Zonohedral Approximation of Spherical Structuring Element for Volumetric Morphology

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Performing dilation and erosion using large structuring elements can be computationally slow – a problem especially pronounced when processing volumetric data. To reduce the computational complexity of dilation/erosion using spherical structuring elements, we propose a method for approximating a sphere with a zonohedron. Since zonohedra can be created via successive dilations/erosions of line segments, this allows morphological operations to be performed in constant time per voxel. As the complexity of commonly used methods typically scales with the size of the structuring element, our method significantly improves the run time. We use the proposed approximation to detect large spherical objects in volumetric data. Results are compared with other image analysis frameworks demonstrating constant run time and significant performance gains.
Original languageEnglish
Title of host publicationProceedings of Scandinavian Conference on Image Analysis 2019
Publication date2019
ISBN (Print)9783030202040
Publication statusPublished - 2019
EventScandinavian Conference on Image Analysis - Norrköpings Visualisering Center, Norrköping, Sweden
Duration: 11 Jun 201913 Jun 2019


ConferenceScandinavian Conference on Image Analysis
LocationNorrköpings Visualisering Center
Internet address
SeriesLecture Notes in Computer Science


  • Morphology
  • Computational Efficiency
  • Zonohedra

Cite this

Jensen, P. M., Trinderup, C. H., Dahl, A. B., & Dahl, V. A. (2019). Zonohedral Approximation of Spherical Structuring Element for Volumetric Morphology. In Proceedings of Scandinavian Conference on Image Analysis 2019 (pp. 128-139). Springer. Lecture Notes in Computer Science, Vol.. 11482 https://doi.org/10.1007/978-3-030-20205-7_11