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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.
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