Alina Zare and Paul Gader Department of Computer & Information Science & Engineering University of Florida Gainesville, Florida

Hyperspectral Imagery

Endmembers are the spectral signatures of the unique materials in the scene. Endmember Detection: Estimate each material’s spectral signature Spectral Unmixing: Determine the proportion of each endmember in every pixel

Hyperspectral Unmixing based on the Convex Geometry Model

Non-Convex Hyperspectral Imagery The Convex Geometry Model assumes that Hyperspectral Pixels lie in a Convex Region. This is not always the case.

AVIRIS Indian Pines Dataset PCA Dimensionality Reduction, 220 to 3 bands

Non-Convex Hyperspectral Imagery The Convex Geometry Model assumes that Hyperspectral Pixels lie in a Convex Region. This is not always the case.

VIS/NIR Face Image PCA Dimensionality Reduction, 160 to 3 bands

Piece-wise Convex Endmember Detection Unsupervised endmember detection algorithm that simultaneously: • Partitions the spectra into distinct sets (multiple sets of endmembers) • Estimate the number of sets of endmembers • Estimates endmembers • Estimates abundance values • Represents endmembers using Endmember Distributions

Spectra of skin from VIS/NIR Hyperspectral Imagery Endmembers are generally represented as single points in a high dimensional space. Spectra of particular materials have variation. We can capture this variation using endmember distributions.

Wheat Spectra from VIS/NIR Hyperspectral Imagery

Gaussian Endmember Distributions: Resulting Convex Geometry Model:

*Note on Notation: Capital bold letters = Matrices Lowercase bold letters = Vectors

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Ce P

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ri E xi

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μ E Ce

μ E Ce

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μ E Ce

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Sample Proportions

Sample Endmembers

Sample Endmember Prior Mean

Sample Endmember Prior Covariance

Sample Partition Label for each Data Point

• Hyperspectral data are often non-convex and can be represented well using piece-wise convex representations • The proposed algorithm partitions a hyperspectral image into multiple convex regions where, for each partition, endmember distributions and proportion values are estimated.

• Incorporate Spatial Information • Estimate the number of endmember distributions per convex region • Estimate each endmember distributions’ covariance