The Euclidean granulometries are generalized to allow the introduction of a positive increasing function h(t), as the scalar multiplier instead of t in the granulometry ($Psi$-t$/). A rather general result for the k$+th$/ pattern spectrum moment is derived. For polynomial choice of h$+$MIN@1$/(t), the asymptotic expressions for the mean and variance of the pattern spectrum moments can be obtained and the asymptotic distribution can be shown to be normal. For other choices, the asymptotic expressions for the mean and variance are shown to provide excellent agreement with simulated pattern spectra, but the asymptotic distribution is not known.
展开▼
