A test for discrete Boolean models

Abstract

For a discrete random set defined on a bounded subset B ⊂ ℤ2, the paper proposes a test for checking the Boolean hypothesis against its natural alternatives: models whose process of germs show a major tendency versus regularity or aggregation represented by a hardcore process or Poisson's cluster process. The test is based on the contents, T, of the difference XD - X, where X is the original model and XD = X ⊕ C is its dilation by the structurant element C.