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:

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

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

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

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)

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)

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.

2-dimensional case – Montserrat / Soufriere Hills volcano

2 PCIs2 bands

2-dimensional case – Montserrat / Soufriere Hills volcano

Comparison to ash-cloud analysis

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.

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

5-band transform (GOES Imager)

5-band transform (GOES Imager)

5-band transform(GOES Imager)

5 bands 5 PCIs

5 bands (GOES Imager)

5 PCIs (GOES Imager)

Signal-to-Noise(GOES Imager)

5 bands

5 PCIs

19-band transform(GOES Sounder)

19 bands

19 PCIs

19-band transform (GOES Sounder)

19-band transform (GOES Sounder)

19 bands (GOES Sounder)

19 PCIs (GOES Sounder)

Signal-to-Noise(GOES Sounder)

19 bands

19 PCIs

Analysis of MODIS

Analysis of MODIS

Northeast UT fog/status: 7 Dec 2002 18 UTC

Northeast UT fog/status: 12 Dec 2002 18 UTC

Arizona fires – 21 June 2002 1806 UTC (MODIS)

Principal Component Images of fire hot spots and smoke

rings of fire

smoke

smoke

clouds clouds

Arizona fires – 23 June 2002 1754 UTC (MODIS)

Principal Component Images of fire hot spots and smoke

rings of fire

smoke

smoke

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