A New Class of Morphological Pyramids for Multiresolution Image Analysis

Abstract

We study nonlinear multiresolution signal decomposition based on morphological pyramids. Motivated by a problem arising in multiresolution volume visualization, we introduce a new class of morphological pyramids. In this class the pyramidal synthesis operator always has the same form, i.e. a dilation by a structuring element A, preceded by upsampling, while the pyramidal analysis operator is a certain operator R (n) A indexed by an integer n, followed by downsampling. For n = 0, R (n) A equals the erosion εA with structuring element A, whereas for n > 0, R (n) A equals the erosion εA followed by n conditional dilations, which for n → ∞ is the opening by reconstruction. The resulting pair of analysis and synthesis operators is shown to satisfy the pyramid condition for all n. The corresponding pyramids for n = 0 and n = 1 are known as the adjunction pyramid and Sun-Maragos pyramid, respectively. Experiments are performed to study the approximation quality of the pyramids as a function of the number of iterations n of the conditional dilation operator.