### PCA - Principal component
analysis of image sequences

PCA is in BIJ, the Bio-medical
Imaging in Java site.

Version 1.0.

**Description**

Mathematically, principal component analysis is a matrix diagonalization
process that determines the mixture eigenvectors, with the eigenvalues
corresponding to the relative presence of each of these mixtures in the image.
The (spatial) eigenvectors can also be called 'eigenimages', while the
coordinates of each of the eigenimages can be seen as the timecourses for the
presence of that eigenimage.

For a NxWxH stack, after PCA there will be N eigenimages of WxH and and a NxN
coordinate matrix, with N coordinates for each corresponding eigenimage.

A somewhat poetic description by Bill Christens-Barry:

"Imagine a painting drawn using a palette of n different paints mixtures, each
made by using different amounts of a common set of pigments. Imagine also that
there is some spectral noise, and that each point of the painting was drawn
using only a single paint mixture. Principal component analysis can be used to
determine the linear combination of the pure pigments that was used to make each
mixture. Each mixture is termed a "principal component". PCA is widely
used from face recognition to cardiac cycle analysis."

**References**

Please reference
me if you use my implementation:

M. D. Abràmoff, Y. H. Kwon, D. Y. Ts'o, H. Li, E. S. Barriga, and R. Kardon.
A spatial truncation approach to the analysis of optical imaging of the retina
in humans and cats.* Proc IEEE International Symposium on Biomedical Imaging
2004* 2:1115-1118, 2004.

The original
paper by Sirovich, L. and Kirby, M.
Low-dimensional procedure for the characterization of
human faces, *J. Optical Soc. Am, * 4:519-524, 1987,
can currently
(2004) be found here:
http://camelot.mssm.edu/publications/larry/ld.pdf.
There are many websites out there about using PCA for face
recognition.

Some examples in geophysics are here:
http://www.geop.ubc.ca/CDSST/eigenfaces.html.

Last updated 2004/4/20.