A new class of morphological pyramids for multiresolution image analysis

  • Authors:

  • Jos B. T. M. Roerdink

  • Affiliations:

  • Institute for Mathematics and Computing Science, University of Groningen, Groningen, The Netherlands

  • Venue:
  • Proceedings of the 11th international conference on Theoretical foundations of computer vision
  • Year:
  • 2002

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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 RA(n) indexed by an integer n, followed by downsampling. For n = 0, RA(n) equals the erosion ɛA with structuring element A, whereas for n 0, RA(n) equals the erosion ɛA 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.