Hyperspectral Image Classification
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Transcript Hyperspectral Image Classification
Jonatan Gefen
28/11/2012
Outline
Introduction to classification
Whole Pixel
Subpixel Classification
Linear Unmixing
Matched Filtering (partial unmixing)
More Classification techniques
Image Classification
Spatial Classification
Spectral Classification
Image
Classification
Spatial Image classification:
Based on the structures in the
image (clear edges)
Based on neighbor pixels
Depends on the spatial resolution
Can be done manually
Image
Classification
Spectral Image classification:
Increase of information per pixel
Increase of dimensionality
Can’t be done manually (but can
be done Automatically)
Based on spectral sig.
Based on single pixel
Spectral Classification
Whole Pixel
Sub-Pixel
Others (advanced)
Supervised / Unsupervised
Based on known a priori through a combination of
fieldwork, map analysis, and personal experience
On-screen selection of polygonal training data (ROI),
and/or
On-screen seeding of training
The seed program begins at a single x, y location
Expands as long as it finds pixels with spectral similar to
the original seed pixel
This is a very effective way of collecting homogeneous
training information
From spectral library of field measurements
Whole Pixel classification
Assumes that each pixel contains
single material and noise
Tries to determine if a Target is in
the pixel
Whole Pixel classification
Euclidean Distance
SAM
Spectral Feature Fitting
Sub-pixel
Tries to measure the
abundance of the Target in
the pixel
Assumes that a pixel can
represent more than one
material
Sub-pixel
Linear Unmixing
Filter Match
Spectral classification
Definitions:
Target
Endmember
Infeasibility
Linear Unmixing
A model assumption that each pixel is a
Linear-Combination of materials
𝒙𝒊 =
𝒏
𝒋=𝟏
𝒂𝒊𝒋 ∗ 𝒔𝒊𝒋 + 𝒆𝒊
𝑥 – is the pixel value at band 𝑖
𝑎 – spectral value of the 𝑗 endmember
𝑠 – the abundance factor of the 𝑗 endmember
𝑒 – noise
Linear Unmixing
Linear Unmixing is trying to solve 𝑛
linear equations to find possible
endmembers and their fraction of the
pixel.
𝑛 – the number of bands
General Linear Unmixing
Minimizing:
𝐶 𝐴, 𝑆 =
𝑋 − 𝐴𝑆
2
Find Least min square.
𝑚𝑖𝑛 𝑋 − 𝐴𝑆
𝑇
𝑋 − 𝐴𝑆
L1 Unmixing
Assumes that all the elements are non negative.
Minimizing:
𝑎
1-
called regulator
Using NMF (Nonnegative matrix factorization)
NMF(original form)
𝐶 𝐴, 𝑆 =
𝑋 − 𝐴𝑆
2
Algorithm:
𝐴 = 𝑎𝑏𝑠 𝑟𝑎𝑛𝑑 𝑚, 𝑘
𝑆 = 𝑎𝑏𝑠 𝑟𝑎𝑛𝑑 𝑘, 𝑛
𝑓𝑜𝑟 𝑖 = 1 𝑡𝑜 𝑚𝑎𝑥𝑖𝑡𝑒𝑟
𝑆 = 𝑆.∗ 𝐴𝑇 𝑋 ./(𝐴𝑇 𝐴𝑆 + 10−9 )
𝐴 = 𝐴.∗ 𝑋𝑆 𝑇 ./(𝐴𝑆𝑆 𝑇 + 10−9 ) (in our case already
known)
Match Filter(Partial Unmixing)
This technique is used to find specific Targets in the
image only user chosen targets are mapped.
Matched Filtering “filters” the input image for good
matches to the chosen target spectrum
The technique is best used on rare Targets in the
image.
Match Filter(Partial Unmixing)
Likelihood Ratio
Using a threshold to decide if signal is present at the
pixel.
Match Filter(Partial Unmixing)
The Matched Filter result calculation:
The T(x) will hold the MF value of the endmember at
pixel x if > 0 the endmember present.
MNF (Minimum Noise Fraction)
Λ is a diagonal matrix containing the eigenvalues
corresponding to V
MNF:
is the covariance matrix of the signal (generally
taken to be the covariance matrix of the image)
is the covariance matrix of the noise (can be
estimated using various procedures)
Match Filter(Partial Unmixing)
Mixture-Tuned Matched Filtering
𝑣 − matched filter vector
𝐶𝑀𝑁𝐹 - MNF Covariance matrix
𝑡 − the target vector in MNF space
Match Filter(Partial Unmixing)
𝐼𝑖 − infeasibility value
𝑒 − the interpolated vector of
eigenvalues
𝑐 − the target vector component
𝑠 - the MNF spectra for pixel
After filter result
More techniques
Non-linear mixing
Linear unmixing
Non Linear unmixing
Sub-Pixel Summery
Can allow search of item that is a very small part of a
given pixel
Can give data about abundance of Targets
Issues:
Highly dependent on the contrast of the target to the
background of the pixel
One potential problem with Matched Filtering is that it
is possible to end up with false positive results
More techniques
Spatial-spectral classification
References
N. Keshava - “A Survey of Spectral Unmixing Algorithms”
P. Shippert, “Introduction to Hyperspectral Image Analysis” , Earth Science
Applications Specialist Research Systems, Inc.
Uttam Kumar, Norman Kerle , and Ramachandra T V – “Constrained
Linear Spectral Unmixing Technique for Regional Land Cover Mapping
Using MODIS Data”
Yuliya Tarabalka, Jón Atli Benediktsson , Jocelyn Chanussot, James C.
Tilton – “Hyperspectral Data Classification Using Spectral-Spatial
Approaches”
Jacob T. Mundt, David R. Streutker, Nancy F. Glenn – “PARTIAL
UNMIXING OF HYPERSPECTRAL IMAGERY: THEORY AND METHODS “
B. Ball, A. Brooks, A. Langville - Nonnegative matrix factorization
Z. Guo, T. Wittman and S. Osher - L1 Unmixing and its Application to
Hyperspectral Image Enhancement