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Consistency in the Reconstruction of Patterns from Sample Data

Published online by Cambridge University Press:  20 November 2018

Marc Moore
Marc Moore*
Affiliation:
Ecole Polytechnique, Montréal, Québec
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Let A be a k-dimensional Euclidean region having unit volume. An m-colors pattern is a partition PA of A into m sets Ai, i—1,…, m with positive volume. PA is called a random pattern if in addition the partition of A is a realization of a random process with the following stationarity and isotropy properties:

  • (i) for all points s ∊ A, P(s ∊ Ai) =pi9, i = 1,..., m

  • (ii) for all pair of points s, s'∊ A with distance |s—s|=d between them, P(s' ∊ Ai | s ∊ Aj)Pij(d) i,j= 1,..., m.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 2 , June 1972 , pp. 305 - 307
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Switzer, P., Reconstructing patterns from sample data, Ann. Math. Statist. 38 (1967), 138-154.Google Scholar
2. Switzer, P., Mapping a geographically correlated environment, Technical Report No. 145, Stanford University, 1969.Google Scholar