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JMIV
2010

Expectations of Random Sets and Their Boundaries Using Oriented Distance Functions

10 years 2 months ago
Expectations of Random Sets and Their Boundaries Using Oriented Distance Functions
Shape estimation and object reconstruction are common problems in image analysis. Mathematically, viewing objects in the image plane as random sets reduces the problem of shape estimation to inference about sets. Currently existing definitions of the expected set rely on different criteria to construct the expectation. This paper introduces new definitions of the expected set and the expected boundary, based on oriented distance functions. The proposed expectations have a number of attractive properties, including inclusion relations, convexity preservation and equivariance with respect to rigid motions. The paper introduces a special class of separable oriented distance functions for parametric sets and gives the definition and properties of separable random closed sets. Further, the definitions of the empirical mean set and the empirical mean boundary are proposed and empirical evidence of the consistency of the boundary estimator is presented. In addition, the paper gives loss...
Hanna K. Jankowski, Larissa I. Stanberry
Added 28 Jan 2011
Updated 28 Jan 2011
Type Journal
Year 2010
Where JMIV
Authors Hanna K. Jankowski, Larissa I. Stanberry
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