Stereology and structuring elements

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.