes would be shared on the web.

I. INTRODUCTION

Hyperspectral unmixing is challenging because mixed pixels and unknown endmembers complicate estimation, while limited shared datasets and ground truths constrain research. The paper responds with labeling and dataset resources, synthetic data, algorithm implementations, and benchmark comparisons.

I. INTRODUCTION

  • HU estimates endmembers and their pixel-wise abundances, but in the unsupervised setting both are unknown.Mixed spectra arise from multiple substances, and unknown endmembers make HU challenging.Source: §I · p. 1
  • The paper introduces a general HU labeling method and proposes transforming HyC datasets for HU research.The labeling method covers endmembers, abundances, and evaluation of labeling results.Source: §I · p. 1
  • The authors provide 15 real hyperspectral images and 18 ground-truth versions as resources for HU evaluation.The images include selected subimages (ROIs) from seven popular hyperspectral images.Source: §I · p. 1, Figure 1 · p. 2, Table I · p. 2
  • The paper reviews and implements a complex synthetic-image generation method for testing HU algorithms under different conditions.Its code is to be shared on the web.Source: §I · p. 1
  • The authors review 10 state-of-the-art HU methods, provide code for five, and compare five benchmark methods on 15 real images.The paper presents the comparisons as benchmark HU performance.Source: §I · pp. 1–2

II. THE THREE CATEGORIES OF HU METHODS

  • Supervised HU assumes endmembers are known, whereas weakly supervised methods select spectra from a pre-collected material library.The library can be inconsistent across sensors, band ranges, and recording conditions, limiting its suitability.Source: §II · pp. 2–3
  • Unsupervised HU learns endmembers and abundances from the image; geometric methods include N-FINDR and VCA, while statistical methods include NMF.Geometric methods can be fast but require pure pixels, which the authors describe as unreliable in practice.Source: §II · p. 3

III. REVIEW OF THE STATE-OF-THE-ART HU METHODS

The section formulates HU as a nonnegative factorization of the hyperspectral data into endmembers and abundances, then reviews NMF and its constrained extensions. Because the joint objective is non-convex, NMF extensions add priors to restrict the solution space.

III. REVIEW OF THE STATE-OF-THE-ART HU METHODS

  • HU models the nonnegative data matrix X as the product of an endmember matrix M and an abundance matrix A, with constraints on either factor.Each abundance vector contains the endmember proportions for one pixel.Source: §III · p. 3

A. Nonnegative Matrix Factorization (i.e., NMF) [51, 52]

  • With Euclidean loss, the model becomes standard NMF, whose joint objective is non-convex and makes finding global minima unrealistic.Lee and Seung's multiplicative updates are non-increasing; active-set, alternating nonnegative least squares, and projected-gradient methods are also noted.Source: A. Nonnegative Matrix Factorization… · p. 3
  • NMF extensions restrict the solution space by imposing priors on abundances, endmembers, or both.The section identifies abundance and endmember constraints as the two broad extension types for HU.Source: A. Nonnegative Matrix Factorization… · p. 3

B. The NMF extensions with constraints on the abundances

Abundance-constrained NMF extensions encode sparsity and spatial structure, with some adapting sparsity to pixel-level mixing and robustness to outlier channels. The approaches vary in whether their abundance penalties are fixed, graph-based, or data-guided.

1) W-NMF [61] (or G-NMF [64]):

  • W-NMF combines spectral and spatial information in a local-neighborhood weight matrix, while its graph-Laplacian penalty regularizes the abundance maps.G-NMF forms its graph using pixel features only; W-NMF's Laplacian is learned from the hyperspectral image.Source: 1) W-NMF [61] (or G-NMF [64]) · p. 3

B. The NMF extensions with constraints on the abundances

  • Sparsity-constrained NMF assumes pixels mix only parts of the endmembers; ℓ1/2-NMF was proposed because ℓ1 sparsity may be limited under full additivity.The cited ℓ1-NMF and ℓ1/2-NMF impose abundance penalties.Source: 1) W-NMF [61] (or G-NMF [64]) · pp. 3–4
  • The reviewed abundance constraints include sparsity penalties balanced by λ and graph regularization based on a Laplacian.W-NMF's λ balances the graph constraint; the cited sparsity methods use λ for their sparsity constraints.Source: 1) W-NMF [61] (or G-NMF [64]) · pp. 3–4

3) DgS-NMF [14] and RRLbS [16]:

  • DgS-NMF uses a data-guided map of pixel mixing levels to apply an adaptive ℓp sparsity constraint; constant map values recover ℓ1-NMF or ℓ1/2-NMF.A map of zeros gives ℓ1-NMF, while values of 1/2 give ℓ1/2 regularization.Source: 3) DgS-NMF [14] and RRLbS [16] · p. 4
  • RRLbS uses an ℓ2,1 reconstruction loss to reduce outlier-channel influence and learns its DgMaps simultaneously with the abundances.Its map is tied to the abundances, and its update rule differs from DgS-NMF because of the robust loss and simultaneous map learning.Source: 3) DgS-NMF [14] and RRLbS [16] · p. 4

4) Structure (or Graph) and Sparsity constrained NMF (SS-NMF [15] and GL-NMF [63]):

This section reviews methods that combine graph structure with sparsity, followed by a correntropy-based NMF that addresses outlier sensitivity through reweighting. The graph construction differs between SS-NMF and GL-NMF.

4) Structure (or Graph) and Sparsity constrained NMF (SS-NMF [15] and GL-NMF [63]):

  • SS-NMF combines graph and ℓ1 sparsity constraints, learning its graph Laplacian from both spectral and spatial information.Its abundance penalty combines a Laplacian term with an ℓ1 term.Source: 4) Structure (or Graph) and Sparsity… · p. 4
  • GL-NMF combines graph and ℓ1/2 sparsity constraints but constructs its graph Laplacian using spectral information only.The method ignores spatial information when constructing the graph.Source: 4) Structure (or Graph) and Sparsity… · p. 4

5) Correntropy based NMF (CE-NMF) [2]:

  • CE-NMF uses correntropy to measure reconstruction error and ℓ1 sparsity, with half-quadratic optimization producing iteratively reweighted NMF.The reweighting assigns smaller weights to noisy channels and emphasizes noise-free channels.Source: 5) Correntropy based NMF (CE-NMF) [2] · pp. 4–5

C. The NMF extensions with constraints on the endmembers

Endmember-constrained NMF extensions impose priors on M while leaving abundance constraints inactive. The reviewed methods constrain either simplex volume or endmember smoothness and dissimilarity.

C. The NMF extensions with constraints on the endmembers

1) Minimum Volume Constrained NMF (MVC-NMF) [27]:

  • MVC-NMF combines geometric and statistical properties by seeking endmembers that form the minimum-volume simplex circumscribing the data.Its objective uses Euclidean representation error and a projected-gradient update; the endmember transform uses principal components of the data.Source: 1) Minimum Volume Constrained NMF… · p. 5

2) Endmember Dissimilarity Constrained NMF (EDC-NMF) [37]:

  • EDC-NMF assumes endmember spectra should be smooth across bands and as different from one another as possible.Its constraint uses spectral gradients and its optimization uses multiplicative updates.Source: 2) Endmember Dissimilarity Constrained… · p. 5
  • EDC-NMF's derivative introduces negative values into its endmember update, requiring projection to a given nonnegative value and restricting λ selection.The authors state that this limits the method's efficacy.Source: 2) Endmember Dissimilarity Constrained… · p. 5

IV. HOW TO LABEL GROUND TRUTHS IN THE HU?

The paper proposes a general procedure for labeling HU ground truths, which comprise endmember and abundance labels. It addresses how to produce those labels and how to check them.

IV. HOW TO LABEL GROUND TRUTHS IN THE HU?

  • Ground-truth labeling for HU comprises endmember labeling and abundance labeling, and this paper presents a general method for both.The authors identify earlier work as briefly covering only HYDICE Urban labeling.Source: §IV · p. 5

A. The Endmember labeling

  • Endmembers are problem-dependent: scene expertise, published endmember information, simpler scenes, and virtual dimensionality can guide their selection.Signatures may be selected from the image or obtained from the USGS mineral spectral library.Source: A. The Endmember labeling · pp. 5–6

B. The Abundance labeling

  • Because continuous abundances are difficult and labor-intensive to label manually, the authors estimate them using constrained least squares with fixed endmembers.They describe nonnegative and full-additivity constraints, and note that supervised unmixing methods can estimate abundances while treating endmembers as fixed inputs.Source: B. The Abundance labeling · p. 6

C. How to verify our labeling ground truth for the HU study?

  • Labeling checks include visual comparison with published illustrations, scene-consistency review, and checking whether similar spectra correspond to similar abundances.Library-selected Cuprite endmembers are treated as not requiring verification; settings may be varied to improve a labeling.Source: C. How to verify our labeling ground… · p. 6

D. How to transform the benchmark hyperspectral classifica-

The paper proposes transforming benchmark hyperspectral classification datasets for HU, addressing a gap between the tasks. Its procedure adapts class labels and candidate endmembers into endmember and abundance estimates.

D. How to transform the benchmark hyperspectral classifica-

  • The proposed transformation addresses the gap between HU and HyC, whose benchmark datasets and publicly available ground truths are more common and easier to interpret.The paper describes this as a promising route to use benchmark HyC datasets for HU research.Source: tion (HyC) datasets for the HU research? · p. 6
  • Similar HyC classes are combined so the resulting class count matches the number of HU endmembers.The authors note that supervised HyC algorithms can handle more classes than HU has endmembers.Source: tion (HyC) datasets for the HU research? · p. 6
  • For each class, high-quality labeled pixels provide candidate endmember signatures, represented by their mean or median spectrum.Source: tion (HyC) datasets for the HU research? · p. 6
  • Classification algorithms predict pixel labels, which can serve as abundances under an anchoring constraint or guide supervised unmixing with fixed candidate endmembers.The anchoring constraint keeps abundances around high-accuracy classification results; alternatively, candidate endmembers can initialize a model that updates both endmembers and abundances.Source: tion (HyC) datasets for the HU research? · pp. 6–7
  • The stated objective combines an abundance constraint with sparse or spatial priors and a reconstruction-error term.The passages identify the abundance constraint as anchoring abundances around classification results.Source: tion (HyC) datasets for the HU research? · p. 6

V. SUMMARIZATION OF THE 15 REAL HYPERSPECTRAL IMAGES AND THEIR 18 GROUND TRUTHS

The supplied passages describe selected Samson and Jasper Ridge subimages and their ground-truth endmembers and abundance maps. Samson’s three regions are equal-sized, while the Jasper Ridge examples show differing endmember sets.

  • The 952 × 952 Samson image has 156 bands, and three regions were selected because they contain large transitional areas with many mixed pixels.The passages identify the regions as Samson#1, Samson#2, and Samson#3.Source: A. Samson’s three subimages · p. 7
  • The Jasper Ridge figure presents three selected subimages with endmember and abundance-map illustrations; the supplied examples identify five endmembers for Jasper Ridge#1 and four for Jasper Ridge#2.Source: Figure 3 · p. 7, A. Samson’s three subimages · p. 7
  • Each Samson region is 95 × 95 pixels and uses three endmembers: Soil, Tree, and Water.The selected regions occupy different locations in the original image.Source: A. Samson’s three subimages · p. 7

B. Jasper Ridge’s three subimages

The Jasper Ridge passages describe image preprocessing and three selected subimages, including a previously shared benchmark region. The Urban passages document alternative ground-truth endmember counts and two challenging subimages.

B. Jasper Ridge’s three subimages

  • Jasper Ridge’s 224 bands are reduced to 198 after removing bands affected by water vapor and atmospheric effects.The full image is described as too complex for ground-truth labeling, motivating the use of three subimages.Source: B. Jasper Ridge’s three subimages · p. 7
  • Jasper Ridge#2 has four endmembers and a published ground truth that has been used in more than 10 HU papers.The three selected regions have distinct sizes and endmember sets.Source: B. Jasper Ridge’s three subimages · p. 8

C. HYDICE Urban and its two subimages

D. Cuprite

The section describes three real-image datasets and the ground-truth choices used for HU: Cuprite, Moffett Field, and San Diego Airport.

D. Cuprite

  • Cuprite uses a 250 × 190 subimage with 188 retained bands and 12 endmembers, although prior ground truths use 10 or 14.The paper adopts Dr. Lu’s 12-endmember setting; small differences in endmember settings can make results across prior studies differ.Source: D. Cuprite · p. 9

E. Moffett Field

  • Moffett Field uses two 60 × 60 subimages, each labeled with Soil, Tree, and Water as its three endmembers.The image has 196 retained bands after noisy bands are removed.Source: E. Moffett Field · p. 9

F. San Diego Airport

G. Washington DC Mall (WDM)

The section presents Washington DC Mall subimages, a configurable synthetic-image procedure, and a five-method benchmark comparison across real hyperspectral images.

G. Washington DC Mall (WDM)

  • WDM#1 and WDM#2 are subimages with six endmembers each, using different listed material labels and selections from the 1208 × 307-pixel HYDICE image.The full image has 191 bands after removal of bands affected by water vapor and atmospheric effects.Source: G. Washington DC Mall (WDM) · p. 10

VI. THE SIMULATED HYPERSPECTRAL IMAGE

  • The synthetic-image procedure selects 2–15 candidate spectra from 15 USGS signatures and generates abundance maps from randomly filled regions.A spatial low-pass filter creates transitional mixed areas; pixels with a largest abundance above 0.8 are replaced by equal mixtures of two endmembers, and noise can be added.Source: §VI · p. 10
  • The synthetic image is intended to test HU algorithms across noise robustness, pixel count, endmember count, and generalization to the number of bands.The endmember count is varied from 2 to 15, and the pixel count is set by z.Source: §VI · p. 10

VII. EXPERIMENTS RESULTS OF 5 BENCHMARK HU METHODS ON THE 18 HYPERSPECTRAL IMAGES

  • Five benchmark HU methods are compared on 15 real hyperspectral images to provide benchmark results for evaluating new methods.The selected methods are described as widely compared against state-of-the-art HU methods.Source: §VII · p. 10

A. Five Benchmark Methods Compared in this Section

B. Experiment Settings and Experiment Results

The experiments compare five benchmark methods across the paper’s real-image datasets, with the conclusion emphasizing shared HU ground truths and benchmark results as resources for new-method evaluation.

B. Experiment Settings and Experiment Results

  • All five methods use VCA to initialize endmembers and abundances on all 15 datasets, with coarse-to-fine grid search for hyperparameters.The paper gives reproducibility as one reason for using the same VCA initialization.Source: B. Experiment Settings and Experiment… · p. 11
  • SAD evaluates estimated endmembers and RMSE evaluates estimated abundances; the reported tables give means over 50 repetitions.The tables cover the Samson, Cuprite, Urban, JasperRidge, Moffett Field, Washington DC Mall, and San Diego Airport results.Source: B. Experiment Settings and Experiment… · p. 11
  • Tables II–VI report results for Samson, Cuprite, the full HYDICE Urban image and its subimages, and JasperRidge.Cuprite is evaluated only on endmembers because its ground-truth abundances are unavailable; the full Urban image has three ground-truth versions.Source: B. Experiment Settings and Experiment… · p. 11
  • Tables VII–IX cover Moffett Field, Washington DC Mall, and the two San Diego Airport ground-truth versions.The Washington DC Mall results cover two subimages.Source: B. Experiment Settings and Experiment… · p. 11

VIII. CONCLUSION

  • The paper provides a general labeling method, summarizes and labels up to 15 images, and proposes transforming HyC datasets for HU research.It also reviews and implements a synthetic image for verification under four conditions.Source: §VIII · pp. 11–12
  • The paper compares five benchmark HU algorithms on 15 hyperspectral images and presents the results as a baseline for evaluating new methods.The authors describe this as their first comparison of benchmark algorithms across this many real hyperspectral images.Source: §VIII · p. 12

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