Fitting Spherical Laguerre Voronoi Diagrams to Real-World Tessellations Using Planar Photographic Images
There are many natural phenomena displayed as polygonal tessellations on curved surfaces, typically found in fruit skin patterns. The paper proposes a method to fit given tessellations with spherical Laguerre Voronoi diagrams. The main target of this paper is fruit skin patterns such as jackfruit and lychee covered by tessellation patterns in which each cell contains a unique spike dot that can be considered as a generator. The problem of estimating the weights is reduced to an optimization problem, and can be solved efficiently. The experiments were done with ideal data and real fruit skin data, which show the validity of the method. We also propose related problems for further studies.
KeywordsSpherical Laguerre Voronoi diagram Voronoi approximation Tessellation fitting Fruit skin patterns
The first author acknowledges the support of the MIMS Ph.D. Program of the Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, and the DPST of IPST, Ministry of Education, Thailand. This research is partly supported by Grant-in-Aid for Basic Research No. 24360039 of MEXT.
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