Geodesic
Consistency in the Reconstruction of Patterns from Sample Data
Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 305-307

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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. 
Moore, Marc. Consistency in the Reconstruction of Patterns from Sample Data. Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 305-307. doi: 10.4153/CMB-1972-057-5
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[1] 1. Switzer, P., Reconstructing patterns from sample data, Ann. Math. Statist. 38 (1967), 138-154. Google Scholar

[2] 2. Switzer, P., Mapping a geographically correlated environment, Technical Report No. 145, Stanford University, 1969. Google Scholar

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