The geometrical modeling of granular objects is a complex challenge that exists in many scientific fields, such as the modeling of granular materials or rocks and coarse aggregates with applications in civil, mechanical, and chemical engineering. In this paper, a model called SPHERE (Stochastic Process for Highly Effective Radial Expansion) is proposed, which is based on the deformation of an ellipsoid mesh using multiple 3D Gaussian random fields. The model is designed to be flexible (full control over 2D and 3D morphological properties of granular objects), ultra-fast (over 1000 aggregates in less than 5 s), and independent of the mesh and base shape used (as long as it is a star-shaped object). The flexibility of the model and its ability to reflect real data is illustrated using images of latex nanoparticle aggregates. Using 2D measurements on images from a morphogranulometer, a method based on the SPHERE model is proposed to estimate the 3D morphological properties of aggregates. A multiscale optimization process is applied, in particular using a partial reconstruction of 2D shapes from elliptic Fourier descriptors, in order to best reproduce the shape, angularity and texture of the aggregates using the SPHERE model. Validation of the method on 3D printed data shows relative errors of less than 3% for all measured 2D and 3D morphological characteristics, and validation on a population of synthetic objects shows relative errors of less than 6%. The results are compared and discussed with those obtained using other models based on overlapping spheres and show consistency with previous work. Finally, suggestions for improvement are given.