Base-object location problems for base-monotone regions

Jinhee Chun, Takashi Horiyama, Takehiro Ito, Natsuda Kaothanthong, Hirotaka Ono, Yota Otachi, Takeshi Tokuyama, Ryuhei Uehara, Takeaki Uno

Research output: Contribution to journalArticle

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 base-lines (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×n pixel grid. We then present an O(n3)-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.

Original languageEnglish
Pages (from-to)71-84
Number of pages14
JournalTheoretical Computer Science
Volume555
Issue numberC
DOIs
Publication statusPublished - Jan 1 2014

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Location Problem
Monotone
Pixels
Pixel
Grid
Baseline
Cell
Disjoint
Approximation algorithms
Problem Decomposition
Image segmentation
NP-hardness
Image Segmentation
Shortest path
Hardness
Polynomials
Approximation Algorithms
Decomposition
Polynomial time
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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Chun, J., Horiyama, T., Ito, T., Kaothanthong, N., Ono, H., Otachi, Y., ... Uno, T. (2014). Base-object location problems for base-monotone regions. Theoretical Computer Science, 555(C), 71-84. https://doi.org/10.1016/j.tcs.2013.11.030

Base-object location problems for base-monotone regions. / Chun, Jinhee; Horiyama, Takashi; Ito, Takehiro; Kaothanthong, Natsuda; Ono, Hirotaka; Otachi, Yota; Tokuyama, Takeshi; Uehara, Ryuhei; Uno, Takeaki.

In: Theoretical Computer Science, Vol. 555, No. C, 01.01.2014, p. 71-84.

Research output: Contribution to journalArticle

Chun, J, Horiyama, T, Ito, T, Kaothanthong, N, Ono, H, Otachi, Y, Tokuyama, T, Uehara, R & Uno, T 2014, 'Base-object location problems for base-monotone regions', Theoretical Computer Science, vol. 555, no. C, pp. 71-84. https://doi.org/10.1016/j.tcs.2013.11.030
Chun J, Horiyama T, Ito T, Kaothanthong N, Ono H, Otachi Y et al. Base-object location problems for base-monotone regions. Theoretical Computer Science. 2014 Jan 1;555(C):71-84. https://doi.org/10.1016/j.tcs.2013.11.030
Chun, Jinhee ; Horiyama, Takashi ; Ito, Takehiro ; Kaothanthong, Natsuda ; Ono, Hirotaka ; Otachi, Yota ; Tokuyama, Takeshi ; Uehara, Ryuhei ; Uno, Takeaki. / Base-object location problems for base-monotone regions. In: Theoretical Computer Science. 2014 ; Vol. 555, No. C. pp. 71-84.
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