New Approaches for Feature Extraction in Hyperspectral Imagery

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New Approaches for Feature Extraction in
Hyperspectral Imagery

• Stefan A. Robila
• Lukasz Maciak
• Department of Computer Science
• www.csam.montclair.edu/robila

IEEE LISAT, 2006
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Hyperspectral Images

• Spectral Image Image format representation of
  the measurement of the brightness (for a
  certain interval of energy frequencies) of a
  phenomenon, object, region, etc.

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Goal

• Develop new feature extraction algorithms for
  hyperspectral images
• Ensure that the new methods meet the
  particularities of the data

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Hyperspectral Imagery

• Data collected as hundreds of images (spectral
  images or spectral bands), with each image
  corresponding to narrow contiguous wavelength
  intervals
• Multispectral Many spectra (bands)
• Hyperspectral Huge numbers of continuous bands

Electromagnetic Spectrum
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Hyperspectral Imagery

• Pixel vectors (or spectra) - formed of pixel
  intensities from the same location, across the
  bands
• Each pixel corresponds to a certain region of the
  scene surveyed and will represent the spectral
  information for that region.

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Hyperspectral Imagery

• Hyperspectral remote sensing provides a
  continuous, essentially complete record of
  spectral responses of materials over the
  wavelengths considered

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Processing Hyperspectral Data

• Hyperspectral Image Processing
• group in classes pixel vectors with similar
  spectral characteristics
• detect pixel vectors whose spectral
  characteristics are similar to the ones of known
  materials
• Importance
• Abundance of data in hyperspectral imagery leads
  to increased processing accuracy
• Hyperspectral sensors have been installed on
  aircrafts (HYDICE, AVIRIS), satellites
  (Hyperion), and have been started to be produced
  commercially (SOC 700) indicating large data
  availability in the near future

Processing of the full image cube is not
desirable due to its size as well as its
redundancy
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Feature Extraction

• The process of projecting the data from the
  original feature space to a lower dimensional
  subspace that provides a more effective
  representation
• The efficiency of the representation is viewed
  through the separation between the classes within
  each feature

• Supervised
• uses information provided by subsets of pixel
  vectors ground data
• - the classes are considered to be represented by
  the ground data

• Unsupervised
• no ground data is used
• concentrates mainly on redundancy reduction

ground data may be unreliable or impossible to
obtain
class statistics cannot be computed or estimated
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Feature (Band) Extraction

• Principal Component Analysis
• Independent Component Analysis
• other

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Principal Component Analysis (PCA)
For the multidimensional random vector x, PCA
finds a linear transform W such that the obtained
components are uncorrelated YWx (1) Th
e transform is obtained as W
AxT (2) Where Ax is the matrix formed of the
normalized eigenvectors for the covariance matrix
Sx.
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Independent Component Analysis (ICA)
Given a random vector s, and a matrix A of size ,
the problem is to recover this pair (s, A) from
the available observations x defined as
xAs (3) knowing that the vector s
is formed of independent non-Gaussian
components
(4) where p(.) refers to the probability
density function and si refers to the components
of the vector s.
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Issues

• No clear relationship to hyperspectral imagery
• Strong restrictions on the IC / PC transform
• Does not fit the (Linear) Mixing Model

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Linear Mixing Model (LMM)
Each n-dimensional observed pixel vector x can be
expressed as
(6)
S is the nxm matrix of spectra (s1, .., sm)
endmembers a is an m-dimensional vector -
abundance vector w is the additive noise
vector The elements of the abundance vector are
assumed to be positive and with unit sum
(7)
(8)
Linear Unmixing - find the endmembers and their
abundances.
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Issues (cont)

• In PCA and ICA we have orthogonality of the
  endmembers
• The abundance maps are not positive
• The abundance maps do not add up to one

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Nonnegative Matrix Factorization (NMF)
Given the observed data x, the goal of NMF is to
find s and a linear mixing transform W both
positively defined such that xWs (9)
This approach can be understood as factorizing a
data matrix subject to positive constraints.
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NMF Solution

• Constrain positivity
• Optimize based on gradient

(10)
(11)
(12)
(function based on the Euclidean norm)
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NMF Algorithm
1. Randomly initialize W and s to positive
values 2. Scale the columns of s to sum up to
one 3. Repeat 4. 5. 6. Scale the
columns of s to sum up to one while non
convergence
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NMF Algorithm

• Convergence based on the value of f(W,s) from
  eq. 12
• Stop when converging to 0
• Alternative stop when value is stable
• Epsilon factor used for speedup
• Algorithm enforces summation to one for s
• Algorithm maintains positivity of W and s

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Experiments
Hyperspectral Digital Imagery Collection
Experiment (HYDICE)

• Foliage scene
• spatial resolution of 1.5m
• 210 bands with wavelengths between 400nm and 2.5
  micron.

• Rows of panels made of 8 different materials
• Sizes 1mx1m, 2mx2m, 3mx3m
• Small forest patch
• Exposed ground

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Experiments

• Relative fast stability

Error rate vs. iteration
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Experiments
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Experiments
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Experiments
Surface Optics (SOC 700)

• artificial
• and
• natural vegetation
• 120 bands with wavelengths between 400nm and 900nm

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Experiments

• Relative fast stability

Error rate vs. iteration
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Experiments
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Future Work

• Number of features to be extracted
• Avoid local optima
• Speedup through distributed processing
• Real time unmixing tool

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Conclusions

• Feature extraction remains an attractive approach
  in processing hyperspectral images. The current
  techniques are focused on strong restrictions on
  the separability of the resulting bands and do
  not have a natural interpretation for the nature
  of hyperspectral data.
• NMF provides an elegant approach that simply
  assumes that the features must be separable and
  positively defined. When adding the condition
  that the features must also sum up to one
  pixelwise we discover that NMF also provides a
  solution to the classical linear unmixing
  problem.
• Results suggest that NMF reaches optimal
  solutions that clearly separate endmember
  information for the data.
• Consider NMF as a viable approach for feature
  extraction.

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Thank you