Robust Affine Set Fitting and Fast Simplex Volume Max-Min for Hyperspectral Endmember Extraction

Spectral unmixing represents both an application per se and a pre-processing step for several applications involving data acquired by imaging spectrometers. However, there is still a lack of publicly available reference data sets suitable for the validation and comparison of different spectral unmixing methods. In this paper, we introduce the DLR HyperSpectral Unmixing (DLR HySU) benchmark dataset, acquired over German Aerospace Center (DLR) premises in Oberpfaffenhofen. The dataset includes airborne hyperspectral and RGB imagery of targets of different materials and sizes, complemented by simultaneous ground-based reflectance measurements. The DLR HySU benchmark allows a separate assessment of all spectral unmixing main steps: dimensionality estimation, endmember extraction (with and without pure pixel assumption), and abundance estimation. Results obtained with traditional algorithms for each of these steps are reported. To the best of our knowledge, this is the first time that real imaging spectrometer data with accurately measured targets are made available for hyperspectral unmixing experiments. The DLR HySU benchmark dataset is openly available online and the community is welcome to use it for spectral unmixing and other applications.

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A Geometric view of Fast Gram Determinant-Based Endmember Extraction Algorithm for Hyperspectral Imagery

IGARSS 2020 - 2020 IEEE International Geoscience and Remote Sensing Symposium ◽

10.1109/igarss39084.2020.9323991 ◽

2020 ◽

Author(s):

Ning Xu ◽

Yuxin Hu ◽

Xiurui Geng ◽

Yanan Wang

Keyword(s):

Hyperspectral Imagery ◽

Endmember Extraction ◽

Extraction Algorithm ◽

Gram Determinant

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Falconer's formula for the Hausdorff dimension of a self-affine set in R2

Ergodic Theory and Dynamical Systems ◽

10.1017/s0143385700008257 ◽

1995 ◽

Vol 15 (1) ◽

pp. 77-97 ◽

Cited By ~ 32

Author(s):

Irene Hueter ◽

Steven P. Lalley

Keyword(s):

Hausdorff Dimension ◽

Dimensional Hausdorff Measure ◽

Similarity Transformations ◽

Affine Mappings ◽

Finite Set ◽

Self Similar ◽

Image Position ◽

Affine Set ◽

Small Overlap ◽

Box Dimensions

Let A1, A2,…,Ak be a finite set of contractive, affine, invertible self-mappings of R2. A compact subset Λ of R2 is said to be self-affine with affinitiesA1, A2,…,Ak ifIt is known [8] that for any such set of contractive affine mappings there is a unique (compact) SA set with these affinities. When the affine mappings A1, A2,…,Ak are similarity transformations, the set Λ is said to be self-similar. Self-similar sets are well understood, at least when the images Ai(Λ) have ‘small’ overlap: there is a simple and explicit formula for the Hausdorff and box dimensions [12, 10]; these are always equal; and the δ-dimensional Hausdorff measure of such a set (where δ is the Hausdorff dimension) is always positive and finite.

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CONNECTEDNESS OF SELF-AFFINE SETS WITH PRODUCT DIGIT SETS

Fractals ◽

10.1142/s0218348x17500530 ◽

2017 ◽

Vol 25 (06) ◽

pp. 1750053 ◽

Cited By ~ 2

Author(s):

JING-CHENG LIU ◽

JUN JASON LUO ◽

KE TANG

Keyword(s):

Triangular Matrix ◽

Sufficient Condition ◽

Lower Triangular Matrix ◽

Necessary And Sufficient Condition ◽

Lower Triangular ◽

Necessary And Sufficient ◽

Affine Set

Let [Formula: see text] be an expanding lower triangular matrix and [Formula: see text]. Let [Formula: see text] be the associated self-affine set. In the paper, we generalize some connectedness results on self-affine tiles to self-affine sets and provide a necessary and sufficient condition for [Formula: see text] to be connected.

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