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
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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