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  Averaging of random sets based on their distance functions (1998) [7 citations — 2 self]

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by Adrian J. Baddeley, Ilya S. Molchanov
Journal of Mathematical Imaging and Vision
http://maths.uwa.edu.au/~adrian/reprints/95-23.ps.Z
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Abstract:

A new notion of expectation (or distance average) of random closed sets based on their distance function representation is introduced. A general concept of the distance function is exploited to define the expectation, which is the set whose distance function is closest to the expected distance function of the original (random) set. This distance average can be applied to average non-convex and non-connected random sets. We establish some basic properties and prove limit theorems for the empirical distance average of i.i.d. random sets.

Citations

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