On the use of moment invariants for the automated analysis of 3D particle shapes
On the use of moment invariants for the automated analysis of 3D particle shapes
复制标题
关于使用矩不变量进行 3D 颗粒形状的自动分析
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
M. De Graef
中科院分区：
文献类型：
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作者：
J. MacSleyne;J. Simmons;M. De Graef
介绍了一种定量描述两相组织中析出相形状及其演变的数学方法。该方法依赖于不变矩的概念，即相对于仿射和/或相似性变换不变的二阶矩的组合。我们引入了三个不变量，一个是形状鉴别器，另外两个是宽高比鉴别器。一个规范化的形式的不变量的定义，它明确表明，任何3D形状必须属于一个有限区域的规范化不变矩空间。这个区域的形状和边界定义在等周不等式。不变矩的应用程序的两个例子：拟合的第二相沉淀物的形状和双峰相场模拟的时间演化。
A mathematical method is introduced to describe quantitatively the shape and shape evolution of precipitates in a two-phase microstructure. The method relies on the concept of moment invariants, i.e. combinations of second order moments that are invariant with respect to affine and/or similarity transformations. We introduce three invariants, one a shape discriminator, the other two aspect ratio discriminators. A normalized form of the invariants is defined and it is shown explicitly that any 3D shape must belong to a finite region of the normalized moment invariant space. The shape and bounds of this region are defined in terms of isoperimetric inequalities. Two examples of moment invariant applications are given: fitting the shape of second phase precipitates and the time evolution of a bimodal phase field simulation.