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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/13779

Title: Base-Object Location Problems for Base-Monotone Regions
Authors: Chun, Jinhee
Horiyama, Takashi
Ito, Takehiro
Kaothanthong, Natsuda
Ono, Hirotaka
Otachi, Yota
Tokuyama, Takeshi
Uehara, Ryuhei
Uno, Takeaki
Keywords: pixel grid
image segmentation
polynomial time algorithm
approximation algorithm
Issue Date: 2014-10-23
Publisher: Elsevier
Magazine name: Theoretical Computer Science
Volume: 555
Start page: 71
End page: 84
DOI: 10.1016/j.tcs.2013.11.030
Abstract: A base-monotone region with a base is a subset of the cells in a pixel grid such that if a cell is contained in the region then so are the ones on a shortest path from the cell to the base. The problem of decomposing a pixel grid into disjoint base-monotone regions was first studied in the context of image segmentation. It is known that for a given pixel grid and base-lines, one can compute in polynomial time a maximum-weight region that can be decomposed into disjoint base-monotone regions with respect to the given baselines (Chun et al., 2012 [4]). We continue this line of research and show the NP-hardness of the problem of optimally locating k base-lines in a given n x n pixel grid. We then present an O(n^3)-time 2-approximation algorithm for this problem. We also study two related problems, the k base-segment problem and the quad-decomposition problem, and present some complexity results for them.
Rights: Copyright (C)2014, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International license (CC BY-NC-ND 4.0). [http://creativecommons.org/licenses/by-nc-nd/4.0/] NOTICE: This is the author’s version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Jinhee Chun, Takashi Horiyama, Takehiro Ito, Natsuda Kaothanthong, Hirotaka Ono, Yota Otachi, Takeshi Tokuyama, Ryuhei Uehara, and Takeaki Uno, Theoretical Computer Science, 555, 2014, 71-84, http://dx.doi.org/10.1016/j.tcs.2013.11.030
URI: http://hdl.handle.net/10119/13779
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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