Morphological pyramid with alternating sequential filters

Aldo Morales, Raj Acharya

Research output: Contribution to journalConference articlepeer-review


The aim of this paper is to find a relationship between alternating sequential filters and the morphological sampling theorem developed by Haralick4. First, we show an alternative proof for opening and closing in the sampled and unsampled domain. This is done by using basis functions. This decomposition is used then to show the relationship of opening-closing in the sampled and unsampled domain. An upper and a lower bound, for the previous relationships, were found. Under certain circumstances, an equivalence is shown for opening-closing between the sampled and the unsampled domain. An extension to more complicated algorithms is also considered, namely ; union of openings and intersection of closings. The reason to consider such transformations is that in some applications we would like to eliminate pixels removed by individual openings (closings).

Original languageEnglish (US)
Pages (from-to)258-269
Number of pages12
JournalProceedings of SPIE - The International Society for Optical Engineering
StatePublished - Jun 1 1991
EventImage Processing Algorithms and Techniques II 1991 - San Jose, United States
Duration: Feb 1 1991Feb 7 1991

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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