论文信息 - Estimation of the directional measure of planar random sets by digitization

Estimation of the directional measure of planar random sets by digitization

Estimation methods for the directional measure of a stationary planar random set Z, based only on discretized realizations of Z, are discussed. Properties of the discretized set that can be derived by comparing neighbouring grid points are used. Larger grid configurations of more than two grid points are considered. It is shown that the probabilities of observing the various types of configurations can be expressed in terms of the first contact distribution function of Z (with a finite structuring element). An important prerequisite result concerning deterministic dilation areas is also established. The inference on the mean normal measure based on 2×2 configurations is discussed in detail.

M. Kiderlen | E. B. Jensen

[1] G. Matheron. Éléments pour une théorie des milieux poreux , 1967 .

[2] G. Matheron. Hyperplans poissoniens et compacts de Steiner , 1974, Advances in Applied Probability.

[3] Stochastische Geometrie , 1983 .

[4] Jean Serra,et al. Image Analysis and Mathematical Morphology , 1983 .

[5] R. Schneider. Convex Bodies: The Brunn–Minkowski Theory: Minkowski addition , 1993 .

[6] Estimation of oriented direction distribution of a planar body , 1996, Advances in Applied Probability.

[7] Bernd Steinbach,et al. Efficient texture analysis of binary images , 1998 .

[8] Heinrich. Statistics of the Boolean Model for Practitioners and Mathematicians , 1998 .

[9] Daniel Hug,et al. On support measures in Minkowski spaces and contact distributions in stochastic geometry , 2000 .

[10] W. Weil,et al. A Survey on Contact Distributions , 2002 .

[11] Peihua Qiu,et al. Statistical Analysis of Microstructures in Materials Science , 2002, Technometrics.

[12] M. Kiderlen. Determination of the mean normal measure from isotropic means of flat sections , 2002, Advances in Applied Probability.

[13] On Set Covariance and Three-Point Test Sets , 2004 .