Type-2 Fuzzy Markov Random Fields and Their Application to Handwritten Chinese Character Recognition

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 pattern representation. On the one hand, the T2 membership function (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 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. 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 system. The overall recognition rate is 99.07%, which confirms the effectiveness of the proposed method.