Statistics Seminars: Expectations of Random Sets and Their Boundaries Using Oriented Distance Functions
5 June 2009 14:15 in CM107
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 talk will introduce 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. Further, the definitions of the empirical mean set and the empirical mean boundary will be proposed and empirical evidence of the consistency of the boundary estimator will be presented. In addition, the talk will describe loss functions for set inference in frequentist framework. The proposed definitions of the set and boundary expectations will be illustrated on theoretical examples and real data.
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