alpha hull

 转自:http://www.r-bloggers.com/alpha-shapes-with-r-and-lattice/

Introduction

A fundamental problem in pattern recognition is that of pattern classification. In many applications, it is necessary to put shapes (patterns) into classes. This is no trivial task; especially if continuous shapes are to be classified. The main problem comes from finiteness --- anything that is done by a digital computer, must be represented in a finite manner. A natural such representation of two dimensional shapes is a finite subset of the shape. These points may be assumed (more often than not) to be uniformly selected from within the shape. In such cases, there is a nice theory that may go a long way toward consistent shape classification. It consists of defining an object called the alpha -hull of the sampled points. It is an inherently ambiguous representation as it involves the tuning of a parameter (alpha). Mandal and Murthy (see [5] ) propose a consistent procedure for selecting this parameter. This page is devoted to presenting their approach.

First, we shall review the fundamental concepts behind alpha-hulls (such as the definition!). An approach for computing them is also provided. Then, the discussion will concentrate on the problem of finding a suitable parameter alpha.

A note to the beginner: Do not let the mathematical notation scare you. When something is stated formally, it is explained in an intuitive way nearby -- either before or after. This approach is used in order to maintain a certain level of completeness while not overwhelming the reader with (largely) unnecessary math scripture.