This paper proposes a Bayesian approach to image recognition based on separable lattice hidden Markov models (SL-HMMs). The geometric variations of the object to be recognized, e.g., size, location, and rotation, are an essential problem in image recognition. SL-HMMs, which have been proposed to reduce the effect of geometric variations, can perform elastic matching both horizontally and vertically. This makes it possible to model not only invariances to the size and location of the object but also nonlinear warping in both dimensions. The maximum likelihood (ML) method has been used in training SL-HMMs. However, in some image recognition tasks, it is difficult to acquire sufficient training data, and the ML method suffers from the over-fitting problem when there is insufficient training data. This study aims to accurately estimate SL-HMMs using the maximum a posteriori (MAP) and variational Bayesian (VB) methods. The MAP and VB methods can utilize prior distributions representing useful prior information, and the VB method is expected to obtain high generalization ability by marginalization of model parameters. Furthermore, to overcome the local maximum problem in the MAP and VB methods, the deterministic annealing expectation maximization algorithm is applied for training SL-HMMs. Face recognition experiments performed on the XM2VTS database indicated that the proposed method offers significantly improved image recognition performance. Additionally, comparative experiment results showed that the proposed method was more robust to geometric variations than convolutional neural networks.

This paper proposes an enhanced model of Random Projection Outlyingness (RPO) for unsupervised outlier detection. When datasets have multiple modalities, the RPOs have frequent detection errors. The proposed model deals with this problem via unsupervised clustering and a local score weighting. The experimental results demonstrate that the proposed model outperforms RPO and is comparable with other existing unsupervised models on benchmark datasets, in terms of in terms of Area Under the Curves (AUCs) of Receiver Operating Characteristic (ROC).

In this paper, a novel statistical model based on 2-D HMMs for image recognition is proposed. Recently, separable lattice 2-D HMMs (SL2D-HMMs) were proposed to model invariance to size and location deformation. However, their modeling accuracy is still insufficient because of the following two assumptions, which are inherited from 1-D HMMs: i) the stationary statistics within each state and ii) the conditional independent assumption of state output probabilities. To overcome these shortcomings in 1-D HMMs, trajectory HMMs were proposed and successfully applied to speech recognition and speech synthesis. This paper derives 2-D trajectory HMMs by reformulating the likelihood of SL2D-HMMs through the imposition of explicit relationships between static and dynamic features. The proposed model can efficiently capture dependencies between adjacent observations without increasing the number of model parameters. The effectiveness of the proposed model was evaluated in face recognition experiments on the XM2VTS database.

This paper proposes a new generative model which can deal with rotational data variations by extending Separable Lattice 2-D HMMs (SL2D-HMMs). In image recognition, geometrical variations such as size, location and rotation degrade the performance. Therefore, the appropriate normalization processes for such variations are required. SL2D-HMMs can perform an elastic matching in both horizontal and vertical directions; this makes it possible to model invariance to size and location. To deal with rotational variations, we introduce additional HMM states which represent the shifts of the state alignments among the observation lines in a particular direction. Face recognition experiments show that the proposed method improves the performance significantly for rotational variation data.