Fractal analysis of surface roughness by using spatial data
Fractal analysis of surface roughness by using spatial data
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DOI：
10.1111/1467-9868.00160
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发表时间：
1999-01-01
影响因子：
5.8
通讯作者：
Hall, P
中科院分区：
文献类型：
--
作者：
Davies, S;Hall, P
我们开发分形方法的数据采取的形式的表面。分形分析的一个优点是，它分区的表面粗糙度特性成一个无标度的组件（分形维数）和属性，纯粹取决于规模，特别强调的是各向异性，我们表明，对于许多表面，在表面上的线横断面的分形维数必须要么是恒定的，在每个方向上，或在每个方向上是恒定的，除了一个。分形维数的虚方向不变性提供了分形分析的另一个典型特征，补充了其标度不变性，并增强了其作为概括粗糙度特性的方法的吸引力。粗糙度对方向的依赖性可以用尺度而不是尺寸来解释，并且可以随取向而变化。尺度可以用光滑的周期函数来描述，并且可以非参数地估计。我们的结果和技术被应用于分析土壤和塑料食品包装表面的数据。对于土壤数据，人们的兴趣集中在表面粗糙度对雨水保留的影响上，数据记录为一系列随时间变化的数字图像。我们的分析捕捉到了分维和尺度随降雨量或等效地随时间变化的方式。食品包装数据比土壤数据更精细，并且特别各向异性。分析使我们能够确定生产最光滑包装的制造过程，微生物粘附的趋势最小。
We develop fractal methodology for data taking the form of surfaces. An advantage of fractal analysis is that it partitions roughness characteristics of a surface into a scale-free component (fractal dimension) and properties that depend purely on scale, Particular emphasis is given to anisotropy where we show that, for many surfaces, the fractal dimension of line transects across a surface must either be constant in every direction or be constant in each direction except one. This virtual direction invariance of fractal dimension provides another canonical feature of fractal analysis, complementing its scale invariance properties and enhancing its attractiveness as a method for summarizing properties of roughness. The dependence of roughness on direction may be explained in terms of scale rather than dimension and can vary with orientation. Scale may be described by a smooth periodic function and may be estimated nonparametrically. Our results and techniques are applied to analyse data on the surfaces of soil and plastic food wrapping. For the soil data, interest centres on the effect of surface roughness on retention of rain-water, and data are recorded as a series of digital images over time. Our analysis captures the way in which both the fractal dimension and the scale change with rainfall, or equivalently with time. The food wrapping data are on a much finer scale than the soil data and are particularly anisotropic. The analysis allows us to determine the manufacturing process which produces the smoothest wrapping, with least tendency for micro-organisms to adhere.