53 KB2284 KB32 KB200020242003Nagel, WernerOhser, JoachimSchladitz, Katjaštevilka:1letnik:229 stranistr. 11-19ISSN:1580-3139COBISSID:16048601URN:URN:NBN:SI:doc-DYM4LQR0enDruštvo za stereologijo in kvantitativno analizo slike, Medicinska fakultetaImage analysis and stereologycrystallographyDelec, velikostEulerjevo številoImage Processing, Computer-Assistedkristalografijamatematični modelimaterialiMateriali, testiranjeMaterials TestingModeli teoretskiModels, TheoreticalParticle SizeSlika, obdelava z računalnikomstrukturaThe Euler number of discretised sets - surprinsing results in three dimensions|The problem of estimating the Euler-Poincare characteristic (Euler number for short) of a set in the 3d Euclidean space is considered, given that this set is observed in the points of a lattice. In this situation, which is typical inimage analysis, the choice of an appropriate data-based discretisation of the set is crucial. Four versions of a discretisation method which is based onthe notion of adjacency systems are presented; these versions are referred to as (14.1,14.1), (14.2,14.2), (6, 26), and (26, 6). A comparative assessmentof the four approaches is performed with respect to the systematic error occuring in application to Boolean models. It is a surprising result that, except for (26, 6), the estimators yield infinitely large systematic errors when the lattice spacing goes to zero. Furthermore, the measurements ofthe Euler number from 3d data of autoclaved aerated concrete illustrate the influence of the choice of adjacency and the behaviour of the estimatorsTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaDruštvo za stereologijo in kvantitativno analizo slike