Ridges in Image and Data Analysis
Ridges in Image and Data Analysis
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DOI：
10.1007/978-94-015-8765-5
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发表时间：
1996-09
期刊：
影响因子：
2.6
通讯作者：
D. Eberly
中科院分区：
文献类型：
--
作者：
D. Eberly
脊的概念在图像处理文献中已经出现了很多次。有时这个词是在一种直观的意义上使用的。有时候，会给出具体的定义。在几乎所有情况下，该概念都用于非常具体的应用。在分析图像或数据集时，科学家通过考虑数据的最大值或最小值来衡量关键行为是非常自然的。这些临界点相对容易计算。数值软件包总是提供对求根或优化的支持，无论是通过二分法、牛顿法、共轭梯度法还是其他标准方法。科学家们从更高层次的意义上考虑临界行为是不自然的。作为临界点流形的岭的概念是作为孤立临界点的局部极大值概念的自然推广。然而，几乎没有注意到正式的概念。需要有一个正式的发展。需要理解在实现中出现的计算问题。这本书的目的是通过提供一个正式的数学基础和脊的计算框架来解决这两个需求。本书的目标读者包括任何对探索岭在数据分析中的用途感兴趣的人。
The concept of ridges has appeared numerous times in the image processing liter ature. Sometimes the term is used in an intuitive sense. Other times a concrete definition is provided. In almost all cases the concept is used for very specific ap plications. When analyzing images or data sets, it is very natural for a scientist to measure critical behavior by considering maxima or minima of the data. These critical points are relatively easy to compute. Numerical packages always provide support for root finding or optimization, whether it be through bisection, Newton's method, conjugate gradient method, or other standard methods. It has not been natural for scientists to consider critical behavior in a higher-order sense. The con cept of ridge as a manifold of critical points is a natural extension of the concept of local maximum as an isolated critical point. However, almost no attention has been given to formalizing the concept. There is a need for a formal development. There is a need for understanding the computation issues that arise in the imple mentations. The purpose of this book is to address both needs by providing a formal mathematical foundation and a computational framework for ridges. The intended audience for this book includes anyone interested in exploring the use fulness of ridges in data analysis.