Fitting an ellipse to an arbitrary shape: implications for strain analysis
Fitting an ellipse to an arbitrary shape: implications for strain analysis
复制标题
DOI：
10.1016/s0191-8141(03)00093-2
复制
发表时间：
2004-01-01
影响因子：
3.1
通讯作者：
Choudhury, KR
中科院分区：
文献类型：
--
作者：
Mulchrone, KF;Choudhury, KR
使用应用于边界数据的线性最小二乘法，可以将椭圆拟合为任意形状。或者，这个问题也可以通过计算整个区域的二阶矩来解决，这是一种在图像分析应用中流行的技术。如果不规则形状可以近似为一个多边形，那么格林定理可以有效地计算二阶矩。如果形状是像素化的，那么二阶矩可以通过简单的求和过程来计算。通过考虑这些拟合方法的行为，随着变形的增加，它表明，作为一个任意形状被动变形，最适合的椭圆也表现得好像它是被动变形。这意味着，所有的应变分析技术，以前仅限于人口的椭圆形物体，现在可以适用于人口的任意形状，提供最佳拟合椭圆计算的方法之一，这里描述。此外，这意味着基于形状的选择性采样或基于形状的加权方法是无效的，并且倾向于使原始数据有偏差。(C)2003 Elsevier Ltd.保留所有权利。
An ellipse can be fit to an arbitrary shape using a linear least squares approach applied to boundary data. Alternatively, this problem can also be solved by calculating the second moments of the entire region, a technique popular in image analysis applications. If the irregular shape can be approximated by a polygon then Greens theorem allows efficient calculation of the second moments. If the shape is pixelated then the second moments can be calculated by a simple summation process. By considering the behaviour of these fitting methods with increasing deformation it is shown that as an arbitrary shape passively deforms, the best-fit ellipse also behaves as if it were deforming passively. This implies that all techniques of strain analysis that were previously restricted to populations of elliptical objects may now be applied to populations of arbitrary shapes, provided the best-fit ellipse is calculated by one of the methods described here. Furthermore it implies that selective sampling based on shape or methods of weighting based upon shape are invalid and tend to bias the raw data. (C) 2003 Elsevier Ltd. All rights reserved.