GRAPE: A Stochastic Geometrical 3D Model for Aggregates of Particles With Tunable 2D Morphological Projected Properties

Abstract

The main goal of this paper is to propose a method for the 3D morphological characterization of compact aggregates using 2D image analysis. The problem at hand is the 3D morphometric characterization of latex nanoparticle aggregates. The only available information is 2D projection images of these aggregates, one projection per aggregate. In this context, a method to estimate the 3D morphological characteristics of an aggregate such as the Volume, Surface Area or Solidity from a single projection is proposed. This method is based on a stochastic geometric model called GRAPE (Geometrical Random Aggregation of Particles Emulation) and requires some strong assumptions, and in particular prior estimation of the volume. The model is based on an iterative packing of spheres of identical radii. For each iteration, a fitting function allows to reach objectives corresponding to the desired 2D properties (Area, Perimeter, Aspect Ratio, ...). In order to implement the method, an optimization process must be performed on two parameters of the model: the radius of the elementary particles r and an overlapping distance di. As a validation, this process will be applied to synthetic aggregates, themselves generated from the GRAPE model, then to a population of 10⁴ synthetic aggregates, and finally to 3D printed aggregates whose 3D morphological properties are known thanks to an STL file, and whose projected images have been produced using a morphogranulometer. The results obtained show an excellent approximation of 2D properties by the GRAPE model, and very good results for 3D properties, with less than 5% error on average and less than 2% error in most cases.