Confidence Regions for Means of Random Sets using Oriented Distance Functions

TL;DR

This paper develops a method for constructing confidence regions for the mean of random sets in image analysis, using oriented distance functions to estimate and infer the expected shape with proven consistency.

Contribution

It introduces a new approach to define set expectation via oriented distance functions and provides a method to compute confidence regions with theoretical guarantees.

Findings

The empirical set converges consistently to the true expected set.

The method effectively constructs confidence regions in both real and simulated data.

Applications demonstrate the practical utility of the proposed approach.

Abstract

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.