PhD Courses in Denmark

Course Description

Quantitative image analysis and stochastic 3D modeling play an important role in modern research across science and engineering, for example, in materials science, biomedicine, geoscience and process engineering. This PhD course introduces methods in image processing, machine learning and statistical/stochastic microstructure modeling. Participants will learn how to extract, model and predict structural information from 2D and 3D imaging data acquired by various imaging techniques (e.g., scanning electron microscopy, micro-computed tomography, etc.). The course will address both data-driven and model-based approaches and emphasizes their synergies for understanding and simulating complex spatial morphologies.

Knowledge, Skills and Competences

The students will learn and discuss the following topics within an interdisciplinary context:

• Image processing and feature extraction techniques to 2D/3D image data.
• Machine learning methods for image-based analysis of microstructures.
• Stochastic 3D models (point processes, random fields, tessellations) that enable the generation of virtual, but realistic microstructures
• Machine learning to calibrate stochastic 3D modeling to 2D/3D image data.

Importantly, the course will be relatively independent of the specific material system, scale or imaging technique, as the methods and models deployed for characterizing and modeling microstructures will be largely scale-independent. This allows participants to transfer and apply the techniques across different disciplines.

Course Content

1. Image Processing and Feature Extraction. Methods for analyzing microstructures in 2D/3D image data, including data preprocessing, segmentation and quantitative feature extraction techniques. Besides conventional algorithms from digital image processing, methods from machine learning are considered as well for the extraction of microstructural features.

2. Stochastic 3D Modeling of Microstructures. Theory and computational implementation of random fields and random tessellations for generating virtual but realistic microstructures. Besides conventional models, also methods from machine learning are considered (e.g., generative adversarial networks, diffusion models).

3. Combination of Data-Driven and Model-Based Approaches. Strategies for calibrating stochastic 3D models to image data are considered, with a particular focus on combining machine learning and stochastic 3D modeling methods to improve model calibration.

4. Applications. Case studies demonstrating the use of combined data-driven and stochastic methods for analyzing, simulating and predicting material microstructures. Examples include the application of stereological techniques, i.e., to reconstruct 3D microstructures from 2D image data, thereby significantly reducing measurement effort.

Teaching format: Lectures, tutorials in Python and project work.

Course language: English.
 

Prerequisites

Basic knowledge of probability and statistics, linear algebra and programming (e.g., Python or MATLAB).

Learning Outcomes

Knowledge:

• Understand the principles of image processing for microstructural 2D/3D image data.
• Understand different data-driven and model-based approaches for stochastically modeling 3D microstructures.

Skills:

• Able to deploy image processing pipelines for preprocessing (e.g., denoising), segmenting image data.
• Able to compute quantitative features that characterize microstructures observed in segmented image data, in order to fit stochastic 3D models.

Competences:

• Able to combine data-driven machine learning techniques with stochastic modeling approaches to analyze and simulate realistic 3D microstructures from imaging data.
• Capable of designing and executing an independent project involving quantitative image analysis and stochastic 3D modeling, including interpreting and communicating results.

Examination / Evaluation

Small project based on individual or group work, presented as a short talk or poster. Evaluation according to the Danish grading system.

Course Type and Target Group

PhD-level course. Intended for PhD students in applied mathematics, statistics, computer science, materials science, process engineering and related fields.

Workload and Schedule

Lectures: 20 hours
Tutorials: 10 hours
Project work and self-study: 95 hours
Total workload: approx. 125 hours = 5 ECTS

Suggested Literature / References

• Goodfellow, I., Bengio, Y., Courville, A. Deep Learning, MIT Press, 2016.
• Burger, W., Burge, M. J. Digital Image Processing, Springer, 2016.
• Chiu, S. N., Stoyan, D., Kendall, W. S., Mecke, J. Stochastic Geometry and Its Applications, Wiley, 2013.
• Jeulin, D. Morphological Models of Random Structures, Springer, 2021.

Length

5 weeks lecture + 4 weeks project work


Price/Course fee

Free for Danish PhD students (direct costs only); DKK 1200 per ECTS for external participants