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A New Class of Morphological Pyramids for Multiresolution Image Analysis

  • Jos B. T. M. Roerdink
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2616)

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)Aequals the erosion εA with structuring element A, whereas for n > 0, R(n)Aequals 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.

Keywords

Volume Rendering Approximation Quality Dilation Operator Perfect Reconstruction Detail Signal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jos B. T. M. Roerdink
    • 1
  1. 1.Institute for Mathematics and Computing ScienceUniversity of GroningenGroningenThe Netherlands

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