论文标题
通过Fisher评分向量对材料微观结构的非平稳性分析
Nonstationarity Analysis of Materials Microstructures via Fisher Score Vectors
论文作者
论文摘要
微观结构对于材料的物理特性至关重要。在多种材料中通常观察到随机微观结构,基于传统的描述符的图像分析可能具有挑战性。在本文中,我们引入了一个强大而多功能的基于得分的框架,用于分析随机材料微观结构中的非机构性。该框架涉及训练参数监督的学习模型,以使用微观结构图像(称为显微照片)中的相邻像素来预测像素值,并且该预测模型提供了微观结构随机性质的隐含表征。我们方法的基础是在每个显微照片像素上相对于预测模型的参数,定义为对数似然的梯度的Fisher得分向量。分数向量的基本特性是,如果该像素附近的预测关系保持不变,则是零均值,我们将其等同于微观结构的局部随机性保持不变。相反,如果局部随机性质发生变化,那么得分矢量的平均值通常与零不同。我们的框架分析了分数矢量的本地平均值如何在一个或多个图像示例上变化:(1)通过指示新样本在统计上与参考样本的统计学上是否有所不同,并且(2)通过相应地识别出相应的样本的不同类型的随机微结构和标记来监视非平稳性。与基于特征的方法不同,我们的方法几乎完全是一般的,并且不需要先前了解非组织性的性质。使用许多真实和模拟的显微照片,包括聚合物复合材料和多相合金,我们证明了该方法的功率和多功能性。
Microstructures are critical to the physical properties of materials. Stochastic microstructures are commonly observed in many kinds of materials and traditional descriptor-based image analysis of them can be challenging. In this paper, we introduce a powerful and versatile score-based framework for analyzing nonstationarity in stochastic materials microstructures. The framework involves training a parametric supervised learning model to predict a pixel value using neighboring pixels in images of microstructures~(as known as micrographs), and this predictive model provides an implicit characterization of the stochastic nature of the microstructure. The basis for our approach is the Fisher score vector, defined as the gradient of the log-likelihood with respect to the parameters of the predictive model, at each micrograph pixel. A fundamental property of the score vector is that it is zero-mean if the predictive relationship in the vicinity of that pixel remains unchanged, which we equate with the local stochastic nature of the microstructure remaining unchanged. Conversely, if the local stochastic nature changes, then the mean of the score vector generally differs from zero. Our framework analyzes how the local mean of the score vector varies across one or more image samples to: (1) monitor for nonstationarity by indicating whether new samples are statistically different than reference samples and where they may differ and (2) diagnose nonstationarity by identifying the distinct types of stochastic microstructures and labeling accordingly the corresponding regions of the samples. Unlike feature-based methods, our approach is almost completely general and requires no prior knowledge of the nature of the nonstationarities. Using a number of real and simulated micrographs, including polymer composites and multiphase alloys, we demonstrate the power and versatility of the approach.