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                <term xml:lang="en">stochastic geometry</term>
                <term xml:lang="en">PSD</term>
                <term xml:lang="en">image analysis</term>
                <term xml:lang="en">in situ analysis</term>
                <term xml:lang="fr">modélisation géométrique.</term>
                <term xml:lang="fr">Analyse in-situ</term>
                <term xml:lang="fr">analyse d’image</term>
                <term xml:lang="fr">géométrie stochastique</term>
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              <p>The geometrical and morphological characteristics of crystals (i.e. their particle size and shape distributions) involve a considerable impact on their properties of use. In situ image acquisition enables the temporal evolution of particles to be followed during the crystallization process. In this way, image analysis provides the geometrical characteristics of such crystals. Nevertheless, the 2-D imaging system gives only access to the projection of crystals and consequently to potential overlapping (specifically for a dense media). Consequently, it is required to develop specific image analysis methods for determining the geometrical and morphometrical characteristics of the crystals. This paper presents a method based on stochastic geometrical tools. The images can be modelized by using a random geometrical model, representing the population of crystals. It is then possible to estimate the statistical moments (mean, variance …) of their geometrical characteristics such as the area, the perimeter or the diameter. The proposed method has been carried out on simulated data so as to evaluate its performance. This geometrical characterization could allow to improve the crystallization models and then the process of manufacturing.</p>
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              <p>Les caractéristiques géométriques et morphométriques des cristaux (c’est-à-dire les distributions en taille et en forme) ont un impact considérable sur l’ensemble des propriétés d’usage de ces particules. L’utilisation de capteurs d’images 2-D « in situ » permet de suivre l'évolution temporelle de ces particules au cours du processus de cristallisation. L’analyse de ces images fournit alors les caractéristiques granulométriques de ces cristaux. Cependant, l’acquisition d’images numériques 2-D donne accès uniquement aux projections de ces cristaux et donc à des potentielles superpositions (notamment dans un milieu dense). Par conséquent, il est nécessaire de développer des méthodes spécifiques d’analyse d’image afin de déterminer les distributions géométriques et morphométriques de ces cristaux. Ce papier présente une méthode basée sur des outils de la géométrie stochastique. Les images sont décrites par un modèle de géométrie aléatoire, représentant la population de cristaux, dans lequel il est possible d’estimer les moments statistiques (espérance, variance…) de leurs caractéristiques granulométriques telles que l’aire, le périmètre ou le diamètre. La méthode proposée est appliquée sur des images simulées afin d’évaluer sa performance. En conséquence, cette caractérisation géométrique et morphométrique pourrait permettre d’améliorer les modèles de cristallisation et par suite les procédés d’élaboration des solides.</p>
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