Using Difference Intervals for Time-Varying Isosurface Visualization

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Using Difference Intervals for Time-Varying
Isosurface Visualization

• Kenneth W. Waters
• Christopher S. Co
• Kenneth I. Joy
• Institute for Data Analysis and Visualization
• Department of Computer Science
• University of California, Davis

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Goals

• Target out-of-core time-varying isosurface
  extraction
• Interesting data sets are many times the size of
  core memory
• Extend an existing out-of-core value space
  isosurface extraction method to work with
  time-varying data
• Reduces development effort
• Trade a long pre-processing step for fast
  visualization of all isosurfaces within a data
  set
• Trade increased disk space usage for decreased
  disk traffic
• Disk space is cheap
• Disk access is very slow

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Terms

• Full Extraction is the determination of which
  cells are active for a particular isosurface from
  a particular time step
• This is provided to us by the underlying non
  time-varying isosurface extraction algorithm
• Incremental Extraction is the process of
  extracting only the differences between an
  isosurface in one time step and the same
  isosurface in the next time step.
• This work focuses on adding incremental
  extraction using the machinery of the underlying
  extraction algorithm
• If you scalar volume data is incoherent the
  difference between two successive isosurfaces may
  be larger than the isosurfaces themselves, in
  this case our method is slower than the naive
  approach.

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Span Space Review

• Developed by Livnat et. al.
• 2-D virtual space where cells are represented by
  points located by their minimum and maximum
  intensity values
• Isosurface extraction is reduced to finding which
  points lie within the rectangle corresponding to
  the isovalue
• Each point in span space represents an interval
  of intensity values

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Cell Movement
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Cell Movement
1.1
1.0
1.0
0.9
0.7
0.4
0.5
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Difference Intervals

• These two intervals break the scalar value space
  into five intervals.
• Suppose you have the complete isosurface for a
  particular isovalue for the first time step

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Difference Intervals

• Suppose you had the isosurface, with isovalue q
  lt a.
• This cell is not active in either time step
• No work needs to be done for this cell to
  transform the isosurface from the first time step
  to the second time step

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Difference Intervals - Add

• Suppose you had the isosurface, with isovalue a lt
  q lt b.
• This cell is not active in the first time step
  but is active in the second time step
• We need to add this cell to the isosurface to
  transform from the first time step to the second
  time step

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Difference Intervals

• Suppose you had the isosurface, with isovalue b lt
  q lt c.
• This cell is active in both the first time step
  and the second time step
• No work needs to be done for this cell to
  transform the isosurface from the first time step
  to the second time step
• This is where we save time and disk traffic
• A full extraction of second time step would
  re-extract this interval, we can avoid reading
  this interval from disk

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Difference Intervals - Remove

• Suppose you had the isosurface, with isovalue c
  lt q lt d.
• This cell is active in the first time step but is
  not active in the second time step
• We need to remove this cell from the isosurface
  to transform from the first time step to the
  second time step

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Difference Intervals

• Suppose you had the isosurface, with isovalue q
  gt d.
• Identical to the first case
• This cell is not active in either the first time
  step or the second time step
• No work needs to be done for this cell to
  transform the isosurface from the first time step
  to the second time step

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Difference Intervals

• We now have two intervals which describe when
  work needs to be done to transform our isosurface
• These two intervals can be inserted as cells into
  our existing extraction algorithm
• There are 11 different ways a cell can move in
  the span space
• The two difference intervals are always smaller
  than the intervals for the original cell
• The two difference intervals are always disjoint

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Using Difference Intervals - Preprocessing

• Between every two time steps compute the set of
  difference intervals which can be used to
  transform the isosurface for any isovalue
• Insert these difference intervals into our
  existing out-of-core isosurface extractor, there
  will be a different instance of the extractor for
  each pair of time steps.
• Label these structures Dn
• Create key frame extraction structures, use the
  existing out-of-core isosurface extractor on
  select key frames as if they where non
  time-varying data sets
• Label these structures kn
• We chose every 4th time step

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Using Difference Intervals - Extraction

• To view the isosurface for isovalue q,
  progressing through all of the time steps
• Extract the isosurface for the first time step,
  using k0
• Extract the difference intervals for value q,
  from D0
• Apply the extracted add and remove operations to
  the isosurface for the first time step, to
  extract the isosurface for the second time step
• Repeat with the difference intervals from D1 to
  get to the isosurface for the third time step,
  etc.
• To change the isovalue or seek to a different
  time step
• Do a full extraction from the nearest key frame
• Apply difference intervals until your at the
  desired time step

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Preview Rendering

• We only load data from disk when a cell becomes
  active or inactive
• We have no information about the intensity values
  for an active cell in a particular time step
• We cannot use a traditional rendering method to
  draw the isosurface
• Render all the active cells as screen aligned
  points.
• Using the depth buffer approximate normals and
  lighting in screen space
• If the user pauses to take a close look at a
  particular time step, load the full data for that
  time step off disk, for higher quality rendering

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Compression

• A generalized versions of the compression
  provided by the Temporal Hierarchical Index Tree
  Shen 98
• Compress each cell independently
• If a cell moves less than e in span space over
  several time steps move that cell to its
  extreme value for all of those time steps
• Makes the cell stationary for several time steps,
  before jumping a long (gt e) distance in span
  space
• Produces only false positives
• If a cell doesnt move in span space between two
  frames, it produces no difference intervals
• Creates fewer but wider difference intervals

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Data Sets

• Tested using two datasets
• 5jet
• 128 x 128 x 128
• 1,000 time steps
• Float data
• 7.81 GiB
• Argon Bubble
• 640 x 256 x 256
• 131 time steps
• Float data
• 20.4 GiB

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Extraction Time
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Build Time and Disk Usage

• 5jet
• e 50
• 2.94 false positive rate
• 96 minute differential span space generation time
• 11,574 MiB for difference intervals, 6,000 MiB
  for key frames
• 46.8 GiB uncompressed difference interval size
• Argon Bubble
• e 0.025
• 3.34 false positive rate
• 83 minute differential span space generation time
• 7,496 MiB for difference intervals, 20,948 MiB
  for key frames
• 121.8 GiB uncompressed difference interval size

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Conclusion

• Extended any existing value-spaced out-of-core
  isosurface extraction algorithm to work on
  time-varying data by generating difference
  intervals
• Difference intervals allow us to skip extracting
  cells which remain active from time step to time
  step
• Reduces disk traffic
• Applied compression to the data before difference
  interval generation
• Reduces disk space usage
• Rendered the isosurface with only the active cell
  positions
• Eliminates the need to fetch volume data from
  disk for rendering
• Extraction for the 5jet data set averaged 200ms.
• Extraction for the larger data set was not
  real-time, but the results where promising.

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Questions?