arXiv subjects

Claudia Redenbach

Publications and source records attributed to Claudia Redenbach.

At least 37 records · Page 2Linked to original sources

arXiv2024

An in-silico approach to meniscus tissue regeneration: Modeling, numerical simulation, and experimental analysis

We develop a model the dynamics of human mesenchymal stem cells (hMSCs) and chondrocytes evolving in a nonwoven polyethylene terephtalate (PET) scaffold impregnated with hyaluron and supplied with a differentiation medium. The scaffold and the cells are assumed to be contained in a bioreactor with fluid perfusion. The differentiation of hMSCs into chondrocytes favors the production of extracellular matrix (ECM) and is influenced by fluid stress. The model takes deformations of ECM and PET scaffold into account. The scaffold structure is explicitly included by statistical assessment of the fibre distribution from CT images. The effective macroscopic equations are obtained by appropriate upscaling from dynamics on lower (microscopic and mesoscopic) scales and feature in the motility terms an explicit cell diffusion tensor encoding the assessed anisotropic scaffold structure. Numerical simulations show its influence on the overall cell and tissue dynamics.

q-bio.TO↗

arXiv2024

Riesz networks: scale invariant neural networks in a single forward pass

Scale invariance of an algorithm refers to its ability to treat objects equally independently of their size. For neural networks, scale invariance is typically achieved by data augmentation. However, when presented with a scale far outside the range covered by the training set, neural networks may fail to generalize. Here, we introduce the Riesz network, a novel scale invariant neural network. Instead of standard 2d or 3d convolutions for combining spatial information, the Riesz network is based on the Riesz transform which is a scale equivariant operation. As a consequence, this network naturally generalizes to unseen or even arbitrary scales in a single forward pass. As an application example, we consider detecting and segmenting cracks in tomographic images of concrete. In this context, 'scale' refers to the crack thickness which may vary strongly even within the same sample. To prove its scale invariance, the Riesz network is trained on one fixed crack width. We then validate its performance in segmenting simulated and real tomographic images featuring a wide range of crack widths. An additional experiment is carried out on the MNIST Large Scale data set.

cs.CV↗

arXiv2024

Riesz feature representation: scale equivariant scattering network for classification tasks

Scattering networks yield powerful and robust hierarchical image descriptors which do not require lengthy training and which work well with very few training data. However, they rely on sampling the scale dimension. Hence, they become sensitive to scale variations and are unable to generalize to unseen scales. In this work, we define an alternative feature representation based on the Riesz transform. We detail and analyze the mathematical foundations behind this representation. In particular, it inherits scale equivariance from the Riesz transform and completely avoids sampling of the scale dimension. Additionally, the number of features in the representation is reduced by a factor four compared to scattering networks. Nevertheless, our representation performs comparably well for texture classification with an interesting addition: scale equivariance. Our method yields superior performance when dealing with scales outside of those covered by the training dataset. The usefulness of the equivariance property is demonstrated on the digit classification task, where accuracy remains stable even for scales four times larger than the one chosen for training. As a second example, we consider classification of textures.

cs.CV↗

arXiv2023

Mathematical morphology on directional data

We define morphological operators and filters for directional images whose pixel values are unit vectors. This requires an ordering relation for unit vectors which is obtained by using depth functions. They provide a centre-outward ordering with respect to a specified centre vector. We apply our operators on synthetic directional images and compare them with classical morphological operators for grey-scale images. As application examples, we enhance the fault region in a compressed glass foam and segment misaligned fibre regions of glass fibre reinforced polymers.

math.ST↗

arXiv2023

MorphFlow: Estimating Motion in In Situ Tests of Concrete

We present a novel algorithm explicitly tailored to estimate motion from time series of 3D images of concrete. Such volumetric images are usually acquired by Computed Tomography and can contain for example in situ tests, or more complex procedures like self-healing. Our algorithm is specifically designed to tackle the challenge of large scale in situ investigations of concrete. That means it cannot only cope with big images, but also with discontinuous displacement fields that often occur in in situ tests of concrete. We show the superior performance of our algorithm, especially regarding plausibility and time efficient processing. Core of the algorithm is a novel multiscale representation based on morphological wavelets. We use two examples for validation: A classical in situ test on refractory concrete and and a three point bending test on normal concrete. We show that for both applications structural changes like crack initiation can be already found at low scales -- a central achievement of our algorithm.

eess.IV↗

arXiv2023

Improved Anisotropic Gaussian Filters

Elongated anisotropic Gaussian filters are used for the orientation estimation of fibers. In cases where computed tomography images are noisy, roughly resolved, and of low contrast, they are the method of choice even if being efficient only in virtual 2D slices. However, minor inaccuracies in the anisotropic Gaussian filters can carry over to the orientation estimation. Therefore, this paper proposes a modified algorithm for 2D anisotropic Gaussian filters and shows that this improves their precision. Applied to synthetic images of fiber bundles, it is more accurate and robust to noise. Finally, the effectiveness of the approach is shown by applying it to real-world images of sheet molding compounds.

eess.IV↗

arXiv2023

Hybrid quantum transfer learning for crack image classification on NISQ hardware

Quantum computers possess the potential to process data using a remarkably reduced number of qubits compared to conventional bits, as per theoretical foundations. However, recent experiments have indicated that the practical feasibility of retrieving an image from its quantum encoded version is currently limited to very small image sizes. Despite this constraint, variational quantum machine learning algorithms can still be employed in the current noisy intermediate scale quantum (NISQ) era. An example is a hybrid quantum machine learning approach for edge detection. In our study, we present an application of quantum transfer learning for detecting cracks in gray value images. We compare the performance and training time of PennyLane's standard qubits with IBM's qasm\_simulator and real backends, offering insights into their execution efficiency.

quant-ph↗

arXiv2023

An Analytical Representation of the 2d Generalized Balanced Power Diagram

Tessellations are an important tool to model the microstructure of cellular and polycrystalline materials. Classical tessellation models include the Voronoi diagram and Laguerre tessellation whose cells are polyhedra. Due to the convexity of their cells, those models may be too restrictive to describe data that includes possibly anisotropic grains with curved boundaries. Several generalizations exist. The cells of the generalized balanced power diagram are induced by elliptic distances leading to more diverse structures. So far, methods for computing the generalized balanced power diagram are restricted to discretized versions in the form of label images. In this work, we derive an analytic representation of the vertices and edges of the generalized balanced power diagram in 2d. Based on that, we propose a novel algorithm to compute the whole diagram.

cs.CG↗

arXiv2022

Quantiles and depth for directional data from elliptically symmetric distributions

We present canonical quantiles and depths for directional data following a distribution which is elliptically symmetric about a direction $μ$ on the sphere $\mathcal{S}^{d-1}$. Our approach extends the concept of Ley et al. [1], which provides valuable geometric properties of the depth contours (such as convexity and rotational equivariance) and a Bahadur-type representation of the quantiles. Their concept is canonical for rotationally symmetric depth contours. However, it also produces rotationally symmetric depth contours when the underlying distribution is not rotationally symmetric. We solve this lack of flexibility for distributions with elliptical depth contours. The basic idea is to deform the elliptic contours by a diffeomorphic mapping to rotationally symmetric contours, thus reverting to the canonical case in Ley et al. [1]. A Monte Carlo simulation study confirms our results. We use our method to evaluate the ellipticity of depth contours and for trimming of directional data. The analysis of fibre directions in fibre-reinforced concrete underlines the practical relevance.

math.ST↗

arXiv2022

Crack Modeling via Minimum-Weight Surfaces in 3d Voronoi Diagrams

Shortest paths play an important role in mathematical modeling and image processing. Usually, shortest path problems are formulated on planar graphs that consist of vertices and weighted arcs. In this context, one is interested in finding a path of minimum weight from a start vertex to an end vertex. The concept of minimum-weight surfaces extends shortest paths to 3d. The minimum-weight surface problem is formulated on a cellular complex with weighted facets. A cycle on the arcs of the complex serves as input and one is interested in finding a surface of minimum weight bounded by that cycle. In practice, minimum-weight surfaces can be used to segment 3d images. Vice versa, it is possible to use them as a modeling tool for geometric structures such as cracks. In this work, we present an approach for using minimum-weight surfaces in bounded Voronoi diagrams to generate synthetic 3d images of cracks.

cs.GR↗

arXiv2022

Persistent homology based goodness-of-fit tests for spatial tessellations

Motivated by the rapidly increasing relevance of virtual material design in the domain of materials science, it has become essential to assess whether topological properties of stochastic models for a spatial tessellation are in accordance with a given dataset. Recently, tools from topological data analysis such as the persistence diagram have allowed to reach profound insights in a variety of application contexts. In this work, we establish the asymptotic normality of a variety of test statistics derived from a tessellation-adapted refinement of the persistence diagram. Since in applications, it is common to work with tessellation data subject to interactions, we establish our main results for Voronoi and Laguerre tessellations whose generators form a Gibbs point process. We elucidate how these conceptual results can be used to derive goodness of fit tests, and then investigate their power in a simulation study. Finally, we apply our testing methodology to a tessellation describing real foam data.

math.ST↗

arXiv2022

A hybrid quantum image edge detector for the NISQ era

Edges are image locations where the gray value intensity changes suddenly. They are among the most important features to understand and segment an image. Edge detection is a standard task in digital image processing, solved for example using filtering techniques. However, the amount of data to be processed grows rapidly and pushes even supercomputers to their limits. Quantum computing promises exponentially lower memory usage in terms of the number of qubits compared to the number of classical bits. In this paper, we propose a hybrid method for quantum edge detection based on the idea of a quantum artificial neuron. Our method can be practically implemented on quantum computers, especially on those of the current noisy intermediate-scale quantum era. We compare six variants of the method to reduce the number of circuits and thus the time required for the quantum edge detection. Taking advantage of the scalability of our method, we can practically detect edges in images considerably larger than reached before.

quant-ph↗

arXiv2021

Methods for segmenting cracks in 3d images of concrete: A comparison based on semi-synthetic images

Concrete is the standard construction material for buildings, bridges, and roads. As safety plays a central role in the design, monitoring, and maintenance of such constructions, it is important to understand the cracking behavior of concrete. Computed tomography captures the microstructure of building materials and allows to study crack initiation and propagation. Manual segmentation of crack surfaces in large 3d images is not feasible. In this paper, automatic crack segmentation methods for 3d images are reviewed and compared. Classical image processing methods (edge detection filters, template matching, minimal path and region growing algorithms) and learning methods (convolutional neural networks, random forests) are considered and tested on semi-synthetic 3d images. Their performance strongly depends on parameter selection which should be adapted to the grayvalue distribution of the images and the geometric properties of the concrete. In general, the learning methods perform best, in particular for thin cracks and low grayvalue contrast.

cs.CV↗

arXiv2021

Wasserstein Patch Prior for Image Superresolution

In this paper, we introduce a Wasserstein patch prior for superresolution of two- and three-dimensional images. Here, we assume that we have given (additionally to the low resolution observation) a reference image which has a similar patch distribution as the ground truth of the reconstruction. This assumption is e.g. fulfilled when working with texture images or material data. Then, the proposed regularizer penalizes the $W_2$-distance of the patch distribution of the reconstruction to the patch distribution of some reference image at different scales. We demonstrate the performance of the proposed regularizer by two- and three-dimensional numerical examples.

cs.CV↗

arXiv2021

Improved FRQI on superconducting processors and its restrictions in the NISQ era

In image processing, the amount of data to be processed grows rapidly, in particular when imaging methods yield images of more than two dimensions or time series of images. Thus, efficient processing is a challenge, as data sizes may push even supercomputers to their limits. Quantum image processing promises to encode images with logarithmically less qubits than classical pixels in the image. In theory, this is a huge progress, but so far not many experiments have been conducted in practice, in particular on real backends. Often, the precise conversion of classical data to quantum states, the exact implementation, and the interpretation of the measurements in the classical context are challenging. We investigate these practical questions in this paper. In particular, we study the feasibility of the Flexible Representation of Quantum Images (FRQI). Furthermore, we check experimentally what is the limit in the current noisy intermediate-scale quantum era, i.e. up to which image size an image can be encoded, both on simulators and on real backends. Finally, we propose a method for simplifying the circuits needed for the FRQI. With our alteration, the number of gates needed, especially of the error-prone controlled-NOT gates, can be reduced. As a consequence, the size of manageable images increases.

quant-ph↗

arXiv2019

Detecting anomalies in fibre systems using 3-dimensional image data

We consider the problem of detecting anomalies in the directional distribution of fibre materials observed in 3D images. We divide the image into a set of scanning windows and classify them into two clusters: homogeneous material and anomaly. Based on a sample of estimated local fibre directions, for each scanning window we compute several classification attributes, namely the coordinate wise means of local fibre directions, the entropy of the directional distribution, and a combination of them. We also propose a new spatial modification of the Stochastic Approximation Expectation-Maximization (SAEM) algorithm. Besides the clustering we also consider testing the significance of anomalies. To this end, we apply a change point technique for random fields and derive the exact inequalities for tail probabilities of a test statistics. The proposed methodology is first validated on simulated images. Finally, it is applied to a 3D image of a fibre reinforced polymer.

stat.ME↗

arXiv2018

Application of Clustering Methods to Anomaly Detection in Fibrous Media

The paper considers the problem of anomaly detection in 3D images of fibre materials. The spatial Stochastic Expectation Maximisation algorithm and Adaptive Weights Clustering are applied to solve this problem. The initial 3D grey scale image was divided into small cubes subject to clustering. For each cube clustering attributes values were calculated: mean local direction and directional entropy. Clustering is conducted according to the given attributes. The proposed methods are tested on the simulated images and on real fibre materials.

stat.AP↗

arXiv2018

A review on anisotropy analysis of spatial point patterns

A spatial point pattern is called anisotropic if its spatial structure depends on direction. Several methods for anisotropy analysis have been introduced in the literature. In this paper, we give an overview of nonparametric methods for anisotropy analysis of (stationary) point patterns in $\mathbf{R}^2$ and $\mathbf{R}^3$. We discuss methods based on nearest neighbour and second order summary statistics as well as spectral and wavelet analysis. All techniques are illustrated on both a clustered and a regular example. Finally, we discuss methods for testing for isotropy as well as for estimating preferred directions in a point pattern.

stat.ME↗