Confidence Regions for Means of Random Sets using Oriented Distance Functions

Details Confidence Regions for Means of Random Sets using Oriented Distance Functions Confidence Regions for Means of Random Sets using Oriented Distance Functions

2009-03-10

arxiv.org/abs/0903.1869v2

Statistics

Methodology

26 pages, 10 figures

Scientific paper

Image analysis frequently deals with shape estimation and image reconstruction. The ob jects 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.

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