GPU Pro 4

232 III Image Space

J

ρ

(x). The eigenvalues are real, since J

ρ

(x) is symmetric, and nonnegative, since

J

ρ

(x) is positive semidefinite. The major eigenvalue measures the squared rate

of change in the direction of the major eigenvector. Its square root can thus be

regarded as a generalized gradient strength. The minor eigenvalue, on the other

hand, can be regarded as a measure for the error of the approximation.

Up to now, only the case of grayscale images has been considered. The most

straightforward way to extend the previous discussion to color images is by solving

Equation (5.1) jointly for all color channels, resulting in the following generaliza- ...