multispectral remote sensing multispec program from purduemultispec on information extraction...
Post on 21-Dec-2015
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Multispectral Remote Sensing
• Multispec program from Purdue
• On Information Extraction Principles for Hyperspectral Data, David Landgrebe, School of Electrical and Computer Engineering, Purdue University.
Spaces
• Image space– rendering of data from (usually) up to three of
the many sensors
• Spectral space– Function space with elements being spectra or
linear combinations of spectra
• Feature space– representation, representation, representation
• http://www.nasm.edu/ceps/RPIF/LANDSAT/
Image Space
Feature Space
• Choosing features can be hard.
• Start with native data representation, for example:– sensor responses at band centers– mean sensor response in band– other weighted averages– sensor response at specified wavelengths
ClassifyingRoadVegetation
Sen
s or
resp
onse
at
1
Sensor response at 2
Nearest mean may be wrong
Second order better (Gaussian ML decision boundary)
Statistical Moments
Nf = num features, Ns = num samples
Samples x(i,j), i=1…Ns, j=1...Nf from a class C
CC(x) = mean of x(: , j)
C = CovC(r,s) =
mean{ (x(:,r)- C(r)) (x(:,s)- i(s))}
These are the sample moments. Training = finding enough samples to make these be good estimates of the true moments
Quadratic (Gaussian) Classifier
• x an element of an unknown class (e.g. a pixel of unknown classification). It’s a col. vector of size Nf. What class is it in?
• gC(x) = -(1/2)ln(|C|) - (1/2)(x-C)tC-1(x-C)
• Choose C if gC(x) >= gD(x) for all other classes D
• If all the classes are Gaussian, this is a maximum likelihood classifier. Among all possible classifiers it minimizes a reasonable error measure.