Time-Varying Analysis

1. Introduction

In this project, we seek to make a fast algorithm for time dependent isosurface extraction where each connected component of isosurface is identified and tracked over time. Since time-varying data set is often very large and has complex features, efficient and effective visualization of such data set is important. Especially when the data set contains many evolving components, the user prefers to isolate interesting components and follow the evolution of them rather than look at whole components. Our proposed algorithm identifies each individual components of isosurface by tracking connected surface from a pre-generated seed set. Once each components of isosurface is constructed, we can efficiently trace the evolution of each component by progressively tracing and updating the deformation of the isosurface component over time as a result of input function changes. To extract newly created isosurface component which cannot be tracked from isosurface of previous time step, the pre-generated seed set is used and checked to detect and construct the new component. We show our algorithm is fast enough for interactive visualization and very effective for capturing correlation between successive isosurfaces with no demand of complex correspondence matching test.

[ Figure1 : standard isosurface visualization of time-varying volticity magnitude ]

[ Figure2 : conponent identified isosurface visualization of time-varying volticity magnitude]

[ Figure3 : conponent isolated isosurface visualization of time-varying volticity magnitude]

2. Algorithm Overview

In this section, we describe an overall algorithm for extracting time dependent isosurface with feature tracking capability. Although feature can be any form of particular interesting regions, we assume a feature is defined as each individual isosurface component or regions inside the particular isosurface component in this paper.
There are two basic operations, spatial contour tracking from seed cell and temporal contour tracking as shown in Figure 4. Seed set is used for finding cells each of which intersects with each requested isosurface components. Spatial contour tracking is performed on each seed cell to construct isosurface component which contains the seed cell. Temporal contour tracking traces the movement of specific isosurface component and progressively approximates succeeding isosurface component by iterative local update around the surface.
The approach is applicable to any structured and unstructured grid of cells on which a scalar field is defined. The scalar field itself is only assumed to be continuous in space and time. Overall algorithm is shown in Figure 4 and also specified as following.

[ Figure 4. algorithm overview ]

3. Contribution

efficiency : we give an algorithm which can extract time dependent isosurface with minimal cost of time. The efficiency is mainly from reducing search space for cells intersecting with isosurface and keeping minimal size of search structure, which can minimize expensive disk I/O access.
effectiveness :
- component tracking : When isosurface has many evolving components including noise, the user often wants to find and follow the interesting isosurface components. This can protect the user from distracted by uninteresting components and provide informative statistics on the interaction among the components.
- vertex tracking : Our algorithm for isosurface tracking over time can trace the movement of each vertices and quantify the movement. For example, we can visualize the degree of deformation over time on each point of surface.
user interface design for time-dependent isosurface visualization : Since time dependent data set is very large, the user need an interface which can guide to find interesting features and track the behavior of them.

4. Examples

[ Figure 5. isosurface visualization of three time steps in Jet Shockwave data set ]

[ Figure 6. isosurface visualization with component identification of ocean speed change data ]

[ Figure 7. isosurface visualization of ocean temparature data ]

* Jet Shockwave data is part of the Advanced Visualization Technology Center's data repository and appears courtesy of Andrea Malagoli and Milena Micono of the Laboratory for Astrophysics and Space Research(LASR) at the University of Chicago.