Level sets estimation and Vorob’ev expectation of random compact sets

Abstract The issue of a “mean shape” of a random set X often arises, in particular in image analysis and pattern detection. There is no canonical definition but one possible approach is the so-called Vorob’ev expectation E V ( X ) , which is closely linked to level or quantile sets. In this paper, we propose a consistent and ready to use estimator of E V ( X ) built from independent copies of X with spatial discretisation. The control of discretisation errors is handled with a mild regularity assumption on the boundary of X . Several examples are developed and an application to cosmological data is presented.

• Publication year

  2010

• Venue

  spatial statistics

• Publication date

  2010-06-26

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1016/j.spasta.2012.10.001arXiv 1006.5135
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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