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

这个项目的目标是：开发一个可以同时表示图像的长相关和短相关结构的随机场模型；研究长记忆和短记忆随机场模型中的稳健估计器；以及利用该项目中的理论模型开发分割和恢复算法。通过加入自回归滑动平均(ARMA)类模型的短记忆结构，对长记忆模型进行推广。至少将使用两种方法：长记忆模型的输入过程将由ARMA模型来表示；以及长记忆模型中的分数差分项将被分数差分自回归过程修正。对于广义长记忆模型中的参数估计，将得到稳健的M-估计器；目标函数将通过度量Winsory似然函数或最小二乘准则来获得。与M估计有关的问题，如尺度方差、假设分布下的效率、渐近性质、收敛等，将被研究。将开发用于图像恢复的二维鲁棒卡尔曼滤波和用于分割的最大似然判决规则。基于模型的视觉算法的性能直接关系到算法的建模能力，并将在很大程度上得益于这些长记忆和短记忆模型。

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.