Dept. of Inf. Technol. and Commun., Virginia Univ., Charlottesville, VA.
IEEE Trans Image Process. 1996;5(6):938-49. doi: 10.1109/83.503910.
Statistical approaches to image modeling have largely relied upon random models that characterize the 2-D process in terms of its first- and second-order statistics, and therefore cannot completely capture phase properties of random fields that are non-Gaussian. This constrains the parameters of noncausal image models to be symmetric and, therefore, the underlying random field to be spatially reversible. Research indicates that this assumption may not be always valid for texture images. In this paper, higher- than second-order statistics are used to derive and implement two classes of inverse filtering criteria for parameter estimation of asymmetric noncausal autoregressive moving-average (ARMA) image models with known orders. Contrary to existing approaches, FIR inverse filters are employed and image models with zeros on the unit bicircle can be handled. One of the criteria defines the smallest set of cumulant lags necessary for identifiability of these models to date, Consistency of these estimators is established, and their performance is evaluated with Monte Carlo simulations as well as texture classification and synthesis experiments.
基于统计的图像建模方法主要依赖于随机模型，这些模型用一阶和二阶统计来描述二维过程，因此无法完全捕捉到非高斯随机场的相位特性。这限制了非因果图像模型的参数必须是对称的，因此，潜在的随机场必须是空间可逆的。研究表明，对于纹理图像，这种假设并不总是有效的。在本文中，使用高于二阶的统计量来推导和实现两类具有已知阶数的非因果自回归移动平均（ARMA）图像模型的参数估计的逆滤波准则。与现有方法不同的是，采用了有限脉冲响应（FIR）逆滤波器，并且可以处理单位单位圆上有零点的图像模型。其中一个准则定义了迄今为止这些模型可识别性所需的最小阶累积滞后量集。这些估计量的一致性得到了确立，并通过蒙特卡罗模拟以及纹理分类和合成实验对其性能进行了评估。
