Computationally efficient, one-pass algorithm for morphological filters

  • Authors:
  • Petr Dokládal;Eva Dokládalová

  • Affiliations:
  • Center of Mathematical Morphology, Department Mathematics and Systems, Mines PARISTECH, 35, rue St. Honoré, 77 300 Fontainebleau Cedex, France;Unité mixte de recherche CNRS-UMLV-ESIEE, UMR 8049, Université Paris-Est, Cité Descartes B.P.99, 93 162, Noisy le Grand Cedex, France

  • Venue:
  • Journal of Visual Communication and Image Representation
  • Year:
  • 2011

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Abstract

Many useful morphological filters are built as long concatenations of erosions and dilations: openings, closings, size distributions, sequential filters, etc. This paper proposes a new algorithm implementing morphological dilation and erosion of functions. It supports rectangular structuring element, runs in linear time w.r.t. the image size and constant time w.r.t. the structuring element size, and has minimal memory usage. It has zero algorithm latency and processes data in stream. These properties are inherited by operators composed by concatenation, and allow their efficient implementation. We show how to compute in one pass an Alternate Sequential Filter (ASF^n) regardless the number of stages n. This algorithm opens the way to such time-critical applications where the complexity and memory requirements of serial morphological operators represented a bottleneck limiting their usability.