Ranking Viscous Finger Simulations to an Acquired Ground Truth with Topology-aware Matchings

This application paper presents a novel framework based on topological data analysis for the automatic evaluation and ranking of viscous finger simulation runs in an ensemble with respect to a reference acquisition. Individual fingers in a given time-step are associated with critical point pairs in the distance field to the injection point, forming persistence diagrams. Different metrics, based on optimal transport, for comparing time-varying persistence diagrams in this specific applicative case are introduced. We evaluate the relevance of the rankings obtained with these metrics, both qualitatively thanks to a lightweight web visual interface, and quantitatively by studying the deviation from a reference ranking suggested by experts. Extensive experiments show the quantitative superiority of our approach compared to traditional alternatives. Our web interface allows experts to conveniently explore the produced rankings. We show a complete viscous fingering case study demonstrating the utility of our approach in the context of porous media fluid flow, where our framework can be used to automatically discard physically-irrelevant simulation runs from the ensemble and rank the most plausible ones. We document an in-situ implementation to lighten I/O and performance constraints arising in the context of parametric studies.

Lifted Wasserstein Matcher for Fast and Robust Topology Tracking

This paper presents a robust and efficient method for tracking topological features in time-varying scalar data. Structures are tracked based on the optimal matching between persistence diagrams with respect to the Wasserstein metric. This fundamentally relies on solving the assignment problem, a special case of optimal transport, for all consecutive timesteps. Our approach relies on two main contributions. First, we revisit the seminal assignment algorithm by Kuhn and Munkres which we specifically adapt to the problem of matching persistence diagrams in an efficient way. Second, we propose an extension of the Wasserstein metric that significantly improves the geometrical stability of the matching of domain-embedded persistence pairs. We show that this geometrical lifting has the additional positive side-effect of improving the assignment matrix sparsity and therefore computing time. The global framework implements a coarse-grained parallelism by computing persistence diagrams and finding optimal matchings in parallel for every couple of consecutive timesteps. Critical trajectories are constructed by associating successively matched persistence pairs over time. Merging and splitting events are detected with a geometrical threshold in a post-processing stage. Extensive experiments on real-life datasets show that our matching approach is an order of magnitude faster than the seminal Munkres algorithm. Moreover, compared to a modern approximation method, our method provides competitive runtimes while yielding exact results. We demonstrate the utility of our global framework by extracting critical point trajectories from various simulated time-varying datasets and compare it to the existing methods based on associated overlaps of volumes. Robustness to noise and temporal resolution downsampling is empirically demonstrated.

Topological Data Analysis Made Easy with the Topology ToolKit

This tutorial presents topological methods for the analysis and visualization of scientific data from a user's perspective, with the Topology ToolKit (TTK), a recently released open-source library for topological data analysis. Topological methods have gained considerably in popularity and maturity over the last twenty years and success stories of established methods have been documented in a wide range of applications (combustion, chemistry, astrophysics, material sciences, etc.) with both acquired and simulated data, in both post-hoc and in-situ contexts. While reference textbooks have been published on the topic, no tutorial at IEEE VIS has covered this area in recent years, and never at a software level and from a user's point-of-view. This tutorial fills this gap by providing a beginner's introduction to topological methods for practitioners, researchers, students, and lecturers. In particular, instead of focusing on theoretical aspects and algorithmic details, this tutorial focuses on how topological methods can be useful in practice for concrete data analysis tasks such as segmentation, feature extraction or tracking. The tutorial describes in detail how to achieve these tasks with TTK. First, after an introduction to topological methods and their application in data analysis, a brief overview of TTK's main entry point for end users, namely ParaView, will be presented. Second, an overview of TTK's main features will be given. A running example will be described in detail, showcasing how to access TTK's features via ParaView, Python, VTK/C++, and C++. Third, hands-on sessions will concretely show how to use TTK in ParaView for multiple, representative data analysis tasks. Fourth, the usage of TTK will be presented for developers, in particular by describing several examples of visualization and data analysis projects that were built on top of TTK. Finally, some feedback regarding the usage of TTK as a teaching platform for topological analysis will be given. Presenters of this tutorial include experts in topological methods, core authors of TTK as well as active users, coming from academia, labs, or industry. A large part of the tutorial will be dedicated to hands-on exercises and a rich material package (including TTK pre-installs in virtual machines, code, data, demos, video tutorials, etc.) will be provided to the participants. This tutorial mostly targets students, practitioners and researchers who are not experts in topological methods but who are interested in using them in their daily tasks. We also target researchers already familiar to topological methods and who are interested in using or contributing to TTK.

Topologically Controlled Lossy Compression

This paper presents a new algorithm for the lossy compression of scalar data defined on 2D or 3D regular grids, with topological control. Certain techniques allow users to control the pointwise error induced by the compression. However, in many scenarios it is desirable to control in a similar way the preservation of higher-level notions, such as topological features , in order to provide guarantees on the outcome of post-hoc data analyses. This paper presents the first compression technique for scalar data which supports a strictly controlled loss of topological features. It provides users with specific guarantees both on the preservation of the important features and on the size of the smaller features destroyed during compression. In particular, we present a simple compression strategy based on a topologically adaptive quantization of the range. Our algorithm provides strong guarantees on the bottleneck distance between persistence diagrams of the input and decompressed data, specifically those associated with extrema. A simple extension of our strategy additionally enables a control on the pointwise error. We also show how to combine our approach with state-of-the-art compressors, to further improve the geometrical reconstruction. Extensive experiments, for comparable compression rates, demonstrate the superiority of our algorithm in terms of the preservation of topological features. We show the utility of our approach by illustrating the compatibility between the output of post-hoc topological data analysis pipelines, executed on the input and decompressed data, for simulated or acquired data sets. We also provide a lightweight VTK-based C++ implementation of our approach for reproduction purposes.