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Polynomial Time Algorithms for Ratio Regions and a Variant of Normalized Cut
May 2010 (vol. 32 no. 5)
pp. 889-898
ASCII Text
x 
 
Dorit S. Hochbaum, "Polynomial Time Algorithms for Ratio Regions and a Variant of Normalized Cut," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 32, no. 5, pp. 889-898, May, 2010.
 
 
BibTex
x
 
@article{ 10.1109/TPAMI.2009.80,
author = {Dorit S. Hochbaum},
title = {Polynomial Time Algorithms for Ratio Regions and a Variant of Normalized Cut},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {32},
number = {5},
issn = {0162-8828},
year = {2010},
pages = {889-898},
doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2009.80},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - Polynomial Time Algorithms for Ratio Regions and a Variant of Normalized Cut
IS - 5
SN - 0162-8828
SP889
EP898
EPD - 889-898
A1 - Dorit S. Hochbaum,
PY - 2010
KW - Grouping
KW - image segmentation
KW - graph theoretic methods
KW - partitioning.
VL - 32
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 
Dorit S. Hochbaum, University of California, Berkeley, Berkeley
In partitioning, clustering, and grouping problems, a typical goal is to group together similar objects, or pixels in the case of image processing. At the same time, another goal is to have each group distinctly dissimilar from the rest and possibly to have the group size fairly large. These goals are often combined as a ratio optimization problem. One example of such a problem is a variant of the normalized cut problem, another is the ratio regions problem. We devise here the first polynomial time algorithms solving optimally the ratio region problem and the variant of normalized cut, as well as a few other ratio problems. The algorithms are efficient and combinatorial, in contrast with nonlinear continuous approaches used in the image segmentation literature, which often employ spectral techniques. Such techniques deliver solutions in real numbers which are not feasible to the discrete partitioning problem. Furthermore, these continuous approaches are computationally expensive compared to the algorithms proposed here. The algorithms presented here use as a subroutine a minimum s,t-cut procedure on a related graph which is of polynomial size. The output consists of the optimal solution to the respective ratio problem, as well as a sequence of nested solutions with respect to any relative weighting of the objectives of the numerator and denominator.

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Index Terms:
Grouping, image segmentation, graph theoretic methods, partitioning.
Citation:
Dorit S. Hochbaum, "Polynomial Time Algorithms for Ratio Regions and a Variant of Normalized Cut," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 32, no. 5, pp. 889-898, May 2010, doi:10.1109/TPAMI.2009.80
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