arXiv subjects

Christoph Garth

Publications and source records attributed to Christoph Garth.

At least 19 recordsLinked to original sources

arXiv2026

Evaluating and Improving Weak Scalability Analysis of Visualization Algorithms

Research on visualizing large-scale datasets traditionally relies on empirical evaluation of scalability, determining the effectiveness of specific computation methods, algorithmic strategies, or implementations. Weak scalability, which assesses the algorithm's performance as problem size and computing resources increase, is a valuable indicator for a method's applicability at scale. However, sufficiently large data sets with increasing size are needed for weak scalability studies. To this end, it is customary to use simple scaling techniques to increase problem size by generating larger input data sets from a base data set. Nevertheless, many visualization algorithms' workload depends on factors beyond input size, such as input data complexity or output size, leading to inaccuracies in the attributed weak scalability. In this work, we highlight different common data scaling methods on multiple algorithms and data sets, recognizing that the suitability of scaling approaches varies across algorithms and data sets. We present a method that effectively mitigates the observed inconsistencies in workload increases for the different scaling methods in a shared-memory setting. With this work, we aim to further the discussion on how to evaluate and report scalable visualization research.

cs.DC↗

arXiv2025

Region-Aware Wasserstein Distances of Persistence Diagrams and Merge Trees

This paper presents a generalization of the Wasserstein distance for both 0th persistence diagrams and merge trees [21], [68] that takes advantage of the regions of their topological features in the input domain. Specifically, we redefine the comparison of topological features as a distance between the values of their extrema-aligned regions. It results in a more discriminative metric than the classical Wasserstein distance and generalizes it through an input parameter adjusting the impact of the region properties in the distance. We present two strategies to control both computation time and memory storage of our method by respectively enabling the use of subsets of the regions in the computation, and by compressing the regions' properties to obtain low-memory representations. Extensive experiments on openly available ensemble data demonstrate the efficiency of our method, with running times on the orders of minutes on average. We show the utility of our contributions with two applications. First, we use the assignments between topological features provided by our method to track their evolution in time-varying ensembles and propose the temporal persistence curves to facilitate the understanding of how these features appear, disappear and change over time. Second, our method allows to compute a distance matrix of an ensemble that can be used for dimensionality reduction purposes and visually represent in 2D all its members, we show that such distance matrices also allow to detect key phases in the ensemble. Finally, we provide a C++ implementation that can be used to reproduce our results.

cs.GR↗

arXiv2025

Categorizing Merge Tree Edit Distances by Stability using Minimal Vertex Perturbation

This paper introduces a novel stability measure for edit distances between merge trees of piecewise linear scalar fields. We apply the new measure to various metrics introduced recently in the field of scalar field comparison in scientific visualization. While previous stability measures are unable to capture the fine-grained hierarchy of the considered distances, we obtain a classification of stability that fits the efficiency of current implementations and quality of practical results. Our results induce several open questions regarding the lacking theoretical analysis of such practical distances.

cs.CG↗

arXiv2025

XAI for Point Cloud Data using Perturbations based on Meaningful Segmentation

We propose a novel segmentation-based explainable artificial intelligence (XAI) method for neural networks working on point cloud classification. As one building block of this method, we propose a novel point-shifting mechanism to introduce perturbations in point cloud data. Recently, AI has seen an exponential growth. Hence, it is important to understand the decision-making process of AI algorithms when they are applied in critical areas. Our work focuses on explaining AI algorithms that classify point cloud data. An important aspect of the methods used for explaining AI algorithms is their ability to produce explanations that are easy for humans to understand. This allows them to analyze the AI algorithms better and make appropriate decisions based on that analysis. Therefore, in this work, we intend to generate meaningful explanations that can be easily interpreted by humans. The point cloud data we consider represents 3D objects such as cars, guitars, and laptops. We make use of point cloud segmentation models to generate explanations for the working of classification models. The segments are used to introduce perturbations into the input point cloud data and generate saliency maps. The perturbations are introduced using the novel point-shifting mechanism proposed in this work which ensures that the shifted points no longer influence the output of the classification algorithm. In contrast to previous methods, the segments used by our method are meaningful, i.e. humans can easily interpret the meaning of the segments. Thus, the benefit of our method over other methods is its ability to produce more meaningful saliency maps. We compare our method with the use of classical clustering algorithms to generate explanations. We also analyze the saliency maps generated for example inputs using our method to demonstrate the usefulness of the method in generating meaningful explanations.

cs.CV↗

arXiv2025

Sequential PatchCore: Anomaly Detection for Surface Inspection using Synthetic Impurities

The appearance of surface impurities (e.g., water stains, fingerprints, stickers) is an often-mentioned issue that causes degradation of automated visual inspection systems. At the same time, synthetic data generation techniques for visual surface inspection have focused primarily on generating perfect examples and defects, disregarding impurities. This study highlights the importance of considering impurities when generating synthetic data. We introduce a procedural method to include photorealistic water stains in synthetic data. The synthetic datasets are generated to correspond to real datasets and are further used to train an anomaly detection model and investigate the influence of water stains. The high-resolution images used for surface inspection lead to memory bottlenecks during anomaly detection training. To address this, we introduce Sequential PatchCore - a method to build coresets sequentially and make training on large images using consumer-grade hardware tractable. This allows us to perform transfer learning using coresets pre-trained on different dataset versions. Our results show the benefits of using synthetic data for pre-training an explicit coreset anomaly model and the extended performance benefits of finetuning the coreset using real data. We observed how the impurities and labelling ambiguity lower the model performance and have additionally reported the defect-wise recall to provide an industrially relevant perspective on model performance.

cs.CV↗

arXiv2025

Accelerating Computation of Stable Merge Tree Edit Distances using Parameterized Heuristics

In this paper, we present a novel heuristic algorithm for the stable but NP-complete deformation-based edit distance on merge trees. Our key contribution is the introduction of a user-controlled look-ahead parameter that allows to trade off accuracy and computational cost. We achieve a fixed parameter tractable running time that is polynomial in the size of the input but exponential in the look-ahead value. This extension unlocks the potential of the deformation-based edit distance in handling saddle swaps, while maintaining feasible computation times. Experimental results demonstrate the computational efficiency and effectiveness of this approach in handling specific perturbations.

cs.CG↗

arXiv2024

Distributed Path Compression for Piecewise Linear Morse-Smale Segmentations and Connected Components

This paper describes the adaptation of a well-scaling parallel algorithm for computing Morse-Smale segmentations based on path compression to a distributed computational setting. Additionally, we extend the algorithm to efficiently compute connected components in distributed structured and unstructured grids, based either on the connectivity of the underlying mesh or a feature mask. Our implementation is seamlessly integrated with the distributed extension of the Topology ToolKit (TTK), ensuring robust performance and scalability. To demonstrate the practicality and efficiency of our algorithms, we conducted a series of scaling experiments on large-scale datasets, with sizes of up to 4096^3 vertices on up to 64 nodes and 768 cores.

cs.DC↗

arXiv2024

DaVE -- A Curated Database of Visualization Examples

Visualization, from simple line plots to complex high-dimensional visual analysis systems, has established itself throughout numerous domains to explore, analyze, and evaluate data. Applying such visualizations in the context of simulation science where High-Performance Computing (HPC) produces ever-growing amounts of data that is more complex, potentially multidimensional, and multimodal, takes up resources and a high level of technological experience often not available to domain experts. In this work, we present DaVE -- a curated database of visualization examples, which aims to provide state-of-the-art and advanced visualization methods that arise in the context of HPC applications. Based on domain- or data-specific descriptors entered by the user, DaVE provides a list of appropriate visualization techniques, each accompanied by descriptions, examples, references, and resources. Sample code, adaptable container templates, and recipes for easy integration in HPC applications can be downloaded for easy access to high-fidelity visualizations. While the database is currently filled with a limited number of entries based on a broad evaluation of needs and challenges of current HPC users, DaVE is designed to be easily extended by experts from both the visualization and HPC communities.

cs.DC↗

arXiv2024

TTK is Getting MPI-Ready

This system paper documents the technical foundations for the extension of the Topology ToolKit (TTK) to distributed-memory parallelism with the Message Passing Interface (MPI). While several recent papers introduced topology-based approaches for distributed-memory environments, these were reporting experiments obtained with tailored, mono-algorithm implementations. In contrast, we describe in this paper a versatile approach (supporting both triangulated domains and regular grids) for the support of topological analysis pipelines, i.e. a sequence of topological algorithms interacting together. While developing this extension, we faced several algorithmic and software engineering challenges, which we document in this paper. We describe an MPI extension of TTK's data structure for triangulation representation and traversal, a central component to the global performance and generality of TTK's topological implementations. We also introduce an intermediate interface between TTK and MPI, both at the global pipeline level, and at the fine-grain algorithmic level. We provide a taxonomy for the distributed-memory topological algorithms supported by TTK, depending on their communication needs and provide examples of hybrid MPI+thread parallelizations. Performance analyses show that parallel efficiencies range from 20% to 80% (depending on the algorithms), and that the MPI-specific preconditioning introduced by our framework induces a negligible computation time overhead. We illustrate the new distributed-memory capabilities of TTK with an example of advanced analysis pipeline, combining multiple algorithms, run on the largest publicly available dataset we have found (120 billion vertices) on a cluster with 64 nodes (for a total of 1536 cores). Finally, we provide a roadmap for the completion of TTK's MPI extension, along with generic recommendations for each algorithm communication category.

cs.DC↗

arXiv2023

Probabilistic Gradient-Based Extrema Tracking

Feature tracking is a common task in visualization applications, where methods based on topological data analysis (TDA) have successfully been applied in the past for feature definition as well as tracking. In this work, we focus on tracking extrema of temporal scalar fields. A family of TDA approaches address this task by establishing one-to-one correspondences between extrema based on discrete gradient vector fields. More specifically, two extrema of subsequent time steps are matched if they fall into their respective ascending and descending manifolds. However, due to this one-to-one assignment, these approaches are prone to fail where, e.g., extrema are located in regions with low gradient magnitude, or are located close to boundaries of the manifolds. Therefore, we propose a probabilistic matching that captures a larger set of possible correspondences via neighborhood sampling, or by computing the overlap of the manifolds. We illustrate the usefulness of the approach with two application cases.

cs.GR↗

arXiv2023

Taming Horizontal Instability in Merge Trees: On the Computation of a Comprehensive Deformation-based Edit Distance

Comparative analysis of scalar fields in scientific visualization often involves distance functions on topological abstractions. This paper focuses on the merge tree abstraction (representing the nesting of sub- or superlevel sets) and proposes the application of the unconstrained deformation-based edit distance. Previous approaches on merge trees often suffer from instability: small perturbations in the data can lead to large distances of the abstractions. While some existing methods can handle so-called vertical instability, the unconstrained deformation-based edit distance addresses both vertical and horizontal instabilities, also called saddle swaps. We establish the computational complexity as NP-complete, and provide an integer linear program formulation for computation. Experimental results on the TOSCA shape matching ensemble provide evidence for the stability of the proposed distance. We thereby showcase the potential of handling saddle swaps for comparison of scalar fields through merge trees.

cs.CG↗

arXiv2023

Merge Tree Geodesics and Barycenters with Path Mappings

Comparative visualization of scalar fields is often facilitated using similarity measures such as edit distances. In this paper, we describe a novel approach for similarity analysis of scalar fields that combines two recently introduced techniques: Wasserstein geodesics/barycenters as well as path mappings, a branch decomposition-independent edit distance. Effectively, we are able to leverage the reduced susceptibility of path mappings to small perturbations in the data when compared with the original Wasserstein distance. Our approach therefore exhibits superior performance and quality in typical tasks such as ensemble summarization, ensemble clustering, and temporal reduction of time series, while retaining practically feasible runtimes. Beyond studying theoretical properties of our approach and discussing implementation aspects, we describe a number of case studies that provide empirical insights into its utility for comparative visualization, and demonstrate the advantages of our method in both synthetic and real-world scenarios. We supply a C++ implementation that can be used to reproduce our results.

cs.GR↗

arXiv2023

Exploration of Differentiability in a Proton Computed Tomography Simulation Framework

Objective. Algorithmic differentiation (AD) can be a useful technique to numerically optimize design and algorithmic parameters by, and quantify uncertainties in, computer simulations. However, the effectiveness of AD depends on how "well-linearizable" the software is. In this study, we assess how promising derivative information of a typical proton computed tomography (pCT) scan computer simulation is for the aforementioned applications. Approach. This study is mainly based on numerical experiments, in which we repeatedly evaluate three representative computational steps with perturbed input values. We support our observations with a review of the algorithmic steps and arithmetic operations performed by the software, using debugging techniques. Main results. The model-based iterative reconstruction (MBIR) subprocedure (at the end of the software pipeline) and the Monte Carlo (MC) simulation (at the beginning) were piecewise differentiable. Jumps in the MBIR function arose from the discrete computation of the set of voxels intersected by a proton path. Jumps in the MC function likely arose from changes in the control flow that affect the amount of consumed random numbers. The tracking algorithm solves an inherently non-differentiable problem. Significance. The MC and MBIR codes are ready for the integration of AD, and further research on surrogate models for the tracking subprocedure is necessary.

physics.med-ph↗

arXiv2023

Parallel Computation of Piecewise Linear Morse-Smale Segmentations

This paper presents a well-scaling parallel algorithm for the computation of Morse-Smale (MS) segmentations, including the region separators and region boundaries. The segmentation of the domain into ascending and descending manifolds, solely defined on the vertices, improves the computational time using path compression and fully segments the border region. Region boundaries and region separators are generated using a multi-label marching tetrahedra algorithm. This enables a fast and simple solution to find optimal parameter settings in preliminary exploration steps by generating an MS complex preview. It also poses a rapid option to generate a fast visual representation of the region geometries for immediate utilization. Two experiments demonstrate the performance of our approach with speedups of over an order of magnitude in comparison to two publicly available implementations. The example section shows the similarity to the MS complex, the useability of the approach, and the benefits of this method with respect to the presented datasets. We provide our implementation with the paper.

cs.GR↗

arXiv2022

A Deformation-based Edit Distance for Merge Trees

In scientific visualization, scalar fields are often compared through edit distances between their merge trees. Typical tasks include ensemble analysis, feature tracking and symmetry or periodicity detection. Tree edit distances represent how one tree can be transformed into another through a sequence of simple edit operations: relabeling, insertion and deletion of nodes. In this paper, we present a new set of edit operations working directly on the merge tree as an geometrical or topological object: the represented operations are deformation retractions and inverse transformations on merge trees, which stands in contrast to other methods working on branch decomposition trees. We present a quartic time algorithm for the new edit distance, which is branch decomposition-independent and a metric on the set of all merge trees.

cs.CG↗

arXiv2022

Branch Decomposition-Independent Edit Distances for Merge Trees

Edit distances between merge trees of scalar fields have many applications in scientific visualization, such as ensemble analysis, feature tracking or symmetry detection. In this paper, we propose branch mappings, a novel approach to the construction of edit mappings for merge trees. Classic edit mappings match nodes or edges of two trees onto each other, and therefore have to either rely on branch decompositions of both trees or have to use auxiliary node properties to determine a matching. In contrast, branch mappings employ branch properties instead of node similarity information, and are independent of predetermined branch decompositions. Especially for topological features, which are typically based on branch properties, this allows a more intuitive distance measure which is also less susceptible to instabilities from small-scale perturbations. We describe a quartic runtime algorithm for computing optimal branch mappings, which is faster than the only other branch decomposition-independent method in the literature by more than a linear factor. Furthermore, we compare the results of our method on synthetic and real-world examples to demonstrate its practicality and utility.

cs.CG↗

arXiv2022

PREVIS -- A Combined Machine Learning and Visual Interpolation Approach for Interactive Reverse Engineering in Assembly Quality Control

We present PREVIS, a visual analytics tool, enhancing machine learning performance analysis in engineering applications. The presented toolchain allows for a direct comparison of regression models. In addition, we provide a methodology to visualize the impact of regression errors on the underlying field of interest in the original domain, the part geometry, via exploiting standard interpolation methods. Further, we allow a real-time preview of user-driven parameter changes in the displacement field via visual interpolation. This allows for fast and accountable online change management. We demonstrate the effectiveness with an ex-ante optimization of an automotive engine hood.

cs.HC↗

arXiv2022

A Guide to Particle Advection Performance

The performance of particle advection-based flow visualization techniques is complex, since computational work can vary based on many factors, including number of particles, duration, and mesh type. Further, while many approaches have been introduced to optimize performance, the efficacy of a given approach can be similarly complex. In this work, we seek to establish a guide for particle advection performance by conducting a comprehensive survey of the area. We begin by identifying the building blocks for particle advection and establishing a simple cost model incorporating these building blocks. We then survey existing optimizations for particle advection, using two high-level categories: algorithmic optimizations and hardware efficiency. The sub-categories of algorithmic optimizations include solvers, cell locators, I/O efficiency, and precomputation, while the sub-categories of hardware efficiency all involve parallelism: shared-memory, distributed-memory, and hybrid. Finally, we conclude the survey by identifying current gaps in particle advection performance, and in particular on achieving a workflow for predicting performance under various optimizations.

cs.DC↗