Mathematical Image Processing, Analysis and Modeling of Particle Populations
Résumé
Particle populations are widely used in many industrial applications and fields of science from physics to biology or agronomy. In chemical engineering, in particular, it is generally desired to extract information on geometrical characteristics and on spatial distribution from 2D images of the population of particles involved in the process. For example in pharmaceutics, the size and the shape of crystals of active ingredients are known to have a considerable impact on the final quality of products, such as drugs. Hence, it is of main importance to be able to control in real time the granulometry (size and shape) of the crystals during the process. The first part of this talk will be focused on specific geometrical and morphometrical descriptors giving information on the size, shape and spatial distribution of the particles. They have a compact representation with good mathematical properties and are easy to compute. They are based on integral geometry, shape diagrams and computational geometry. The second part of this talk will show different ways (deterministic and stochastic methods) of image processing, analysis and modeling to geometrically characterize the particles from a sequence of 2-D images acquired by a camera (visualizing the particles during a particular process). The developed methods will be presented by addressing different issues: the perspective projection of the 3-D particle shape onto the image plane, the blurred appearance of unfocused particles, the degree of agglomeration or overlapping, and the random variation in size/shape of the observed particles. The methods are mainly based on image enhancement, restoration, segmentation, tracking, modeling, feature detection, stereology, stochastic geometry, pattern analysis and recognition. The methods will be particularly illustrated on real applications of crystallization processes (for pharmaceutics industry) and multiphase flow processes (for nuclear industry). Some conclusions and prospects will be finally given.