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Green Image
Issue No. 08 - August (2010 vol. 32)
ISSN: 0162-8828
pp: 1406-1425
Lei Zhang , Rensselaer Polytechnic Institute, Troy
Qiang Ji , Rensselaer Polytechnic Institute, Troy
We propose a unified graphical model that can represent both the causal and noncausal relationships among random variables and apply it to the image segmentation problem. Specifically, we first propose to employ Conditional Random Field (CRF) to model the spatial relationships among image superpixel regions and their measurements. We then introduce a multilayer Bayesian Network (BN) to model the causal dependencies that naturally exist among different image entities, including image regions, edges, and vertices. The CRF model and the BN model are then systematically and seamlessly combined through the theories of Factor Graph to form a unified probabilistic graphical model that captures the complex relationships among different image entities. Using the unified graphical model, image segmentation can be performed through a principled probabilistic inference. Experimental results on the Weizmann horse data set, on the VOC2006 cow data set, and on the MSRC2 multiclass data set demonstrate that our approach achieves favorable results compared to state-of-the-art approaches as well as those that use either the BN model or CRF model alone.
Image segmentation, probabilistic graphical model, Conditional Random Field, Bayesian Network, factor graph.

L. Zhang and Q. Ji, "Image Segmentation with a Unified Graphical Model," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 32, no. , pp. 1406-1425, 2009.
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