Eigenvectors of RGB images
The eigenvectors of RGB images are obtained from the covariance
matrix,
where
c_xx = covar(x,y) = sum(sum((x-av(x)).*(y-av(y))))
Example 1
Original image and scaled eigenimages
Eigenvectors (column vectors)
| vec1 | vec2 | vec3 |
|---|
| 0.581 | -0.152 | -0.799 |
| 0.613 | 0.729 | 0.306 |
| 0.536 | -0.668 | 0.517 |
Eigenvalues (relative to maximum)
range of transformed images
| # | max | min |
|---|
| 1 | 1.192197 | 0.389661 |
|---|
| 2 | 0.298003 | -0.213334 |
|---|
| 3 | 0.235442 | -0.473663 |
|---|
positive/negative versions of eigenvectors
The sign of an eigenvector is ambiguous. We can choose either
the positive or negative image, which ever looks better.
Example2
Original image and scaled eigenimages
Eigenvectors (column vectors)
| vec1 | vec2 | vec3 |
|---|
| 0.3793 | 0.9120 | -0.1562 |
| 0.6359 | -0.3795 | -0.6720 |
| 0.6721 | -0.1556 | 0.7239 |
Eigenvalues (relative to maximum)
range of transformed images
| # | max | min |
|---|
| 1 | 1.062522 | -0.566210 |
|---|
| 1 | 0.388267 | -0.27675 |
|---|
| 1 | 0.096484 | -0.077457 |
|---|
Maintained by John
Loomis, last updated June 28, 1997
