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Data Mining / Information Extraction Techniques:
Principal Component Images
Don Hillger
NOAA/NESDIS/RAMMT
CIRA / Colorado State University
20-21 August 2003
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Principal Component Image (PCI) transformation of multi-spectral imagery
Terminology/Definitions:
PCI = Principal Component Image – a new image combination
Eigenvectors = transformation vectors to create PCIs from multi-spectral imagery
Eigenvalues = explained variances (weights) of the principal component images
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Why transform imagery?
• To simplify multi-spectral imagery by reducing redundancy to obtain the independent information
• A new set of images that are optimal combinations of the original spectral-band images for extracting the variance in the available imagery
• Important image combinations for detection of atmospheric and surface features in multi-spectral data
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GOES Imager bandsGOES-8/11
bandCentral
WavelengthSpatial
ResolutionPurpose
1 0.7 um 1 km Cloud cover
2 3.9 um 4 kmLow clouds,
hot spots
3 6.7 um 8 km Water vapor
4 10.7 um 4 kmSurface or cloud-top
temperature
5 12.0 um 4 km Dirty window
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General Case
band(N) PCI(N)
The number of component images resulting from a PCI transformation is equal to the number of spectral-band images input.
The sum of the explained variances of the component images is equal to the sum of the explained variances of the original images (the same information content as the original imagery expressed in a new form)
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General Case
PCI = E Bwhere: PCI = transformed set of N images, at M
horizontal locations (pixels) E = N by N transformation matrix. The rows
of E are the eigenvectors of the symmetric matrix with elements determined by the covariance of each band with every other band (summed over M pixels)
B = set of imagery from N bands, viewing a scene at M horizontal locations (pixels)
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Two-dimensional Case
pci1 = e1 band1 + e2 band2pci2 = f1 band1 + f2 band2
where:pci1 and pci2 = Principal Component Images (PCIs)band1 and band2 = band imagese and f = linear transformation vectors (eigenvectors, or rows in the eigenvector matrix E).
In the two-dimensional case:pci1 usually contains the information that is common to the band1
and band2 imagespci2 contains the information that is different between the band1
and band2 images.
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2-dimensional case – Montserrat / Soufriere Hills volcano
2 PCIs2 bands
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2-dimensional case – Montserrat / Soufriere Hills volcano
Comparison to ash-cloud analysis
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GOES 5-band Imager Covariance Matrix
band 1 2 3 4 5
1 1.
2 -0.622 1.
3 -0.603 0.653 1.
4 -0.760 0.920 0.798 1.
5 -0.758 0.900 0.816 0.998 1.
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GOES 5-bandPrincipal Component Matrix
Band
1 2 3 4 5
PCI
1 -0.320 0.360 0.127 0.618 0.608
2 0.913 0.365 0.009 0.139 0.120
3 -0.241 0.784 -0.422 -0.141 -0.359
4 -0.079 0.324 0.895 -0.207 -0.211
5 0.028 -0.131 0.062 0.732 -0.665
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5-band transform (GOES Imager)
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5-band transform (GOES Imager)
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5-band transform(GOES Imager)
5 bands 5 PCIs
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5 bands (GOES Imager)
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5 PCIs (GOES Imager)
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Signal-to-Noise(GOES Imager)
5 bands
5 PCIs
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19-band transform(GOES Sounder)
19 bands
19 PCIs
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19-band transform (GOES Sounder)
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19-band transform (GOES Sounder)
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19 bands (GOES Sounder)
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19 PCIs (GOES Sounder)
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Signal-to-Noise(GOES Sounder)
19 bands
19 PCIs
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Analysis of MODIS
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Analysis of MODIS
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Northeast UT fog/status: 7 Dec 2002 18 UTC
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Northeast UT fog/status: 12 Dec 2002 18 UTC
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Arizona fires – 21 June 2002 1806 UTC (MODIS)
Principal Component Images of fire hot spots and smoke
rings of fire
smoke
smoke
clouds clouds
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Arizona fires – 23 June 2002 1754 UTC (MODIS)
Principal Component Images of fire hot spots and smoke
rings of fire
smoke
smoke
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In conclusion:Why transform imagery?
• To simplify multi-spectral imagery by reducing redundancy to obtain the independent information
• A new set of images that are optimal combinations of the original spectral-band images for extracting the variance in the available imagery
• Important image combinations for detection of atmospheric and surface features in multi-spectral data