arXiv subjects

Claudia Redenbach

Publications and source records attributed to Claudia Redenbach.

At least 19 recordsLinked to original sources

arXiv2026

Fitting the topology of synthetic particle systems with a novel graph representation

The shape and arrangement of particles in a material determine its macroscopic properties. The generation of synthetic data with varying particle structure, often represented as 3D voxel images, combined with simulation of macroscopic properties reveals structure-property relations. Most particle generation models focus on single-particle characteristics like shape and size. We aim at fitting the topology of the particle system using tools from persistent homology. However, the large size of the required 3D image data makes existing methods computationally infeasible. We bridge this gap by introducing a novel graph representation of particle systems and transferring the computation of persistent homology from the image domain to the graph domain. This yields a postprocessing method for synthetic images of particle systems, that is independent of the underlying generation method and improves topological and geometrical agreement with real particle systems while preserving morphological characteristics such as the particle size distribution.

stat.ME↗

arXiv2026

Synthetic Defect Geometries of Cast Metal Objects Modeled via 2d Voronoi Tessellations

In industry, defect detection is crucial for quality control. Non-destructive testing (NDT) methods are preferred as they do not influence the functionality of the object while inspecting. Automated data evaluation for automated defect detection is a growing field of research. In particular, machine learning approaches show promising results. To provide training data in sufficient amount and quality, synthetic data can be used. Rule-based approaches enable synthetic data generation in a controllable environment. Therefore, a digital twin of the inspected object including synthetic defects is needed. We present parametric methods to model 3d mesh objects of various defect types that can then be added to the object geometry to obtain synthetic defective objects. The models are motivated by common defects in metal casting but can be transferred to other machining procedures that produce similar defect shapes. Synthetic data resembling the real inspection data can then be created by using a physically based Monte Carlo simulation of the respective testing method. Using our defect models, a variable and arbitrarily large synthetic data set can be generated with the possibility to include rarely occurring defects in sufficient quantity. Pixel-perfect annotation can be created in parallel. As an example, we will use visual surface inspection, but the procedure can be applied in combination with simulations for any other NDT method.

cs.CV↗

arXiv2025

Increasing Inter-Fiber Contact in the Altendorf-Jeulin Model

In fields such as material design or biomedicine, fiber materials play an important role. Fiber simulations, also called digital twins, provide a basis for testing and optimizing the material's physical behavior digitally. Inter-fiber contacts can influence the thermal and mechanical behavior of a fiber system; to our knowledge, however, there exist no parametric fiber models allowing for explicit modeling of the number of inter-fiber contacts. Therefore, this paper proposes an extension of the iterative force-biased fiber packing by Altendorf \& Jeulin. In this extension, we model the inter-fiber contacts explicitly and add another force to the force-biased packing to increase the number of contacts. We successfully validate the packing with respect to its parameter accuracy. Moreover, we show that the extension indeed increases the number of contacts, even exceeding theoretical values. Hence, this packing scheme has the potential to achieve higher accuracy in physical simulations.

cs.CE↗

arXiv2025

Fitting Generalized Power Diagrams to 3D Image Data: A Prerequisite for Virtual Materials Testing

This paper reviews algorithmic and modeling approaches for fitting generalized power diagrams to three-dimensional image data, a key step in virtual materials testing (VMT). Beyond their practical relevance to materials science, these tessellation models connect to several active areas of applied mathematics, including optimization, computational geometry, stochastic modeling, and optimal transport. Their formulation combines concepts from convex analysis and geometric clustering, offering a rich interplay between theory and computation. We survey recent applications and quantitatively compare algorithmic strategies for fitting Voronoi diagrams, power diagrams, and generalized balanced power diagrams (GBPDs), including linear and nonlinear programming, stochastic optimization via the cross-entropy method, and gradient-based approaches. Comparative results on real datasets illustrate trade-offs between algorithmic complexity and model accuracy.

cs.CV↗

arXiv2025

Goodness-of-fit tests for spatial point processes: A power study

Spatial point processes are used as models in many different fields ranging from ecology and forestry to cosmology and materials science. In recent years, model validation, and in particular goodness-of-fit testing of a proposed point process model have seen many advances. Most of the proposed tests are based on a functional summary statistic of the observed pattern. In this paper, the empirical powers of many possible goodness-of-fit tests that can be constructed from such a summary statistic are compared in an extensive simulation study. Recently introduced functional summary statistics derived from topological data analysis and new constructions for the test statistic such as the continuous ranked probability score are included in the comparison. We discuss the performance of specific combinations of functional summary statistic and test statistic and their robustness with respect to other tuning parameters. Finally, tests using more than one individual functional summary statistic are also investigated. The results allow us to provide guidelines on how to choose powerful tests in a particular test stetting.

stat.ME↗

arXiv2025

Bayesian inference for Neyman-Scott point processes with anisotropic clusters

There are few inference methods available to accommodate covariate-dependent anisotropy in point process models. To address this, we propose an extended Bayesian MCMC approach for Neyman-Scott cluster processes. We focus on anisotropy and inhomogeneity in the offspring distribution. Our approach provides parameter estimates as well as significance tests for the covariates and anisotropy through credible intervals, which are determined by the posterior distributions. Additionally, it is possible to test the hypothesis of constant orientation of clusters or constant elongation of clusters. We demonstrate the applicability of this approach through a simulation study for a Thomas-type cluster process.

stat.ME↗

arXiv2025

A Novel Distance-Based Metric for Quality Assessment in Image Segmentation

The assessment of segmentation quality plays a fundamental role in the development, optimization, and comparison of segmentation methods which are used in a wide range of applications. With few exceptions, quality assessment is performed using traditional metrics, which are based on counting the number of erroneous pixels but do not capture the spatial distribution of errors. Established distance-based metrics such as the average Hausdorff distance are difficult to interpret and compare for different methods and datasets. In this paper, we introduce the Surface Consistency Coefficient (SCC), a novel distance-based quality metric that quantifies the spatial distribution of errors based on their proximity to the surface of the structure. Through a rigorous analysis using synthetic data and real segmentation results, we demonstrate the robustness and effectiveness of SCC in distinguishing errors near the surface from those further away. At the same time, SCC is easy to interpret and comparable across different structural contexts.

cs.CV↗

arXiv2025

Simulation of microstructures and machine learning

Machine learning offers attractive solutions to challenging image processing tasks. Tedious development and parametrization of algorithmic solutions can be replaced by training a convolutional neural network or a random forest with a high potential to generalize. However, machine learning methods rely on huge amounts of representative image data along with a ground truth, usually obtained by manual annotation. Thus, limited availability of training data is a critical bottleneck. We discuss two use cases: optical quality control in industrial production and segmenting crack structures in 3D images of concrete. For optical quality control, all defect types have to be trained but are typically not evenly represented in the training data. Additionally, manual annotation is costly and often inconsistent. It is nearly impossible in the second case: segmentation of crack systems in 3D images of concrete. Synthetic images, generated based on realizations of stochastic geometry models, offer an elegant way out. A wide variety of structure types can be generated. The within structure variation is naturally captured by the stochastic nature of the models and the ground truth is for free. Many new questions arise. In particular, which characteristics of the real image data have to be met to which degree of fidelity.

cs.CV↗

arXiv2025

Cracks in concrete

Finding and properly segmenting cracks in images of concrete is a challenging task. Cracks are thin and rough and being air filled do yield a very weak contrast in 3D images obtained by computed tomography. Enhancing and segmenting dark lower-dimensional structures is already demanding. The heterogeneous concrete matrix and the size of the images further increase the complexity. ML methods have proven to solve difficult segmentation problems when trained on enough and well annotated data. However, so far, there is not much 3D image data of cracks available at all, let alone annotated. Interactive annotation is error-prone as humans can easily tell cats from dogs or roads without from roads with cars but have a hard time deciding whether a thin and dark structure seen in a 2D slice continues in the next one. Training networks by synthetic, simulated images is an elegant way out, bears however its own challenges. In this contribution, we describe how to generate semi-synthetic image data to train CNN like the well known 3D U-Net or random forests for segmenting cracks in 3D images of concrete. The thickness of real cracks varies widely, both, within one crack as well as from crack to crack in the same sample. The segmentation method should therefore be invariant with respect to scale changes. We introduce the so-called RieszNet, designed for exactly this purpose. Finally, we discuss how to generalize the ML crack segmentation methods to other concrete types.

cs.CV↗

arXiv2025

3D image based stochastic micro-structure modelling of foams for simulating elasticity

Image acquisition techniques such as micro-computed tomography are nowadays widely available. Quantitative analysis of the resulting 3D image data enables geometric characterization of the micro-structure of materials. Stochastic geometry models can be fit to the observed micro-structures. By alteration of the model parameters, virtual micro-structures with modified geometry can be generated. Numerical simulation of elastic properties in realizations of these models yields deeper insight on the influence of particular micro-structural features. Ultimately, this allows for an optimization of the micro-structure geometry for particular applications. Here, we present this workflow at the example of open cell foams. Applicability is demonstrated using an aluminum alloy foam sample. The structure observed in a micro-computed tomography image is modeled by the edge system of a random Laguerre tessellation generated by a system of closely packed spheres. Elastic moduli are computed in the binarized micro-CT image of the foam as well as in realizations of the model. They agree well with the results of a compression test on the real material.

math.NA↗

arXiv2025

Random Tessellations -- An Overview of Models

Random tessellations are a prominent class of models in stochastic geometry. In this chapter, we give an overview of mechanisms that have been used to formulate random tessellation models. First, the notion of a random tessellation and basic geometric characteristics of random tessellations are introduced. Then, several model classes are presented. This includes, but is not limited to, Voronoi tessellations and their weighted generalizations, hyperplane tessellations, and STIT tessellations. Simulation of the tessellation models and approaches for model fitting are also discussed.

math.PR↗

arXiv2025

Goodness-of-fit tests for spatial point processes: A review

In this review, the state-of-the-art for goodness-of-fit testing for spatial point processes is summarized. Test statistics based on classical functional summary statistics and recent contributions from topological data analysis are considered. Different approaches to derive test statistics from functional summary statistics are categorized in a unifying notation. We discuss additional aspects such as the graphical representation in terms of global envelopes and the selection of the parameters in the individual tests.

stat.ME↗

arXiv2024

SYNOSIS: Image synthesis pipeline for machine vision in metal surface inspection

The use of machine learning (ML) methods for development of robust and flexible visual inspection system has shown promising. However their performance is highly dependent on the amount and diversity of training data. This is often restricted not only due to costs but also due to a wide variety of defects and product surfaces which occur with varying frequency. As such, one can not guarantee that the acquired dataset contains enough defect and product surface occurrences which are needed to develop a robust model. Using parametric synthetic dataset generation, it is possible to avoid these issues. In this work, we introduce a complete pipeline which describes in detail how to approach image synthesis for surface inspection - from first acquisition, to texture and defect modeling, data generation, comparison to real data and finally use of the synthetic data to train a defect segmentation model. The pipeline is in detail evaluated for milled and sandblasted aluminum surfaces. In addition to providing an in-depth view into each step, discussion of chosen methods, and presentation of ML results, we provide a comprehensive dual dataset containing both real and synthetic images.

cs.CV↗

arXiv2024

Quantitative Fiber Orientation Analysis of Carbon Fiber Sheet Molding Compounds using Polarization Imaging and X-Ray Computed Tomography

For the quality inspection of carbon fiber sheet molding compounds, polarization imaging is a promising alternative to more established methods like computed tomography, since it is cheaper, faster, and provides a larger field-of-view. For uni- and bidirectional carbon fiber reinforced composite materials, machine vision cameras with on-chip polarized image sensors have been successfully validated for visualizing fiber orientation. Although this imaging technique is already being applied to multidirectional materials, to our knowledge, it has not yet been validated for such materials. In this paper, fiber orientations obtained by angle of linear polarization images (AOLP) of commercially available pressed carbon fiber sheet molding compound materials are compared with orientations estimated from computed tomography scans. The fiber orientations in the computed tomography images are estimated using the maximal response of anisotropic Gaussian filters and the deviation between orientations estimated from polarization and computed tomography images is calculated. Both imaging methods showed encouraging visual similarity, but also notable numerical differences, which are discussed in depth. Moreover, it is shown that the surface layer fiber orientation is representative of the fiber orientation through the entire specimen.

physics.ins-det↗

arXiv2024

Cell seeding dynamics in a porous scaffold material designed for meniscus tissue regeneration

We study the dynamics of a seeding experiment where a fibrous scaffold material is colonized by two types of cell populations. The specific application that we have in mind is related to the idea of meniscus tissue regeneration. In order to support the development of a promising replacement material, we discuss certain rate equations for the densities of human mesenchymal stem cells and chondrocytes and for the production of collagen-containing extracellular matrix. For qualitative studies, we start with a system of ordinary differential equations and refine then the model to include spatial effects of the underlying nonwoven scaffold structure. Numerical experiments as well as a complete set of parameters for future benchmarking are provided.

math.NA↗

arXiv2024

Nonparametric Isotropy Test for Spatial Point Processes using Random Rotations

In spatial statistics, point processes are often assumed to be isotropic meaning that their distribution is invariant under rotations. Statistical tests for the null hypothesis of isotropy found in the literature are based either on asymptotics or on Monte Carlo simulation of a parametric null model. Here, we present a nonparametric test based on resampling the Fry points of the observed point pattern. Empirical levels and powers of the test are investigated in a simulation study for four point process models with anisotropy induced by different mechanisms. Finally, a real data set is tested for isotropy.

stat.ME↗

arXiv2024

Effective stripe artefact removal by a variational method: application to light-sheet microscopy, FIB-SEM and remote sensing images

Light-sheet fluorescence microscopy (LSFM) is used to capture volume images of biological specimens. It offers high contrast deep inside densely fluorescence labelled samples, fast acquisition speed and minimal harmful effects on the sample. However, LSFM images often show strong stripe artifacts originating from light-matter interactions. We propose a robust variational method suitable for removing stripes which outperforms existing methods and offers flexibility through two adjustable parameters. This tool is widely applicable to improve visual quality as well as facilitate downstream processing and analysis of images acquired on systems that do not provide hardware-based destriping methods. An evaluation of methods is performed on LSFM, focused ion beam scanning electron microscopy (FIB-SEM) and remote sensing data, supplemented by synthetic LSFM images. The latter is obtained by simulating the imaging process on virtual samples.

eess.IV↗

arXiv2024

Stochastic Geometry Models for Texture Synthesis of Machined Metallic Surfaces: Sandblasting and Milling

Training defect detection algorithms for visual surface inspection systems requires a large and representative set of training data. Often there is not enough real data available which additionally cannot cover the variety of possible defects. Synthetic data generated by a synthetic visual surface inspection environment can overcome this problem. Therefore, a digital twin of the object is needed, whose micro-scale surface topography is modeled by texture synthesis models. We develop stochastic texture models for sandblasted and milled surfaces based on topography measurements of such surfaces. As the surface patterns differ significantly, we use separate modeling approaches for the two cases. Sandblasted surfaces are modeled by a combination of data-based texture synthesis methods that rely entirely on the measurements. In contrast, the model for milled surfaces is procedural and includes all process-related parameters known from the machine settings.

cs.CE↗