Algorithms for computing the maximum weight region decomposable into elementary shapes

Authors:
Jinhee Chun;Natsuda Kaothanthong;Ryosei Kasai;Matias Korman;Martin Nöllenburg;Takeshi Tokuyama
Affiliations:
Graduate School of Information Sciences, Tohoku University, Japan;Graduate School of Information Sciences, Tohoku University, Japan;Graduate School of Information Sciences, Tohoku University, Japan;Université Libre de Bruxelles (ULB), Belgium;Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany;Graduate School of Information Sciences, Tohoku University, Japan
Venue:
Computer Vision and Image Understanding
Year:
2012

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Abstract

Motivated by the image segmentation problem, we consider the following geometric optimization problem: Given a weighted nxn pixel grid, find the maximum weight region whose shape is decomposable into a set of disjoint elementary shapes. We give efficient algorithms for several interesting shapes. This is in strong contrast to finding the maximum weight region that is the union of elementary shapes for the corresponding cases-a problem that we prove to be NP-hard. We implemented one of the algorithms and demonstrate its applicability for image segmentation.