Local Minkowski measures for random set geometrical characterization.
Résumé
where the sum is across the individual areas Ai of the region of interest as observed at the cut surfaces of the individual slices. The areas may be assessed in various ways, e.g. estimated by point counting. The estimator is unbiased. I.e., by repetition, the mean of the re-estimates converges on the true mean. The basic geometric concepts behind the estimator have been known for millennia – they were familiar to Archimedes of Syracuse (c. 287–212 BC), the Chinese mathematicians Liu Hui (c. 236) and Zu Geng (480–525) as well as to Bonaventura Cavalieri (1598–1647). The stochastic part of the estimator and its finer details evolved among stereologists during the 20th century. The modern estimator was named The Cavalieri Estimator in honor of Cavalieri and his famous theorem known as Cavalieri’s principle. In the recent years, the development of methods to predict the precision of the estimator has been a hot topic in stereological research. Also, various ways to soften the requirements of the estimator has been investigated. Thus, it has been shown that (under come constrains) the estimator is still unbiased even in the case of non-equidistant, uniformly random parallel cuts. Inmy presentation, I will review the past and present of the Cavalieri Estimator and point to some areas of future development.
Format : Papier court
Origine : Fichiers produits par l'(les) auteur(s)
Origine : Fichiers produits par l'(les) auteur(s)