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

The Topology ToolKit

This system paper presents the Topology ToolKit (TTK), a software platform designed for topological data analysis in scientific visualization. TTK provides a unified, generic, efficient, and robust implementation of key algorithms for the topological analysis of scalar data, including: critical points, integral lines, persistence diagrams, persistence curves, merge trees, contour trees, Morse-Smale complexes, fiber surfaces, continuous scatterplots, Jacobi sets, Reeb spaces, and more. TTK is easily accessible to end users due to a tight integration with ParaView. It is also easily accessible to developers through a variety of bindings (Python, VTK/C++) for fast prototyping or through direct, dependence-free, C++, to ease integration into pre-existing complex systems. While developing TTK, we faced several algorithmic and software engineering challenges, which we document in this paper. In particular, we present an algorithm for the construction of a discrete gradient that complies to the critical points extracted in the piecewise-linear setting. This algorithm guarantees a combinatorial consistency across the topological abstractions supported by TTK, and importantly, a unified implementation of topological data simplification for multi-scale exploration and analysis. We also present a cached triangulation data structure, that supports time efficient and generic traversals, which self-adjusts its memory usage on demand for input simplicial meshes and which implicitly emulates a triangulation for regular grids with no memory overhead. Finally, we describe an original software architecture, which guarantees memory efficient and direct accesses to TTK features, while still allowing for researchers powerful and easy bindings and extensions. TTK is open source (BSD license) and its code, online documentation and video tutorials are available on TTK's website

Doctor of Philosophy

dissertationWith modern computational resources rapidly advancing towards exascale, large-scale simulations useful for understanding natural and man-made phenomena are becoming in- creasingly accessible. As a result, the size and complexity of data representing such phenom- ena are also increasing, making the role of data analysis to propel science even more integral. This dissertation presents research on addressing some of the contemporary challenges in the analysis of vector fields--an important type of scientific data useful for representing a multitude of physical phenomena, such as wind flow and ocean currents. In particular, new theories and computational frameworks to enable consistent feature extraction from vector fields are presented. One of the most fundamental challenges in the analysis of vector fields is that their features are defined with respect to reference frames. Unfortunately, there is no single ""correct"" reference frame for analysis, and an unsuitable frame may cause features of interest to remain undetected, thus creating serious physical consequences. This work develops new reference frames that enable extraction of localized features that other techniques and frames fail to detect. As a result, these reference frames objectify the notion of ""correctness"" of features for certain goals by revealing the phenomena of importance from the underlying data. An important consequence of using these local frames is that the analysis of unsteady (time-varying) vector fields can be reduced to the analysis of sequences of steady (time- independent) vector fields, which can be performed using simpler and scalable techniques that allow better data management by accessing the data on a per-time-step basis. Nevertheless, the state-of-the-art analysis of steady vector fields is not robust, as most techniques are numerical in nature. The residing numerical errors can violate consistency with the underlying theory by breaching important fundamental laws, which may lead to serious physical consequences. This dissertation considers consistency as the most fundamental characteristic of computational analysis that must always be preserved, and presents a new discrete theory that uses combinatorial representations and algorithms to provide consistency guarantees during vector field analysis along with the uncertainty visualization of unavoidable discretization errors. Together, the two main contributions of this dissertation address two important concerns regarding feature extraction from scientific data: correctness and precision. The work presented here also opens new avenues for further research by exploring more-general reference frames and more-sophisticated domain discretizations

Multi-touch 3D Exploratory Analysis of Ocean Flow Models

Modern ocean flow simulations are generating increasingly complex, multi-layer 3D ocean flow models. However, most researchers are still using traditional 2D visualizations to visualize these models one slice at a time. Properly designed 3D visualization tools can be highly effective for revealing the complex, dynamic flow patterns and structures present in these models. However, the transition from visualizing ocean flow patterns in 2D to 3D presents many challenges, including occlusion and depth ambiguity. Further complications arise from the interaction methods required to navigate, explore, and interact with these 3D datasets. We present a system that employs a combination of stereoscopic rendering, to best reveal and illustrate 3D structures and patterns, and multi-touch interaction, to allow for natural and efficient navigation and manipulation within the 3D environment. Exploratory visual analysis is facilitated through the use of a highly-interactive toolset which leverages a smart particle system. Multi-touch gestures allow users to quickly position dye emitting tools within the 3D model. Finally, we illustrate the potential applications of our system through examples of real world significance

Master of Science

thesisAnalysis and visualization of flow is an important part of many scientific endeavors. Computation of streamlines is fundamental to many of these analysis and visualization tasks. A streamline is the path a massless particle traces under the instantenous velocities of a given vector field. Flow data are often stored as a sampled vector field over a mesh. We propose a new representation of flow defined by such a vector field. Given a triangulation and a vector field defined over its vertices, we represent flow in the form of its transversal behavior over the edges of the triangulation. A streamline is represented as a set of discrete jumps over these edges. Any information about the actual path taken through the interior of the triangles is discarded. We eliminate the necessity to compute actual paths of streamlines through the interior of each triangle while maintaining the aggregate behavior of flow within each of them. We discretize each edge uniformly into a fixed number of bins and use this discretization to form a combinatorial representation of flow in the form of a directed graph whose nodes are the set of all bins and its edges represent the discrete jumps between these bins. This representation is a combinatorial structure that provides robustness and consistency in expressing flow features like the critical points, streamlines, separatrices and closed streamlines which are otherwise hard to compute consistently

SADA: Semantic Adversarial Diagnostic Attacks for Autonomous Applications

One major factor impeding more widespread adoption of deep neural networks (DNNs) is their lack of robustness, which is essential for safety-critical applications such as autonomous driving. This has motivated much recent work on adversarial attacks for DNNs, which mostly focus on pixel-level perturbations void of semantic meaning. In contrast, we present a general framework for adversarial attacks on trained agents, which covers semantic perturbations to the environment of the agent performing the task as well as pixel-level attacks. To do this, we re-frame the adversarial attack problem as learning a distribution of parameters that always fools the agent. In the semantic case, our proposed adversary (denoted as BBGAN) is trained to sample parameters that describe the environment with which the black-box agent interacts, such that the agent performs its dedicated task poorly in this environment. We apply BBGAN on three different tasks, primarily targeting aspects of autonomous navigation: object detection, self-driving, and autonomous UAV racing. On these tasks, BBGAN can generate failure cases that consistently fool a trained agent.Comment: Accepted at AAAI'2