Journal ArticleDOI
Stereology and structuring elements
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TLDR
An object's quantitative analysis is not purely objective, on the contrary, it results from the interaction of a structuring element chosen by the observer, with the object to be analysed.Abstract:
SUMMARY
An object's quantitative analysis is not purely objective. On the contrary, it results from the interaction of a structuring element chosen by the observer, with the object to be analysed. After defining this relation in a quantitative way (hit-or-miss transformation), and recalling its probabilistic interpretation (Matheron, 1971) some examples of structuring elements are given:
The couple of points which measures the covariances matrix. It allows harmonic analysis and the solving of sample problems.
The segment which measures the chord distribution, and leads to the stereo-logical parameter ‘the star’.
The parallel segments doublet, which measures curvature radius distribution and the number of particles in the two-dimensional space.
The hexagon, which measures bi-dimensional granulometries, etc.
These measurements have been made on the texture analyser, built by us especially for that purpose. As a conclusion, we give an application of structuring elements to clustering measurements.read more
Citations
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The Second-Order Analysis of Stationary Point Processes
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The use of dilation logic on the quantimet to achieve fractal dimension characterisation of textured and structured profiles
Book ChapterDOI
Particle size analysis by image analysis
TL;DR: In this article, various methods of image analysis for particle size analysis are discussed, including optical microscopy, measurement of plane sections through packed beds, experimental techniques, determination of particle size distribution by number, quantitative image analysis, and scanning electron microscopy.
References
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BookDOI
Vorlesungen über Inhalt, Oberfläche und Isoperimetrie
TL;DR: In this article, a vorliegende Buch vereinigt in seinen wesentlichen Teilen den Stoff verschiedener Vorlesungen liber Inhaltstheorie, isoperimetrische Probleme and liber konvexe Karper and allgemeine Integralgeometrie, which ich im Laufe der letten yearre an der Universitat Bern gehalten habe.
Journal ArticleDOI
Random sets theory and its applications to stereology
TL;DR: In this paper, a probabilistic formalism is associated with this experimental technique and facilitates its interpretation, which is closely connected with integral geometry, and interesting classes of functionals T are obtained if A is indefinitely divisible or semi markovian.
Journal ArticleDOI
A generalization of the concept of size
TL;DR: The size of a set is defined without ambiguity as a ratio of homothety with an elementary set having the same shape using the elements of the family {λB} of the homothetics of B as a measure of the object.
Journal ArticleDOI
The stereology of projected images
TL;DR: In this article, a generalized, geometrical approach is adopted in reviewing the basic relationships of projected structures, and expressions that correct for truncation and overlap of particles in thin foils are derived.