Measuring the 3D morphological properties of granular objects such as aggregates is a critical issue in many fields of science and industry, especially when the objects are fragile or hard to sample. For these reasons, non-invasive techniques based on image analysis are being developed. However, most image analysis techniques can only measure 2D properties. This paper presents a new approach based on both image analysis and a 3D stochastic geometric model called VOX-STORM (VOXel-based STOchastic geometRical Model) to estimate 3D morphological properties. By adjusting the parameters of the model, the latter is able to generate populations of objects whose 2D property distributions match those measured by image analysis, and to predict 3D morphological property distributions. The model is based on a dual architecture combining voxelized structure and alpha-shape meshing of the external surface, which makes object generation extremely fast (about 1000 objects in 20 s), while allowing rapid computation of 3D characteristics. The method is validated twice, first on 3D printed aggregates and then on a population of 40,000 synthetic aggregates, with mean errors of less than 2.5% in all cases and less than 1% for 2D properties. It is then applied to two sets of images of latex aggregates captured by a morphogranulometer. The morphological property distributions and fractal dimensions are compared to ground truth in the 2D case and to laser diffraction measurements in the 3D case. The results are also compared with two other recent stochastic geometric models, and the VOX-STORM model outperforms them in all scenarios, as well as in speed of execution, while agreeing with experimental measurements. Finally, directions for future work are suggested.