Toward a new axiomatic for hyper-connections

  • Authors:

  • Benjamin Perret;Sébastien Lefèvre;Christophe Collet

  • Affiliations:

  • Image Science, Computer Science and Remote Sensing Laboratory, LSIIT, UMR 7005, University of Strasbourg-CNRS, Illkirch Cedex France;VALORIA Laboratory, University of South Brittany. Address: VALORIA Lab, Vannes Cedex, France;Image Science, Computer Science and Remote Sensing Laboratory, LSIIT, UMR 7005, University of Strasbourg-CNRS, Illkirch Cedex France

  • Venue:
  • ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
  • Year:
  • 2011

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Abstract

We propose a new class of hyper-connections in order to improve the consistency of hyper-connected filters and to simplify their design. Our idea relies on the principle that the decomposition of an image into h-components must be necessary and sufficient. We propose a set of three equivalent axioms to achieve this goal. We show that an existing h-connection already fulfils these properties and we propose a new h-connection based on flat functions that also fulfils these axioms. Finally we show that this new class brings several new interesting properties that simplify the use of h-connections and guarantee the consistency of h-connected filters as they ensure that: 1) every deletion of image components will effectively modify the filtered image 2) a deleted component can not re-appear in the filtered image.