Task-based Augmented Contour Trees with Fibonacci Heaps

This paper presents a new algorithm for the fast, shared memory, multi-core computation of augmented contour trees on triangulations. In contrast to most existing parallel algorithms our technique computes augmented trees, enabling the full extent of contour tree based applications including data segmentation. Our approach completely revisits the traditional, sequential contour tree algorithm to re-formulate all the steps of the computation as a set of independent local tasks. This includes a new computation procedure based on Fibonacci heaps for the join and split trees, two intermediate data structures used to compute the contour tree, whose constructions are efficiently carried out concurrently thanks to the dynamic scheduling of task parallelism. We also introduce a new parallel algorithm for the combination of these two trees into the output global contour tree. Overall, this results in superior time performance in practice, both in sequential and in parallel thanks to the OpenMP task runtime. We report performance numbers that compare our approach to reference sequential and multi-threaded implementations for the computation of augmented merge and contour trees. These experiments demonstrate the run-time efficiency of our approach and its scalability on common workstations. We demonstrate the utility of our approach in data segmentation applications

Avoiding the Global Sort: A Faster Contour Tree Algorithm

We revisit the classical problem of computing the \emph{contour tree} of a scalar field $f:\mathbb{M} \to \mathbb{R}$, where $\mathbb{M}$ is a triangulated simplicial mesh in $\mathbb{R}^d$. The contour tree is a fundamental topological structure that tracks the evolution of level sets of $f$ and has numerous applications in data analysis and visualization. All existing algorithms begin with a global sort of at least all critical values of $f$, which can require (roughly) $\Omega(n\log n)$ time. Existing lower bounds show that there are pathological instances where this sort is required. We present the first algorithm whose time complexity depends on the contour tree structure, and avoids the global sort for non-pathological inputs. If $C$ denotes the set of critical points in $\mathbb{M}$, the running time is roughly $O(\sum_{v \in C} \log \ell_v)$, where $\ell_v$ is the depth of $v$ in the contour tree. This matches all existing upper bounds, but is a significant improvement when the contour tree is short and fat. Specifically, our approach ensures that any comparison made is between nodes in the same descending path in the contour tree, allowing us to argue strong optimality properties of our algorithm. Our algorithm requires several novel ideas: partitioning $\mathbb{M}$ in well-behaved portions, a local growing procedure to iteratively build contour trees, and the use of heavy path decompositions for the time complexity analysis

Towards Distributed Task-based Visualization and Data Analysis

To support scientific work with large and complex data the field of scientific visualization emerged in computer science and produces images through computational analysis of the data. Frameworks for combination of different analysis and visualization modules allow the user to create flexible pipelines for this purpose and set the standard for interactive scientific visualization used by domain scientists. Existing frameworks employ a thread-parallel message-passing approach to parallel and distributed scalability, leaving the field of scientific visualization in high performance computing to specialized ad-hoc implementations. The task-parallel programming paradigm proves promising to improve scalability and portability in high performance computing implementations and thus, this thesis aims towards the creation of a framework for distributed, task-based visualization modules and pipelines. The major contribution of the thesis is the establishment of modules for Merge Tree construction and (based on the former) topological simplification. Such modules already form a necessary first step for most visualization pipelines and can be expected to increase in importance for larger and more complex data produced and/or analysed by high performance computing. To create a task-parallel, distributed Merge Tree construction module the construction process has to be completely revised. We derive a novel property of Merge Tree saddles and introduce a novel task-parallel, distributed Merge Tree construction method that has both good performance and scalability. This forms the basis for a module for topological simplification which we extend by introducing novel alternative simplification parameters that aim to reduce the importance of prior domain knowledge to increase flexibility in typical high performance computing scenarios. Both modules lay the groundwork for continuative analysis and visualization steps and form a fundamental step towards an extensive task-parallel visualization pipeline framework for high performance computing.Wissenschaftliche Visualisierung ist eine Disziplin der Informatik, die durch computergestützte Analyse Bilder aus Datensätzen erzeugt, um das wissenschaftliche Arbeiten mit großen und komplexen Daten zu unterstützen. Softwaresysteme, die dem Anwender die Kombination verschiedener Analyse- und Visualisierungsmodule zu einer flexiblen Pipeline erlauben, stellen den Standard für interaktive wissenschaftliche Visualisierung. Die hierfür bereits existierenden Systeme setzen auf Thread-Parallelisierung mit expliziter Kommunikation, sodass das Feld der wissenschaftlichen Visualisierung auf Hochleistungsrechnern meist spezialisierten Direktlösungen überlassen wird. An dieser Stelle scheint Task-Parallelisierung vielversprechend, um Skalierbarkeit und Übertragbarkeit von Lösungen für Hochleistungsrechner zu verbessern. Daher zielt die vorliegende Arbeit auf die Umsetzung eines Softwaresystems für verteilte und task-parallele Visualisierungsmodule und -pipelines ab. Der zentrale Beitrag den die vorliegende Arbeit leistet ist die Einführung zweier Module für Merge Tree Konstruktion und topologische Datenbereinigung. Solche Module stellen bereits einen notwendigen ersten Schritt für die meisten Visualisierungspipelines dar und werden für größere und komplexere Datensätze, die im Hochleistungsrechnen erzeugt beziehungsweise analysiert werden, erwartungsgemäß noch wichtiger. Um eine Task-parallele, verteilbare Konstruktionsmethode für Merge Trees zu entwickeln musste der etablierte Algorithmus grundlegend überarbeitet werden. In dieser Arbeit leiten wir eine neue Eigenschaft für Merge Tree Knoten her und entwickeln einen neuartigen Konstruktionsalgorithmus, der gute Performance und Skalierbarkeit aufweist. Darauf aufbauend entwickeln wir ein Modul für topologische Datenbereinigung, welche wir durch neue, alternative Bereinigungsparameter erweitern, um die Flexibilität im Einstaz auf Hochleistungsrechnern zu erhöhen. Beide Module ermöglichen weiterführende Analyse und Visualisierung und setzen einen Grundstein für die Entwicklung eines umfassenden Task-parallelen Softwaresystems für Visualisierungspipelines auf Hochleistungsrechnern

In pursuit of linear complexity in discrete and computational geometry

Many computational problems arise naturally from geometric data. In this thesis, we consider three such problems: (i) distance optimization problems over point sets, (ii) computing contour trees over simplicial meshes, and (iii) bounding the expected complexity of weighted Voronoi diagrams. While these topics are broad, here the focus is on identifying structure which implies linear (or near linear) algorithmic and descriptive complexity. The first topic we consider is in geometric optimization. More specifically, we define a large class of distance problems, for which we provide linear time exact or approximate solutions. Roughly speaking, the class of problems facilitate either clustering together close points (i.e. netting) or throwing out outliers (i.e pruning), allowing for successively smaller summaries of the relevant information in the input. A surprising number of classical geometric optimization problems are unified under this framework, including finding the optimal k-center clustering, the kth ranked distance, the kth heaviest edge of the MST, the minimum radius ball enclosing k points, and many others. In several cases we get the first known linear time approximation algorithm for a given problem, where our approximation ratio matches that of previous work. The second topic we investigate is contour trees, a fundamental structure in computational topology. Contour trees give a compact summary of the evolution of level sets on a mesh, and are typically used on massive data sets. Previous algorithms for computing contour trees took Θ(n log n) time and were worst-case optimal. Here we provide an algorithm whose running time lies between Θ(nα(n)) and Θ(n log n), and varies depending on the shape of the tree, where α(n) is the inverse Ackermann function. In particular, this is the first algorithm with O(nα(n)) running time on instances with balanced contour trees. Our algorithmic results are complemented by lower bounds indicating that, up to a factor of α(n), on all instance types our algorithm performs optimally. For the final topic, we consider the descriptive complexity of weighted Voronoi diagrams. Such diagrams have quadratic (or higher) worst-case complexity, however, as was the case for contour trees, here we push beyond worst-case analysis. A new diagram, called the candidate diagram, is introduced, which allows us to bound the complexity of weighted Voronoi diagrams arising from a particular probabilistic input model. Specifically, we assume weights are randomly permuted among fixed Voronoi sites, an assumption which is weaker than the more typical sampled locations assumption. Under this assumption, the expected complexity is shown to be near linear

Flexible isosurfaces: Simplifying and displaying scalar topology using the contour tree

The contour tree is an abstraction of a scalar field that encodes the nesting relationships of isosurfaces. We show how to use the contour tree to represent individual contours of a scalar field, how to simplify both the contour tree and the topology of the scalar field, how to compute and store geometric properties for all possible contours in the contour tree, and how to use the simplified contour tree as an interface for exploratory visualization

Advances in Computer Recognition, Image Processing and Communications, Selected Papers from CORES 2021 and IP&C 2021

As almost all human activities have been moved online due to the pandemic, novel robust and efficient approaches and further research have been in higher demand in the field of computer science and telecommunication. Therefore, this (reprint) book contains 13 high-quality papers presenting advancements in theoretical and practical aspects of computer recognition, pattern recognition, image processing and machine learning (shallow and deep), including, in particular, novel implementations of these techniques in the areas of modern telecommunications and cybersecurity