A new class of morphological pyramids for multiresolution image analysis

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-A((n)) indexed by an integer n, followed by downsampling. For A n = 0, R-A((n)) equals the erosion epsilon(A) with structuring element A, whereas A for n > 0, R-A(n) equals the erosion epsilon(A) followed by n conditional dilations, A which for n --> infinity 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 axe known as the adjunction pyramid and Sun-Maragos Pyramid, respectively. Experiments axe performed to study the approximation quality of the pyramids as a function of the number of iterations n of the conditional dilation operator.