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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 683176, 9 pages
Research Article

Image Segmentation by Edge Partitioning over a Nonsubmodular Markov Random Field

1Division of Computer and Electronic Systems Engineering, Hankuk University of Foreign Studies, Yongin 449-791, Republic of Korea
2Department of Electrical and Computer Engineering, College of Engineering, Seoul National University, Seoul 151-744, Republic of Korea

Received 26 July 2015; Revised 16 November 2015; Accepted 3 December 2015

Academic Editor: Costas Panagiotakis

Copyright © 2015 Ho Yub Jung and Kyoung Mu Lee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Edge weight-based segmentation methods, such as normalized cut or minimum cut, require a partition number specification for their energy formulation. The number of partitions plays an important role in the segmentation overall quality. However, finding a suitable partition number is a nontrivial problem, and the numbers are ordinarily manually assigned. This is an aspect of the general partition problem, where finding the partition number is an important and difficult issue. In this paper, the edge weights instead of the pixels are partitioned to segment the images. By partitioning the edge weights into two disjoints sets, that is, cut and connect, an image can be partitioned into all possible disjointed segments. The proposed energy function is independent of the number of segments. The energy is minimized by iterating the QPBO--expansion algorithm over the pairwise Markov random field and the mean estimation of the cut and connected edges. Experiments using the Berkeley database show that the proposed segmentation method can obtain equivalently accurate segmentation results without designating the segmentation numbers.