A USE OF MEAN FIELD APPROXIMATION IN MEDIA INFORMATION PROCESSING USING MARKOV MODEL

在图像、语音等媒体信息处理中，马尔可夫模型通常被用来建模观察过程和隐藏过程。在这样的媒体处理中，需要进行观测和隐藏过程的概率密度函数的参数估计、给定观测图像和语音的概率计算以及隐藏过程的估计。对于因果马尔可夫模型，已经提出了进行这种估计和计算的有效算法，但对于非因果马尔可夫模型，还没有提出有效的算法。在本研究项目中，首次提出了基于平均场近似的非因果马尔可夫模型的高效算法。该方法利用平均场近似将整个图像的隐藏过程概率和观测过程概率，甚至是给定观测过程的隐藏过程的后验概率分解为局部像素化概率的乘积。由一组隐藏状态的局部后验概率组成的局部后验向量可用作每个像素的平均场。将该方法应用于真实图像和语音处理中，对其性能进行了评估。在图像处理中，采用马尔可夫随机场模型，重点研究了利用马尔可夫随机场模型对小波变换后的图像进行建模的框架。通过纹理分类和纹理图像分割，该方法有效地克服了传统原始图像建模中只考虑极短距离交互作用的问题。在语音处理中，将该方法应用于说话人识别，并利用序贯概率比检验进行在线说话人确认和识别，取得了较好的效果。

In media information processing such as image and speech processing, Markov models are commonly used to model observation process as well as hidden process. In such media processing, parameter estimation of probability density functions for both observation and hidden processes, probability computation of given observed image and speech, and estimation of hidden process need to be carried out. Efficient algorithms to carry out such estimation and computation have already been proposed for causal Markov models but not for noncausal ones. In this research project, efficient algorithms for noncausal Markov models have first been proposed which are realized using the mean field approximation. The proposed method is based on the fact that the probabilities of hidden process and observation process for a whole image, and even the a posteriori probability of hidden process given observation process are decomposed into the product of local pixelwise probabilities, using the mean field approximation. The local a posteriori vector, which is composed of local a posteriori probabilities for a set of hidden states, can be used as the mean field for each pixel. The proposed method was applied to real image and speech processing to evaluate its performance. In image processing, Markov random field (MRF) model was used and in particular a framework to model wavelet transformed images by the MRF model was investigated. Through texture classification and textured image segmentation, this approach is shown to be very effective to overcome the well-known problem in conventional modeling of original images where very short range interactions are only considered. In speech processing, the proposed method was applied to speaker recognition and is shown to be effective in online speaker verification and identification using the sequential probability ration test.