Hyperspectral Image Classification

Hyperspectral Image ClassificationJonatan Gefen 28/11/2012

OutlineIntroduction to classificationWhole PixelSubpixel ClassificationLinear UnmixingMatched Filtering (partialunmixing)More Classification techniquesImage ClassificationSpatial ClassificationSpectral Classification

Image ClassificationSpatial Image classification:Based on the structures in the image (clear edges)Based on neighbor pixelsDepends on the spatial resolutionCan be done manually

Image ClassificationSpectral Image classification:Increase of information per pixelIncrease of dimensionalityCant be done manually (but can be done Automatically)Based on spectral sig.Based on single pixel

Spectral ClassificationWhole Pixel

Sub-Pixel

Others (advanced)

" 6Supervised / UnsupervisedBased on known a priori through a combination of fieldwork, map analysis, and personal experienceOn-screen selection of polygonal training data (ROI), and/or On-screen seeding of training The seed program begins at a single x, y locationExpands as long as it finds pixels with spectral similar to the original seed pixelThis is a very effective way of collecting homogeneous training informationFrom spectral library of field measurements

Whole Pixel classificationAssumes that each pixel contains single material and noise

Tries to determine if a Target is in the pixel

Whole Pixel classificationEuclidean Distance

SAM

Spectral Feature Fitting

SFF - To match target and reference pixel spectra by examining specific absorption features in the spectra (continuum removed spectrum) .

9Sub-pixelTries to measure the abundance of the Target in the pixelAssumes that a pixel can represent more than one material

Sub-pixelLinear Unmixing

Filter Match

Spectral classificationDefinitions:TargetEndmemberInfeasibilityLinear UnmixingA model assumption that each pixel is a Linear-Combination of materials

A- S E - -1

13Linear Unmixingwhich means that we need more bands than endmember materials. With hyperspectral images, this is almost always true.14General Linear UnmixingMinimizing:

Find Least min square. 15L1 Unmixing

Lambda weight contribution of the spasityF imageM endmembersA weights

In the above equation, is a parameter that balances the sparsity of the solution and the how closely theendmembers describe the signal f. The choice of will depend on how well the endmembers represent the imagedata. This model does not enforce the sum-to-one constraint, which means computational adjustments such asthe shade endmember should be unnecessary. There is a connection between the L1-norm and the sum-to-oneconstraint which explains why the CLS model tends to give sparse solutions. If we assume all coefficients ai 0,then the L1-norm a1 = ai. So the CLS model keeps the L1-norm small by enforcing ||a||1 = 1. The LSL1model (2) can be seen as a relaxation of the CLS model (1). Instead of strictly enforcing a1 = 1, the LSL1model makes a1 minimal.

16NMF(original form)

Add NMF methods.M-bandsK-endmemersN - pixels

17

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 spectrumThe 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.

If (x) is larger than a threshold, then signal present hypothesis is accepted. Otherwise, signal absent hypothesis is Accepted

21Match 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.

where d is the target spectrum, x is the pixel spectrum, is the background mean vector and is the background covariance matrix22MNF (Minimum Noise Fraction) is a diagonal matrix containing the eigenvalues corresponding to VMNF: 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)

Minimum Noise Fraction (MNF) Transform PCA 1. -DATA .- 2.

23Match Filter(Partial Unmixing)

Filter example.Make sure understand v calculation 0 1# Output MF scores are normally distributed and have a mean of zero MF [MNF] MNF24Match Filter(Partial Unmixing)

E- These standardizations (variance thresholds) are determined by the linear interpolation of eigenvalues between the 100% target distribution (eigenvalues are all equal to one, having no mixing freedom and therefore only unit noise variance) and the 100% background distribution (eigenvalues generally much greater than one, representative of high degrees of mixing freedom) 25

After filter result

Line is threshold

27

a) An N-Dimensional Visualization of leafy spurge endmember (green). Additionally, mixed pixels containing some leafy spurge() and some background (red) and spectrally similar vegetation that is not leafy spurge (blue) are indicated. b) The geographic distribution of each of the colored groups in (a), with the leafy spurge training area dominated by 113 green pixels. Boxed pixels represent extreme endmembers used for classification

4 ENDMEMBERS TRANING . , , , .28More techniquesNon-linear mixing

A linearB- non-linear29Linear unmixing

Non Linear unmixing

A linearB- non-linear30Sub-Pixel SummeryCan allow search of item that is a very small part of a given pixelCan give data about abundance of Targets

Issues:Highly dependent on the contrast of the target to the background of the pixelOne potential problem with Matched Filtering is that it is possible to end up with false positive results

In case of low spatial resolustion31

More techniquesSpatial-spectral classification

A linearB- non-linear33ReferencesN. Keshava - A Survey of Spectral Unmixing AlgorithmsP. 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 DataYuliya Tarabalka, Jn Atli Benediktsson , Jocelyn Chanussot, James C. Tilton Hyperspectral Data Classication Using Spectral-Spatial ApproachesJacob T. Mundt, David R. Streutker, Nancy F. Glenn PARTIAL UNMIXING OF HYPERSPECTRAL IMAGERY: THEORY AND METHODS B. Ball, A. Brooks, A. Langville - Nonnegative matrix factorizationZ. Guo, T. Wittman and S. Osher - L1 Unmixing and its Application to Hyperspectral Image Enhancement