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Type-2 Fuzzy Markov Random Fields

Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 591)

Abstract

This chapter integrates type-2 fuzzy sets (T2 FSs) with Markov random fields (MRFs) referred to as T2 FMRFs, which may handle both fuzziness and randomness in the structural pattern representation. On the one hand, the T2 membership function (MF) has a three-dimensional structure in which the primary MF describes randomness, and the secondary MF evaluates the fuzziness of the primary MF. On the other hand, MRFs can represent patterns statistical-structurally in terms of neighborhood system \(\partial i\) and clique potentials \(V_c\), and thus have been widely applied to image analysis and computer vision. In the proposed T2 FMRFs, we define the same neighborhood system as that in classical MRFs. To describe uncertain structural information in patterns, we derive the fuzzy likelihood clique potentials from T2 fuzzy Gaussian mixture models (T2 FGMMs). The fuzzy prior clique potentials are penalties for the mismatched structures based on prior knowledge. Because Chinese characters have hierarchical structures, we use T2 FMRFs to model character structures in the handwritten Chinese character recognition (HCCR) system. The overall recognition rate is \(99.07\,\%\), which confirms the effectiveness of T2 FMRFs for statistical character structure modeling.

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Copyright information

© Tsinghua University Press, Beijing and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of Computer Science and TechnologySoochow UniversitySuzhouChina
  2. 2.School of Creative MediaCity University of Hong KongHong KongChina

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