Type-2 Fuzzy Markov Random Fields and Their Application to Handwritten
Jia Zeng, Zhi-Qiang Liu · 2008
In this paper, we integrate type-2 (T2) fuzzy sets with Markov random fields (MRFs) referred to as T2 FMRFs, which may handle both fuzziness and randomness in the structural pat- tern representation. On the one hand, the T2 membership func- tion (MF) has a 3-D 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 and clique potentials and, thus, have been widely applied to image analysis and computer vision. In the proposed T2 FMRFs, we de- fine 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 mix- ture models. The fuzzy prior clique potentials are penalties for the mismatched structures based on prior knowledge. Because Chi- nese characters have hierarchical structures, we use T2 FMRFs to model character structures in the handwritten Chinese character recognition system. The overall recognition rate is 99.07%, which confirms the effectiveness of the proposed method. Index Terms—Handwritten Chinese character recognition (HCCR), Markov random fields (MRFs), type-2 fuzzy sets (T2 FSs).