Geometrical and morphometrical tools for the inclusion analysis of metallic alloys

International audienceThe mechanical and use properties of metal alloys depend on several factors, including the amount and the geometry of impurities (inclusions). In this context, image analysis enables these inclusions to be studied from digital images acquired by various systems such as optical/electron microscopy or X-ray tomography. This paper therefore aims to present some geometrical and morphometrical tools of image analysis, in order to characterize inclusions in metal alloys. To achieve this quantification, many geometrical and morphometrical features are traditionally used to quantitatively describe a population of objects (inclusions). Integral geometry, via Minkowski’s functionals (in 2D: area, perimeter, Euler-Poincaré number), has been particularly investigated in image analysis. Nevertheless, they are sometimes insufficient for the characterization of complex microstructures (such as aggregates/agglomerates of objects). Other quantitative parameters are then necessary in order to discriminate or group different families of objects. In particular, shape diagrams are mathematical representations in the Euclidean plane for studying the morphology (shape) of objects, regardless of their size. In addition, this representation also makes it possible to analyze the evolution from one shape to another. In conclusion, image analysis using integral geometry and shape diagrams provide efficient tools with known mathematical properties to quantitatively describe inclusions (providing separate information on size and shape). The geometrical characteristics of these inclusions could thereafter be related to the mechanical properties of the metal alloys

A digital analogue of the Jordan curve theorem

AbstractWe study certain closure operations on Z2, with the aim of showing that they can provide a suitable framework for solving problems of digital topology. The Khalimsky topology on Z2, which is commonly used as a basic structure in digital topology nowadays, can be obtained as a special case of the closure operations studied. By proving an analogy of the Jordan curve theorem for these closure operations, we show that they provide a convenient model of the real plane and can therefore be used for studying topological and geometric properties of digital images. We also discuss some advantages of the closure operations investigated over the Khalimsky topology