Confidence Regions for Means of Random Sets Using Oriented Distance Functions
本文利用定向距离函数定义随机集的期望，研究经验集的统计性质，给出一致性条件并介绍计算期望集置信区域的方法，适用于图像分析和形状估计问题。
Abstract. Image analysis frequently deals with shape estimation and image reconstruction. The objects of interest in these problems may be thought of as random sets, and one is interested in finding a representative, or expected, set. We consider a definition of set expectation using oriented distance functions and study the properties of the associated empirical set. Conditions are given such that the empirical average is consistent, and a method to calculate a confidence region for the expected set is introduced. The proposed method is applied to both real and simulated data examples.