Stochastic Modeling in R

Overview:

This project applies stochastic geometry techniques to model and analyze microstructural features in materials. Implemented entirely in R using RStudio, the work involved image-based analysis, probabilistic modeling, and statistical simulation to investigate the geometric and topological properties of random material structures.

Key Contributions:

🔹 Task 1: Morphological Analysis Using Minkowski Functionals

  • Analyzed 2D realizations of random sets.
  • Applied Minkowski functionals (area, perimeter, Euler characteristic) to characterize structural complexity.
  • Compared connectivity and homogeneity across different random set realizations.

🔹 Task 2: Morphological Openings and Boolean Model Evaluation

  • Performed morphological openings to estimate shortest side lengths in grain-like structures.
  • Proposed and validated two Boolean models using global envelope tests with 999 repetitions.
  • Both models showed acceptable fit with p-values of 0.312 and 0.514.

🔹 Task 3: Wicksell Corpuscle Inverse Problem

  • Used segmentation algorithms on 2D slices to infer 3D grain size distributions.
  • Estimated volume fraction, specific surface area, and intensity of spherical inclusions.
  • Provided statistical summaries and visualizations of the diameter distributions.

🔹 Task 4: Monte Carlo Estimation of Quermass Densities

  • Simulated Matern III hard-disc models with varying Poisson intensities.
  • Computed Quermass densities (area fraction, boundary length, Euler number) using Monte Carlo methods.
  • Identified systematic increases in structural metrics with higher intensities.

Tools & Techniques:

  • R & RStudio
  • spatstat, EBImage, ggplot2, dplyr, stats
  • Morphological Image Processing
  • Stochastic Modeling (Boolean and Matern Processes)
  • Monte Carlo Simulations
  • Global Envelope Testing

Outcome:

The project successfully demonstrates the potential of stochastic methods and spatial statistics, implemented in R, to quantify and interpret complex structural behaviors in random materials. This provides a foundation for predictive modeling and digital material design workflows.