This paper discusses first the possibility of characterizing particle samples by functions. The empirical distribution function of classical shape ratios turns out to be a very powerful tool for discriminating samples of particles. Then a simple geometrical model is presented for shape and size development in abrasion processes such as in tumbling barrels. The fundamental operations "erosion" and "opening" of mathematical morphology lead to a satisfactory description of abrasion processes. All this is demonstrated for samples of limestone particles.