Isosurface Extraction in the Visualization Toolkit Using the Extrema Skeleton Algorithm

Generating isosurfaces is a very useful technique in data visualization for understanding the distribution of scalar data. Often, when the size of the data set is really large, as in the case with data produced by medical imaging applications, engineering simulations or geographic information systems applications, the use of traditional methods like marching cubes makes repeated generation of isosurfaces a very time consuming task. This thesis investigated the use of the Extrema Skeleton algorithm to speed up repeated isosurface generation in the visualization package, Visualization Toolkit (VTK). The objective was to reduce the number of non-isosurface cells visited to generate isosurfaces, and to compare the Extrema Skeleton method with the Marching Cubes method by monitoring parameters like time taken for the isosurfacing process and number of cells visited. The results of this investigation showed that the Extrema Skeleton method was faster for most of the datasets tested. For simple datasets with less than 10% isosurface cells and complex datasets with less than 5% isosurface cells, the Extrema Skeleton method was found to be significantly faster than the Marching Cubes method. The time gained by the Extrema Skeleton method for datasets with greater than 15% isosurface cells was found to be insignificant. Based on the results of this study, implementing the Extrema Skeleton method for the VTK software is a change worth making because typical VTK users deal with datasets for which the Extrema Skeleton method is significantly faster and also with datasets for which it is marginally faster than the Marching Cubes method

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

Computing contour trees in all dimensions

AbstractWe show that contour trees can be computed in all dimensions by a simple algorithm that merges two trees. Our algorithm extends, simplifies, and improves work of Tarasov and Vyalyi and of van Kreveld et al

From 3D Point Clouds to Pose-Normalised Depth Maps

We consider the problem of generating either pairwise-aligned or pose-normalised depth maps from noisy 3D point clouds in a relatively unrestricted poses. Our system is deployed in a 3D face alignment application and consists of the following four stages: (i) data filtering, (ii) nose tip identification and sub-vertex localisation, (iii) computation of the (relative) face orientation, (iv) generation of either a pose aligned or a pose normalised depth map. We generate an implicit radial basis function (RBF) model of the facial surface and this is employed within all four stages of the process. For example, in stage (ii), construction of novel invariant features is based on sampling this RBF over a set of concentric spheres to give a spherically-sampled RBF (SSR) shape histogram. In stage (iii), a second novel descriptor, called an isoradius contour curvature signal, is defined, which allows rotational alignment to be determined using a simple process of 1D correlation. We test our system on both the University of York (UoY) 3D face dataset and the Face Recognition Grand Challenge (FRGC) 3D data. For the more challenging UoY data, our SSR descriptors significantly outperform three variants of spin images, successfully identifying nose vertices at a rate of 99.6%. Nose localisation performance on the higher quality FRGC data, which has only small pose variations, is 99.9%. Our best system successfully normalises the pose of 3D faces at rates of 99.1% (UoY data) and 99.6% (FRGC data)

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

09251 Abstracts Collection -- Scientific Visualization

From 06-14-2009 to 06-19-2009, the Dagstuhl Seminar 09251 ``Scientific Visualization \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, over 50 international participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general

Interactive Visualization for Singular Fibers of Functions f : R3 → R2

Scalar topology in the form of Morse theory has provided computational tools that analyze and visualize data from scientific and engineering tasks. Contracting isocontours to single points encapsulates variations in isocontour connectivity in the Reeb graph. For multivariate data, isocontours generalize to fibers—inverse images of points in the range, and this area is therefore known as fiber topology. However, fiber topology is less fully developed than Morse theory, and current efforts rely on manual visualizations. This paper presents how to accelerate and semi-automate this task through an interface for visualizing fiber singularities of multivariate functions R3 → R2. This interface exploits existing conventions of fiber topology, but also introduces a 3D view based on the extension of Reeb graphs to Reeb spaces. Using the Joint Contour Net, a quantized approximation of the Reeb space, this accelerates topological visualization and permits online perturbation to reduce or remove degeneracies in functions under study. Validation of the interface is performed by assessing whether the interface supports the mathematical workflow both of experts and of less experienced mathematicians

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