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

Case study of isosurface extraction algorithm performance

Journal ArticleIsosurface extraction is an important and useful visualization method. Over the past ten years, the field has seen numerous isosurface techniques published, leaving the user in a quandary about which one should be used. Some papers have published complexity analysis of the techniques, yet empirical evidence comparing different methods is lacking. This case study presents a comparative study of several representative isosurface extraction algorithms. It reports and analyzes empirical measurements of execution times and memory behavior for each algorithm. The results show that asymptotically optimal techniques may not be the best choice when implemented on modern computer architectures

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

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

Accelerated isosurface extraction in time-varying fields

Journal ArticleFor large time-varying data sets, memory and disk limitations can lower the performance of visualization applications. Algorithms and data structures must be explicitly designed to handle these data sets in order to achieve more interactive rates. The Temporal Branch-on-Need Octree (T-BON) extends the three-dimensional branch-on-need octree for time-varying isosurface extraction. This data structure minimizes the impact of the I/O bottleneck by reading from disk only those portions of the search structure and data necessary to construct the current isosurface

Geometric algorithms for geographic information systems

A geographic information system (GIS) is a software package for storing geographic data and performing complex operations on the data. Examples are the reporting of all land parcels that will be flooded when a certain river rises above some level, or analyzing the costs, benefits, and risks involved with the development of industrial activities at some place. A substantial part of all activities performed by a GIS involves computing with the geometry of the data, such as location, shape, proximity, and spatial distribution. The amount of data stored in a GIS is usually very large, and it calls for efficient methods to store, manipulate, analyze, and display such amounts of data. This makes the field of GIS an interesting source of problems to work on for computational geometers. In chapters 2-5 of this thesis we give new geometric algorithms to solve four selected GIS problems.These chapters are preceded by an introduction that provides the necessary background, overview, and definitions to appreciate the following chapters. The four problems that we study in chapters 2-5 are the following: Subdivision traversal: we give a new method to traverse planar subdivisions without using mark bits or a stack. Contour trees and seed sets: we give a new algorithm for generating a contour tree for d-dimensional meshes, and use it to determine a seed set of minimum size that can be used for isosurface generation. This is the first algorithm that guarantees a seed set of minimum size. Its running time is quadratic in the input size, which is not fast enough for many practical situations. Therefore, we also give a faster algorithm that gives small (although not minimal) seed sets. Settlement selection: we give a number of new models for the settlement selection problem. When settlements, such as cities, have to be displayed on a map, displaying all of them may clutter the map, depending on the map scale. Choices have to be made which settlements are selected, and which ones are omitted. Compared to existing selection methods, our methods have a number of favorable properties. Facility location: we give the first algorithm for computing the furthest-site Voronoi diagram on a polyhedral terrain, and show that its running time is near-optimal. We use the furthest-site Voronoi diagram to solve the facility location problem: the determination of the point on the terrain that minimizes the maximal distance to a given set of sites on the terrain