ROBUST UNMIXING OF HYPERSPECTRAL IMAGES: APPLICATION TO MARS
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Motivation Necessity of combining physical models and statistical techniques in unmixing Methods of integration of scientiﬁc models & statistical algorithms not always obvious – Enable machine learning techniques to produce scientiﬁcally meaningful results in unsupervised settings Meaningfulinformation not always readily accessible or easily readable – Representation = Simpliﬁcation
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Outline Background – Mineral spectral signatures in VNIR Meaningful features for mineral identiﬁcation Data challenges for planetary data Data processing pipeline Validation: expert assessment Comparison with state-of-the-art Conclusions and future work
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Mineral spectral signatures Each mineral has a distinct spectral shape (signature) Discriminative information mostly in absorption band positions and shapes Difference can be subtle Can create parameters for discrimination
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Mineral spectral signatures Each mineral has a distinct spectral shape (signature) Discriminative information mostly in absorption band positions and shapes Difference can be subtle Can create parameters for discrimination
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Spectral features for minerals Use splines Select knots so that
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Spectral features for minerals Use splines Select knots so that – Reconstruction insensitive to artifacts
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Spectral features for minerals Use splines Select knots so that – Reconstruction insensitive to artifacts – Reconstruction with higher sensitivity in diagnostic areas
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Spectral features for minerals Use splines Select knots so that – Reconstruction insensitive to artifacts – Reconstruction with higher sensitivity in diagnostic areas – Reconstruction sharper (green) for vibrational bands and smoother (red) for electronic transition bands B-splinecoefﬁcients as feature vector
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hyperspectral data challenges Cloud has curved boundaries and is non convex Some dimensions uninformative No apparent clusters, high density Noise creates outliers Most unique spectra = extreme points or “corners” or “image endmembers”
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Objectives for spectral unmixing Separation of spectral pixels in families (image segmentation) Sensitivity to subtle changes in spectral absorption positions and shapes (mineral sub-families) Sensitivity to small (spatial) outcrops Robustness with respect to noise Useful visualization
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Operation modes 100 pixels 50 pixels Two capabilities: – Select areas based on parameter maps (user version) – Divide the image in sections (pipeline version) Operate on each area independently
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Dimensionality reduction: issues Intrinsic dimensionality of data is low: beneﬁt from dimensionality reduction. From movie: – Need nonlinear transform. – Need to preserve local geometry – Need to highlight natural clusters Reduce dimensionality to 2 – 3 for visualization
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Dimensionality reduction High-D Feature Space Low-D Spacex1 , . . . , xn(known) as vertices y1 , . . . , yn (unknown) as of a graph vertices of a graph Edge weights proportional to Edge weights ﬁxed spectral dissimilarities and spatial adjacency x1 x3 y1 y3 x2 y2 yn xn
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Dimensionality reductionHigh-D Feature Space Low-D Space Small distance = small distance p12 q12x1 x3 y1 y3 x2 y2 yn xn
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Dimensionality reductionHigh-D Feature Space Low-D Space Med/big distance = bigger distance p13 q13x1 x3 y1 y3 x2 y2 yn xn
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Graph partitioning as clustering Cluster points in the transformed space to take advantage of separated sections The geometry is nonlinear: need clustering on curved structure Consider the set of vertices yi of the graph and the edge weights qij (yi , yj ) Clustering is equivalent to partitioning graph into disjoint subsets. – can be done by spectral clustering because CNE creates several connected components
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Image segmentation Original SegmentationClustering = mineral image mapfamily mapping =imagesegmentation
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Local endmember detection 1 2 4 3 The clusters in the original space are roughly convex Locally to a cluster can assume linear mixing approximate the data cloud with a conic or convex combination of a small number of “endmembers” Have a way to extrapolate endmembers if the data does not support clear detections
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Robust Nonneg. Matrix Factorization minimize ϕ(Y − W H) + 2 λ||DW ||F subject to W,H ≥ 0, 1T H = 1 T W ∈ Rm×k , H ∈ Rk×n k is the number of local endmembers ϕ is a robust estimator D imposes smoothness and corrects MNF “problems” Solve with alternating projected gradient Zymnis 2009, Parente 2009, Parente 2011
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Spectral pruningFeatures for Features forspectrum 1 spectrum 2 Cross-correlate Spectrum 1 is any local feature vectors endmember candidate Spectrum 2 is either a local endmember or an estimate of the baricenter of the cloud If the score is higher than a threshold Spectrum 1 is pruned Score
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Validation Martian image analysis lacks ground truth Simulation of the complete hyperspectral image formation process (Parente et al. 2010) – Soil mixing, atmosphere, instrument response, noise Comparison with manual expert assessment – the expert can extract the complete spectral variability (3E12) – the expert can only extract partial spectral variability (94F6) – The expert cannot extract spectral variability Self-consistency: comparison with state-of the art (partial)
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Validation: 3E12 Different mineral families evident from RGB Low noise Good spectral variability
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Validation: 3E12Automatically retrieved Manually selected spectraspectra over the whole over the whole scene scene
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Comparison with state of the art Current unmixing algorithms: – require convexity – developed for earth environmental conditions are known ground truth is available – donʼt consider impulsive noise – some require linear assumptions Nonlinear unmixing not yet mature Not able to discriminate subtle spectral differences
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Comparison with other algorithms The proposed algorithm is The SMACC algorithm is insensitive to noise and extremely sensitive to noise picks up more surface components
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B141 Mawrth Vallis ENVI SMACC endmembersProposedapproach
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ABCB: Nili Fossae EndmembersProposed from VCAapproach
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More algorithms(a) Proposed Algorithm (b) N-FINDR (c) PPI (d) SMACC (e) SISAL
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Conclusions Presented a novel method for unmixing The algorithm effectively captures the image spectral variability, down to subtle differences, is robust to noise and outperforms current state-of-the-art algorithms Can be applied to any hyperspectral dataset Produces segmentation and endmember maps We proposed this technique to the CRISM and M3 teams as the “ofﬁcial” data summarization tool for their processing pipelines.
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Future work Include a physical unmixing layer: use radiative transfer theory Provide mechanism to tag “virtual” endmembers Complete validation process with expert feedback
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References L. van deer Maaten and G. Hinton, (2008). Visualizing data using t- SNE, Journal of Machine Learning, 9, pp. 2579-2605. A. Ng, M. Jordan and Y. Weiss, (2001). On spectral clustering: Analysis and an algorithm, NIPS. M. Parente , J.T. Clark, A. Brown and J.L. Bishop (2010). End-to- end simulation of the image generation process for CRISM spectrometer data, IEEE Transactions on Geoscience and Remote Sensing. M. Parente, (2011). Summarization of hyperspectral images: application to Mars, IEEE Transactions on Geoscience and Remote Sensing, (in review). M. Parente, J. L. Bishop and J. F. Bell III, (2009), Spectral unmixing and anomaly detection for mineral identiﬁcation in Pancam images of Gusev soils, Icarus, Vol 203, N. 2, p. 421-436.
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Publications based on project Parente M. and A. Plaza (2010), Survey of geometric and statistical unmixing algorithms for hyperspectral images, IEEE 2nd WHISPERS (Workshop on hyperspectral image and signal processing: evolution of remote sensing) Conf. June 14-16, Reykjavyk, Iceland (invited keynote presentation for special session on “Geometric vs. statistical unmixing algorithms”). M. Parente Spectral unmixing using nonnegative basis learning: comparison of geometrical and statistical endmember extraction algorithms. (invited paper) Space Exploration Technologies, edited by Wolfgang Fink Proc. of SPIE Vol. 6960, 69600P, (2008). doi: 10.1117/12.777895 M. Parente Exploratory data analysis of planetary datasets – new development, (invited talk) Jet Propulsion Laboratory, Pasadena CA, December 4 2008. Parente M., Clark J.T., Brown A.J., and Bishop J.L.. (2009). Simulation of the image generation process for CRISM spectrometer data. IEEE WHISPERS (Workshop on hyperspectral image and signal processing: evolution of remote sensing) Conf. Aug 26-28 Grenoble, France. (Best paper award) Bishop J. L., Noe Dobrea E. Z., McKeown N. K., Parente M., Ehlmann B. L., Michalski J. R., Milliken R. E., Poulet F., Swayze G. A., Mustard J. F., Murchie S. L., and Bibring J.-., P. (2008) Phyllosilicate diversity and past aqueous activity revealed at Mawrth Vallis, Mars. Science 321, DOI: 10.1126/science.1159699, pp. 830-833. Parente, M. and J.L. Bishop, (2010). Extracting endmember spectra from CRISM images: comparison of new Direx image transform technique with MNF, Lunar Planet Science Conf, XLI abstr. #2633.
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MRO-CRISM: VNIR Spectra Can Characterize Small Deposits on Mars Examples of surface features at different CRISM spatial resolutions • Global Mode: 70 channels • Targeted Mode: 544 channels OMEGA CRISM multispectral survey (100-200 CRISM targeted hyperspectral(300-1000 m/pixel, 13 nm/ch.) m/pix, 70 ch.) discovers small (15-38 m/pixel, 6.55 nm/ch) discovers large deposits deposits characterizes deposits
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CRISM Noise sources 1. Vertical striping due to miscalibration of pixel sensors (red arrows). 2. Pixels with elevated bias or abnormal dark ("bad" pixels) create stripe segments (cyan) Both artifacts create spikes in the spectral domain 60/40
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Noise removal with CIRRUS Original CleanedOriginal CIRRUS (CRISM Iterative Recognition and Removal of Unwanted Spiking) Cleaned (Parente 2008) CIRRUS currently in use in CRISM processing pipeline
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Comparison with PCA Proposed approach (3D) PCA (ﬁrst 3 PCs) Natural clusters well Natural clusters not separated evident Between-clusters, similar points can different spectra differ in norm Within-cluster, similar 1st PC illumination spectra gradient
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Comparison with other techniques Proposed approach (3D) PCA (ﬁrst 3 PCs) LLE (3D) Natural clusters well Natural clusters not Natural clusters not separated evident evident Between-clusters, similar points can Some endmembers different spectra differ in norm evident Within-cluster, similar 1st PC illumination Clustering particularly spectra gradient hard
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Clustering performance comparisonOriginal Proposed K-means in K-means with Hierarchical in Hierarchical inimage approach original correlation in original space 3-D space space original space
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K-Eigenvector Clustering (Ng et al. 2001)1. Construct matrix of normalized weights Aʼ2. Decomposition: Find the eigenvectors of Aʼ corresponding to the k largest eigenvalues. These form the the columns of the new matrix X.3. Form the matrix Y – Renormalize each of Xʼs rows to have unit length – Y | – Treat each row of Y as a point in 3. Cluster into k clusters via k-means4. Final Cluster Assignment – Assign point to cluster j iff row i of Y was assigned to cluster jk can be found by maximum spread between eigenvalues
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Validation This software is undergoing extensive validationID Solicitation aimed at conﬁrming that the proposed method can be used pervasively and reliably in the summarization of the whole CRISM database. The validation process starts with requesting Processing from the community image IDʼs with manually selected endmembers. An automated pipeline is in place that sends back via email the spectra retrieved by the Feedback algorithm to each author of manual analysis. Upon receiving feedback on dissimilarities and quality of the detections the pipeline will Validation calculate validation statistics and will send them statistics to the team for review. After validation the production stage will begin.
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