Morphological characterization of aggregates using image analysis is a key problem in many research areas. In particular, the estimation of 3D characteristics from projected 2D images is both complex and necessary. In this paper, a stochastic geometric 3D model called SWARM (Stochastic Wandering particle AgglomeRation Model) is developed based on hard sphere packing and random graphs. A method to adjust the model parameters by image analysis using morphological skeletons is presented and doubly validated on synthetic and 3D printed aggregates. The results obtained show relative errors of the order of 1% in most cases and 4% in the worst case, making it a very efficient model compared to similar models. Finally, limitations are discussed and possible improvements are suggested.