Statistics Group

DFG Project : Superresolution of multiscale images from materials sciences using geometrical features

Recent and ongoing developments in imaging techniques and computational analysis deeply modify the way materials sciences and engineering consider their objects of research. Our project will contribute to this direction of research by developing new superresolution methods guided by high-resolution local subimages of 3D materials data.The mathematical methods of choice will be based on local and global Generalized Gaussian Mixture Models as well as Student-t Mixture Models in conjunction with variational methods. Appropriate geometrical features related to the engineering topics have to be established to provide an evaluation platform for the superresolution images, and to be directly involved into the Bayesian and variational models. The mathematical models will be developed, analyzed and appropriate efficient algorithms will be derived, including an examination of their convergence behavior. The models will be extended to multimodal images, where due to the size of the structures of interest, the high resolution image are taken by serial sectioning (FIB-SEM) tomography and the low resolution images by micro computed tomography. This requires to take the special acquisition of FIB-SEM tomographic images, in particular curtaining effects and the anisotropy with respect to the third dimension into account. A numerical evaluation of the relevance and the benefit of the developed superresolution methods will be performed by comparing the effective properties computed for reactive flow in porous media.



Project partner:

Professorin Dr. Gabriele Steidl

Professor Jean-Francois Aujol, Ph.D.

Professor Dr. Dominique Bernard, Ph.D.

Professor Yannik Berthoumieu, Ph.D.

DFG-Project: Major-Instrumentation Initiative: CT of structural elements under changing load

Computer Tomography has been used for many years in construction materials technology in order to gain knowledge, using small format samples, of the joint structure of construction materials and how they change under different conditions of exposure. However, there is lack of appropriately configured equipment that would enable by means of X-ray technology a better understanding of bearing and deformation behaviour of entire building parts. Hence, in line with the DFG offer to tender, a completely new type of Tomography Portal (TOP) has been conceived; one that can scan building components of real life dimensions under increasing load with high resolution accuracy. It makes use of a high radiation energy, which is indispensable in order for example to illuminate bar-like reinforced concrete components using cross-section dimensions of at least 30 x 30 cm, and imaging of cracks of 0.1 mm width. In addition, a second radiating source has been integrated, which in the case of smaller dimensions or less demanding materials permits higher resolutions. The design has been understood as an interdisciplinary work. The guiding factors in the design were: the needs of the construction industry, machine, X-ray and measuring technology, calibration procedure, mathematical reconstruction of raw data, with their visual preparation and further processing on high performance computers as well as the availability of the research results.



Project partner:

Professor Dr.-Ing. Jürgen Schnell

Professor Dr.-Ing. Manfred Curbach

Professor Dr.-Ing. Josef Hegger

Professorin Dr. Heike Leitte

Professor Dr.-Ing. Harald S. Müller

Professor Dr.-Ing. Ralf Müller

Professor Dr.-Ing. Matthias Pahn

Professor Dr.-Ing. Jörg Seewig

Professor Dr.-Ing. Christos Vrettos

German-French doctoral college

The goal of the research training group is to develop new methods for the analysis, modeling and simulation of complex material structures using image data. In the fourth funding period of the research training group, the following key subjects are to be set:

  • A major focus will be on the temporal evolution of 3D image data. The interest in describing, analyzing and simulating the dynamics of big data has increased considerably in recent years, especially in the materials sciences. A promising mathematical approach is the investigation of the evolution of distributions.
  • Another focus will be spatially weakly distributed data with fast, sharp changes in structure (e. g. foams). Particularly for their analysis and simulation, statistical and morphological methods will be developed.
  • Finally, methods for the detection of anomalies in different materials, such as misorientations of fibers or cellular fractures will be developed in the research training group. To manage the corresponding classification and segmentation problems, the development and implementation of machine learning techniques, including Convolutional Neural Networks (CNN) and Random Forrests, is planned. The goal is to combine "deep learning" techniques with existing variational calculus and morphology methods by using them to support and improve intermediate results.

The inclusion of physical facts as well as prior knowledge about the structure of images will be investigated, also issues such as reliability versus network architecture and 
complexity bounds for NNs.



Project partner:

Professorin Dr. Gabriele Steidl

Dr. Katja Schladitz

Dr. François Willot

Dr. Jesús Angulo

BMBF Project: Oho - Optimization of wood-based insulation

Wood and other cellulose fiber insulating materials are the most commonly used insulating materials made from renewable ressources. However, their thermal conductivity is generally higher than the thermal conductivity of conventional insulation materials. Due to the manufacturing process, the distribution and orientation of the cellulose fibers lead to highly anisotropic thermal conductivity. Besides single fibers, the microstructure also contains fiber bundles of different sizes. To this end, accurate prediction of thermal conductivity as well as further optimization of the board structure to achieve thermal conductivities <35 W/K is difficult.

The goal of the research project is therefore to optimize the structure of highly porous wood fiber insulation boards in order to further reduce their effective thermal conductivity. The potential for this lies precisely in exploiting anisotropy and specifically mixing fiber bundles of different sizes. To exploit this potential, machine learning methods, image based geometric structure modeling and numerical methods for the efficient simulation of heat transfer are to be combined with optimization methods.



Project partner:

Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM

Bergische Universität Wuppertal (BUW)

Martin-Luther-Universität Halle (LUH)


Fagus-GreCon Greten GmbH & Co. KG


BMBF Project: poST - Synthetic data for ML segmentation of FIB-SEM nanotomographs of highly porous structures

The nanostructure of complex materials can be imaged in 3D by the FIB-SEM serial sectioning technique. To analyze the material, its components must be reconstructed from the image data. In the case of high porosity, this is difficult because structures behind the current imaging plane are also visible through the pores.

Machine learning techniques have high potential here. However, training data are difficult to obtain. Manual segmentation is hardly possible, since even humans often cannot decide which structures form the foreground of the current section. Synthetic images for which the correct result is known are an attractive way out. The similarity of the simulated to the real structure has a considerable influence on the quality of the result.



Project partner:

Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM

DFKI Saarbrücken

BMBF Project: SynosIs - Synthetic, Optically Realistic Image Data of Surface Structures for AI-Based Inspection Systems

Artificial intelligence (AI) is used very successfully in image recognition, processing and understanding. However, training an AI-based inspection system for industrial quality assurance requires large amounts of representative annotated image data for all defect types. Manual annotation is laborious and error-prone. Many defects, especially safety-critical ones, occur very rarely.

Realistic synthetic image data help circumvent these problems.

We combine physics, mathematics and computer science to generate synthetic images of typical defects on metallic surfaces with unprecedented realism. These defect images that are guaranteed to be correctly and objectively annotated are available for training and validation of AI systems for optical surface inspection after the end of the project.

More information about the project


Project partner:

Professor Hans Hagen (TUK)

Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM

Fraunhofer-Institut für Angewandte Optik und Feinmechanik IOF

BMBF Project: DAnoBi

The aim of the research project is to develop methods for the detection of anomalies in large image data. This could be e.g. micro cracks in concrete beams, material densification in textile web goods or local fiber misalignments in components made of fiber-reinforced plastic. For this purpose, methods of machine learning, modeling of structures and imaging as well as statistical methods for the detection of abnormalities can be combined. In all this cases mentioned, the structure varies greatly. Methods and measures must therefore be developed in order to decide objectively, robustly and repeatably what an anomaly, i.e. a significant deviation is. The anomalies to be detected rarely occur both statistically and spatially. For this reason, there is a lack of training data for purely machine learning (ML) based solutions, which annotation is also very difficult. One way out is training based on realistic, simulated data, since in this case enough data can be generated and the basic truth is immediately available. An alternative approach is to adapt statistical methods for structure break detection in time series for the detection of spatial anomalies. The spatial component of the image data gives rise to new tasks, such as recognizing complex anomaly regions, which will also be solved in the project. The planned research work focuses on the detection of cracks in concrete components, since this question is of great practical relevance, but also particularly difficult in a methodological sense. ML and statistical methods for solving this specific problem are expected to be transferable to the other use cases mentioned above. Models for concrete and crack structures, on the other hand, are problem-specific, but are already a major challenge in this thematic limitation. 



Project partner:

Universität Ulm

Otto von Guericke-Universität Magdeburg

Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM

BORAPA Ingenieurgesellschaft mbH

MKT Metall-Kunststoff-Technik GmbH & Co KG

C-Con GmbH & Co KG

Dr. Ketterer Ingenieurgesellschaft mbH

Heinze CobiaxDeutschland GmbH

Bekaert GmbH

Completed projects



Other Projects

  • Junior Endowed Professorship
    Statistics of Spatial Structures for Innovations in the Engineering Sciences of the "Carl Zeiss Foundation"

  • Project as Part of the Innovation Centre "Applied System Modeling"
    Applied System Modeling for Multi Scale Materials

  • (CM)²-Project
    Image Processing in Civil Engineering

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