Applied and Computational Harmonic Analysis ( IF 2.5 ) Pub Date : 2019-09-13 , DOI: 10.1016/j.acha.2019.08.007 K. Polisano , M. Clausel , V. Perrier , L. Condat
In this work we give a sense to the notion of orientation for self-similar Gaussian fields with stationary increments, based on a Riesz analysis of these fields, with isotropic zero-mean analysis functions. We propose a structure tensor formulation and provide an intrinsic definition of the orientation vector as eigenvector of this tensor. That is, we show that the orientation vector does not depend on the analysis function, but only on the anisotropy encoded in the spectral density of the field. Then, we generalize this definition to a larger class of random fields called localizable Gaussian fields, whose orientation is derived from the orientation of their tangent fields. Two classes of Gaussian models with prescribed orientation are studied in the light of these new analysis tools.
中文翻译:
基于Riesz的可定位高斯场取向
在这项工作中,我们基于具有恒定各向同性零均值分析功能的这些区域的Riesz分析,对具有固定增量的自相似高斯磁场的方向性概念有所了解。我们提出了一种结构张量公式,并提供了方向向量的固有定义,作为该张量的特征向量。也就是说,我们表明方向矢量不依赖于分析函数,而仅依赖于在场的光谱密度中编码的各向异性。然后,我们将此定义推广到一类称为可本地化的高斯场的较大随机场,其方向是从其切线场的方向得出的。根据这些新的分析工具,研究了具有指定方向的两类高斯模型。