Department of Electrical and Computer Engineering, The George Washington University, Washington, DC 20052, USA.
IEEE Trans Image Process. 2001;10(7):1047-55. doi: 10.1109/83.931099.
A class of random field model having long-correlation characteristics is introduced. Unlike earlier approaches in long-correlation models, the correlation structure is isotropic or elliptical in this new class of random field model. The new model has an advantage of modeling diverse real textures with less than five model parameters. Further, the model parameters match with intuitive attributes of textures, such as smoothness, pattern size, elongation or orientation of patterns. The new long-correlation models are based on the fractional differencing of a two-dimensional (2-D) autoregressive polynomial defined by eight symmetric neighbors, and they are either persistent or periodic models depending whether the roots of the polynomial are real or imaginary. A comprehensive three-step algorithm for parameter estimation is developed, and the statistical properties of the estimators are also discussed. The validity of the new model in modeling textures is tested by synthesizing images from manually selected parameters as well as parameters estimated from real textures. It is shown that an image with desired attributes can be synthesized by selecting proper values of the parameters. Further, it is shown that the models introduced can be used in modeling wide range of textures by synthesizing images resembling real textures from estimated parameters.
引入了一类具有长相关特性的随机场模型。与长相关模型中的早期方法不同，这个新的随机场模型的相关结构是各向同性或椭圆的。新模型具有用少于五个模型参数来模拟各种真实纹理的优势。此外，模型参数与纹理的直观属性（如平滑度、图案大小、图案的拉长或方向）相匹配。新的长相关模型基于由八个对称邻居定义的二维（2-D）自回归多项式的分数差分，并且它们是持久模型或周期模型，具体取决于多项式的根是实根还是虚根。开发了一个用于参数估计的综合三步算法，并讨论了估计器的统计特性。通过从手动选择的参数以及从真实纹理中估计的参数合成图像来测试新模型在纹理建模中的有效性。结果表明，可以通过选择适当的参数值来合成具有所需属性的图像。此外，结果表明，可以通过从估计的参数中合成类似于真实纹理的图像，来使用引入的模型来建模广泛的纹理。
