Robust Random Field Models for Images with Long and Short Term Dependencies

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The objectives of this project are: to develop a random-field model which can represent both long- and short-correlation structures of an image; to investigate robust estimators in the long- and short-memroy random-field models; and to develop segmentation and restoration algorithms using theoretical models found in this project. The long-memory model will be generalized by adding the short- memory structure of autoregressive moving-average (ARMA)-class models. At least two approaches will be used: the input process of the long-memory model will be represented by ARMA models; and the fractional differencing term in the long-memory model will be modified by a fractionally-differenced autoregressive process. Robust M-estimators will be derived for the estimation of parameters in generalized long-memroy models; the objective function will be derived by metricaly Winsorizing either a likelihood function or a least-squares criterion. Issues involved with M-estimators, such as scale variance, efficiency at assumed distribution, asymptotic properties, convergence, etc., will be investigated. Two-dimensional robust Kalman filters for image restoration, and maximum-likelihood decision rules for segmentation, will be developed. The performance of model-based vision algorithms is directly related to the modeling power of the algorithm, and will be greatly aided by these long- and short-memory models.