  We extend the previously developed weak noise scheme, applied to the noisy
Burgers equation in 1D, to the Kardar-Parisi-Zhang equation for a growing
interface in arbitrary dimensions. By means of the Cole-Hopf transformation we
show that the growth morphology can be interpreted in terms of dynamically
evolving textures of localized growth modes with superimposed diffusive modes.
In the Cole-Hopf representation the growth modes are static solutions to the
diffusion equation and the nonlinear Schroedinger equation, subsequently
boosted to finite velocity by a Galilei transformation. We discuss the dynamics
of the pattern formation and, briefly, the superimposed linear modes.
Implementing the stochastic interpretation we discuss kinetic transitions and
in particular the properties in the pair mode or dipole sector. We find the
Hurst exponent H=(3-d)/(4-d) for the random walk of growth modes in the dipole
sector. Finally, applying Derrick's theorem based on constrained minimization
we show that the upper critical dimension is d=4 in the sense that growth modes
cease to exist above this dimension.
