---
_id: '5803'
abstract:
- lang: eng
  text: Different distance metrics produce Voronoi diagrams with different properties.
    It is a well-known that on the (real) 2D plane or even on any 3D plane, a Voronoi
    diagram (VD) based on the Euclidean distance metric produces convex Voronoi regions.
    In this paper, we first show that this metric produces a persistent VD on the
    2D digital plane, as it comprises digitally convex Voronoi regions and hence correctly
    approximates the corresponding VD on the 2D real plane. Next, we show that on
    a 3D digital plane D, the Euclidean metric spanning over its voxel set does not
    guarantee a digital VD which is persistent with the real-space VD. As a solution,
    we introduce a novel concept of functional-plane-convexity, which is ensured by
    the Euclidean metric spanning over the pedal set of D. Necessary proofs and some
    visual result have been provided to adjudge the merit and usefulness of the proposed
    concept.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Ranita
  full_name: Biswas, Ranita
  id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
  last_name: Biswas
  orcid: 0000-0002-5372-7890
- first_name: Partha
  full_name: Bhowmick, Partha
  last_name: Bhowmick
citation:
  ama: 'Biswas R, Bhowmick P. Construction of persistent Voronoi diagram on 3D digital
    plane. In: <i>Combinatorial Image Analysis</i>. Vol 10256. Cham: Springer Nature;
    2017:93-104. doi:<a href="https://doi.org/10.1007/978-3-319-59108-7_8">10.1007/978-3-319-59108-7_8</a>'
  apa: 'Biswas, R., &#38; Bhowmick, P. (2017). Construction of persistent Voronoi
    diagram on 3D digital plane. In <i>Combinatorial image analysis</i> (Vol. 10256,
    pp. 93–104). Cham: Springer Nature. <a href="https://doi.org/10.1007/978-3-319-59108-7_8">https://doi.org/10.1007/978-3-319-59108-7_8</a>'
  chicago: 'Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi
    Diagram on 3D Digital Plane.” In <i>Combinatorial Image Analysis</i>, 10256:93–104.
    Cham: Springer Nature, 2017. <a href="https://doi.org/10.1007/978-3-319-59108-7_8">https://doi.org/10.1007/978-3-319-59108-7_8</a>.'
  ieee: 'R. Biswas and P. Bhowmick, “Construction of persistent Voronoi diagram on
    3D digital plane,” in <i>Combinatorial image analysis</i>, vol. 10256, Cham: Springer
    Nature, 2017, pp. 93–104.'
  ista: 'Biswas R, Bhowmick P. 2017.Construction of persistent Voronoi diagram on
    3D digital plane. In: Combinatorial image analysis. LNCS, vol. 10256, 93–104.'
  mla: Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram
    on 3D Digital Plane.” <i>Combinatorial Image Analysis</i>, vol. 10256, Springer
    Nature, 2017, pp. 93–104, doi:<a href="https://doi.org/10.1007/978-3-319-59108-7_8">10.1007/978-3-319-59108-7_8</a>.
  short: R. Biswas, P. Bhowmick, in:, Combinatorial Image Analysis, Springer Nature,
    Cham, 2017, pp. 93–104.
conference:
  end_date: 2017-06-21
  location: Plovdiv, Bulgaria
  name: 'IWCIA: International Workshop on Combinatorial Image Analysis'
  start_date: 2017-06-19
date_created: 2019-01-08T20:42:56Z
date_published: 2017-05-17T00:00:00Z
date_updated: 2022-01-28T07:48:24Z
day: '17'
department:
- _id: HeEd
doi: 10.1007/978-3-319-59108-7_8
extern: '1'
intvolume: '     10256'
language:
- iso: eng
month: '05'
oa_version: None
page: 93-104
place: Cham
publication: Combinatorial image analysis
publication_identifier:
  isbn:
  - 978-3-319-59107-0
  - 978-3-319-59108-7
  issn:
  - 0302-9743
  - 1611-3349
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Construction of persistent Voronoi diagram on 3D digital plane
type: book_chapter
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 10256
year: '2017'
...