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Data Mining / Information Extraction Techniques: Principal Component Images

Data Mining / Information Extraction Techniques: Principal Component Images. Don Hillger NOAA/NESDIS/RAMMT CIRA / Colorado State University hillger@cira.colostate.edu 20-21 August 2003. Principal Component Image (PCI) transformation of multi-spectral imagery. Terminology/Definitions:

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Data Mining / Information Extraction Techniques: Principal Component Images

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  1. Data Mining / Information Extraction Techniques:Principal Component Images Don Hillger NOAA/NESDIS/RAMMT CIRA / Colorado State University hillger@cira.colostate.edu 20-21 August 2003

  2. 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

  3. 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

  4. GOES Imager bands

  5. 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)

  6. General Case PCI = E @ B where: • 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)

  7. Two-dimensional Case pci1 = e1 @ band1 + e2 @ band2 pci2 = f1 @ band1 + f2 @ band2 where: pci1 and pci2 = Principal Component Images (PCIs) band1 and band2 = band images e 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 images pci2 contains the information that is different between the band1 and band2 images.

  8. 2-dimensional case – Montserrat / Soufriere Hills volcano 2 bands 2 PCIs

  9. 2-dimensional case – Montserrat / Soufriere Hills volcano Comparison to ash-cloud analysis

  10. GOES 5-band Imager Covariance Matrix

  11. GOES 5-bandPrincipal Component Matrix

  12. 5-band transform (GOES Imager)

  13. 5-band transform (GOES Imager)

  14. 5-band transform(GOES Imager) 5 bands 5 PCIs

  15. 5 bands (GOES Imager)

  16. 5 PCIs (GOES Imager)

  17. Signal-to-Noise(GOES Imager)  5 bands 5 PCIs 

  18. 19-band transform(GOES Sounder) 19 bands 19 PCIs

  19. 19-band transform (GOES Sounder)

  20. 19-band transform (GOES Sounder)

  21. 19 bands (GOES Sounder)

  22. 19 PCIs (GOES Sounder)

  23. Signal-to-Noise(GOES Sounder)  19 bands 19 PCIs 

  24. Analysis of MODIS

  25. Analysis of MODIS

  26. Northeast UT fog/status: 7 Dec 2002 18 UTC

  27. Northeast UT fog/status: 12 Dec 2002 18 UTC

  28. Principal Component Images of fire hot spots and smoke clouds clouds smoke smoke rings of fire Arizona fires – 21 June 2002 1806 UTC (MODIS)

  29. Principal Component Images of fire hot spots and smoke smoke rings of fire smoke Arizona fires – 23 June 2002 1754 UTC (MODIS)

  30. 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

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