Construction of Persistent Voronoi Diagram on 3D Digital Plane

R. Biswas, P. Bhowmick, in:, Combinatorial Image Analysis, Springer International Publishing, Cham, 2017, pp. 93–104.

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Abstract
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.
Publishing Year
Date Published
2017-05-17
Book Title
Combinatorial image analysis
Volume
10256
Page
93-104
Conference
IWCIA: International Workshop on Combinatorial Image Analysis
Conference Location
Plovdiv, Bulgaria
Conference Date
2017-06-19 – 2017-06-21
IST-REx-ID

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Biswas R, Bhowmick P. Construction of Persistent Voronoi Diagram on 3D Digital Plane. In: Combinatorial Image Analysis. Vol 10256. Lecture Notes in Computer Science. Cham: Springer International Publishing; 2017:93-104. doi:10.1007/978-3-319-59108-7_8
Biswas, R., & Bhowmick, P. (2017). Construction of Persistent Voronoi Diagram on 3D Digital Plane. In Combinatorial image analysis (Vol. 10256, pp. 93–104). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-59108-7_8
Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” In Combinatorial Image Analysis, 10256:93–104. Lecture Notes in Computer Science. Cham: Springer International Publishing, 2017. https://doi.org/10.1007/978-3-319-59108-7_8.
R. Biswas and P. Bhowmick, “Construction of Persistent Voronoi Diagram on 3D Digital Plane,” in Combinatorial image analysis, vol. 10256, Cham: Springer International Publishing, 2017, pp. 93–104.
Biswas R, Bhowmick P. 2017. Construction of Persistent Voronoi Diagram on 3D Digital Plane. Combinatorial image analysis. IWCIA: International Workshop on Combinatorial Image AnalysisLecture Notes in Computer Science vol. 10256. 93–104.
Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” Combinatorial Image Analysis, vol. 10256, Springer International Publishing, 2017, pp. 93–104, doi:10.1007/978-3-319-59108-7_8.

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