各向异性分数布朗场的完全推论

IF 0.4 Q4 STATISTICS & PROBABILITY
Paul Escande, Frédéric Richard
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引用次数: 0

摘要

各向异性分数布朗场(AFBF)是一种非稳态高斯随机场,已被用于纹理图像建模。在本文中,我们将探讨如何估算该场的函数参数,即拓扑函数和赫斯特函数。我们提出了一种独创的方法,将图像的经验半变量图与近似于 AFBF 的转带场的半变量图进行拟合。我们用可分离的非线性最小平方准则来表示拟合准则,设计了一种受变量投影法启发的最小化算法。该算法还包括一种基于函数参数近似值的从粗到细多网格策略。与现有方法相比,新方法能够在整个定义域内估算两个函数参数。在模拟纹理上,我们发现即使参数近似精度很高,该方法的估计误差也很低。我们还将该方法应用于描述乳房 X 线照片和具有合成实质模式的样本图像。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Full inference for the anisotropic fractional Brownian field
The anisotropic fractional Brownian field (AFBF) is a non-stationary Gaussian random field which has been used for the modeling of textured images. In this paper, we address the open issue of estimating the functional parameters of this field, namely the topothesy and Hurst functions. We propose an original method which fits the empirical semi-variogram of an image to the semi-variogram of a turning-band field that approximates the AFBF. Expressing the fitting criterion in terms of a separable non-linear least square criterion, we design a minimization algorithm inspired by the variable projection approach. This algorithm also includes a coarse-to-fine multigrid strategy based on approximations of functional parameters. Compared to existing methods, the new method enables to estimate both functional parameters on their whole definition domain. On simulated textures, we show that it has a low estimation error, even when the parameters are approximated with a high precision. We also apply the method to characterize mammograms and sample images with synthetic parenchymal patterns.
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CiteScore
1.30
自引率
0.00%
发文量
22
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