On the tractability of estimating the germ process of certain germ-grain random set models and related problems

N. D. Sidiropoulos

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The germ process embedded in a germ-grain random set is often not merely part of a constructive mathematical model, but has physical significance as well, e.g., in the modeling of cell cultures. In such situations, knowledge of the realization of the germ process associated with a particular random set observation is highly desirable. In this paper, it is shown that, for an interesting class of germ-grain models, maximum likelihood estimation of the germ process on the basis of a random set observation is an NP-complete computational problem. Certain additional computational problems associated with the probabilistic specification of morphologically processed random sets are also discussed.

Original languageEnglish (US)
Pages (from-to)1667-1674
Number of pages8
JournalPattern Recognition
Volume32
Issue number9
DOIs
StatePublished - Sep 1999

Keywords

  • Boolean model
  • Germ-grain models
  • Mathematical morphology
  • NP-completeness
  • Random sets

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