ON THE SPECIFIC AREA OF INHOMOGENEOUS BOOLEAN MODELS. EXISTENCE RESULTS AND APPLICATIONS

• Main Author: Elena Villa
• Format: Article
• Language: English
• Published: Slovenian Society for Stereology and Quantitative Image Analysis 2011-05-01
• Series: Image Analysis and Stereology
• Subjects: geometric measure theory; mean surface density; outer Minkowski content; specific area; stochastic geometry
• Online Access: http://www.ias-iss.org/ojs/IAS/article/view/875

The problem of the evaluation of the so-called specific area of a random closed set, in connection with its mean boundary measure, is mentioned in the classical book by Matheron on random closed sets (Matheron, 1975, p. 50); it is still an open problem, in general. We offer here an overview of some recent results concerning the existence of the specific area of inhomogeneous Boolean models, unifying results from geometric measure theory and from stochastic geometry. A discussion of possible applications to image analysis concerning the estimation of the mean surface density of random closed sets, and, in particular, to material science concerning birth-and-growth processes, is also provided.