Solution crystallization processes are widely used in the process industry as separation and purification operations and are expected to produce solids with desirable properties. The properties concerning the size and the shape are known to have a considerable impact on the final quality of products. Hence, it is of main importance to be able to determine the granulometry of the crystals (CSD) in formation. By using an in situ camera, it is possible to visualize in real time the 2D projections of the 3D particles in the suspension.The projection of a 3D object on a 2D plane necessarily involves a loss of information. Determining the size and the shape of a 3D object from its 2D projections is therefore not easy. This is the main goal of this work: to characterize geometrically and morphometrically 3D objects from their 2D projections. First of all, a method based on the maximum likelihood estimation of the probability density functions of projected geometrical measurements has been developed to estimate the size of 3D convex objects. Then, a stereological shape descriptor based on shape diagrams has been proposed. It enables to characterize the shape of a 3D convex object independently of its size and has notably been used to estimate the value of the anisotropy factors of the 3D convex objects. At last, a combination of the two previous studies has allowed to estimate both the size and the shape of the 3D convex objects. This method has been validated with simulated data, has been compared to a method from the literature and has been used to estimate size distributions of ammonium oxalate particles crystallizing in water that have been compared to other CSD methods.
