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Sampling of Non-flat Morphology for Grey Value Images

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Part of the Lecture Notes in Computer Science book series (LNIP,volume 13053)


Sampling is a basic operation in image processing. In previous literature, a morphological sampling theorem has been established showing how sampling interacts with image reconstruction by morphological operations. However, while many aspects of morphological sampling have been investigated for binary images in classic works, only some of them have been extended to grey scale imagery. Especially, previous attempts to study the relation between sampling and grey scale morphology are restricted by construction to flat morphological filters. In order to establish a sampling theory for non-flat morphology, we establish an alternative definition for grey scale opening and closing relying on the umbra notion. Making use of this, we prove a sampling theorem about the interaction of sampling with fundamental morphological operations for non-flat morphology. This allows to make precise corresponding relations between sampling and image reconstruction, extending classic results for flat morphology of grey value images.


  • Sampling theorem
  • Mathematical morphology
  • Opening
  • Closing
  • Non-flat morphology

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Correspondence to Vivek Sridhar .

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Sridhar, V., Breuß, M. (2021). Sampling of Non-flat Morphology for Grey Value Images. In: Tsapatsoulis, N., Panayides, A., Theocharides, T., Lanitis, A., Pattichis, C., Vento, M. (eds) Computer Analysis of Images and Patterns. CAIP 2021. Lecture Notes in Computer Science(), vol 13053. Springer, Cham.

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