Virtual test systems for global spatial sampling in thick, arbitrarily orientated uniform, random sections

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Abstract

Virtual test systems are test systems where the randomization of the stereological probes is made within volume probes of arbitrarily orientated thick uniform, random physical sections. Complete isotropy and 2D uniform, random sampling in the thick section of the virtual test system is performed by a computer. Subsequent sampling is performed by superimposing a computer generated 2D representation of the test system onto live video images of shallow focal planes within the uniformly, random volume probe. The 2D representation of the test system moves across the computer screen during focal plane displacement and dynamically maps the test system that exists in 3D within the volume probe. Test systems based on isotropic lines in 3D are visualized as moving points in the 2D focal plane, and test systems based on isotropic planes in 3D are visualized as moving lines. In principle only the computer power and our imagination are limits for the design of virtual test systems. Test systems that are isotropic in 3D allow for sampling inside a thick, arbitrarily orientated uniform, random physical section (or at worst vertical sections for local estimators and spatial distributions, when the structure is incompletely contained within the thick physical section), thereby reducing considerably the problems associated with estimation under anisotropic conditions. Practical implementation of the principle is exemplified with estimators of length density and total global length. The major practical advantage of this principle is that for most orientation dependent estimators there is complete freedom to choose the most convenient sectioning direction, and that isotropic section, in principle, are no longer required for any estimator.

Om dit artikel te citeren:

Over : Jytte Overgaard Larsen

Over : Hans Jørgen G. Gundersen