Title: A Multiresolution Volume Rendering Framework for Large-Scale Time-Varying Data Visualization
1A Multiresolution Volume Rendering Framework for
Large-Scale Time-Varying Data Visualization
- Chaoli Wang1, Jinzhu Gao2,
- Liya Li1, Han-Wei Shen1
- 1The Ohio State University
- 2Oak Ridge National Laboratory
2Introduction
- Large-scale numerical simulation
- Richtmyer-Meshkov Instability (RMI) data _at_ LLNL
- 2,048 2,048 1,920 grid
- 960 (8 8 15) nodes of the IBM-SP system
- 7.5 GB per time step, output 274 time steps
- Goal
- Data exploration
- Quick overview, detail on demand
- Approach
- Multiresolution data representation
- Error-controlled parallel rendering
3Challenge
- Compact hierarchical data representation
- Allow specifying different spatial and temporal
resolutions for rendering - Long chains of parent-child node dependency
- Data dependency among processors
- Balance the workload for parallel rendering
4Algorithm Overview
The algorithm flow for large-scale time-varying
data visualization
5Wavelet-Based Time Space Partitioning Tree
- The WTSP tree
- Space-time hierarchical data structure to
organize time-varying data - An octree (spatial hierarchy) of binary trees
(temporal hierarchy) - Originate from the TSP tree Shen et al. 1999
- Borrow the idea of the wavelet tree Guthe et al.
2002
6Wavelet-Based Time Space Partitioning Tree
- WTSP tree construction
- Two-stage block-wise wavelet transform and
compression process - Build a spatial hierarchy in the form of an
octree for each time step - Merge the same octree nodes across time into
binary time trees
7Hierarchical Spatial and Temporal Error Metric
se(T) Si0..7MSE(T, Ti) MAXse(Ti)i0..7
- Based on MSE calculation
- Compare the error of each block with its children
te(T) MSE(T, Tl) MSE(T, Tr) MAXte(Tl),
te(Tr)
8Storing Reconstructed Data for Space-Time Tradeoff
- Alleviate data dependency
- EVERY-K scheme
ho 6, ht 4 ko 2, kt 2
9WTSP Tree Partition and Data Distribution
- Eliminate dependency among processors
- Distribution units
ho 6, ht 4 ko 2, kt 2
10WTSP Tree Partition and Data Distribution
- Space-filling curve traversal
- Neighboring blocks of similar spatial-temporal
resolution should be evenly distributed to
different processors - Space-filling curve preserves locality, always
visits neighboring blocks first - Traverse the volume to create a one-dimensional
ordering of the blocks
11WTSP Tree Partition and Data Distribution
- Error-guided bucketization
- Data blocks with similar spatial and temporal
errors should be distributed to different
processors - Create buckets with different spatial-temporal
error intervals
12WTSP Tree Partition and Data Distribution
- Error-guided bucketization
- Bucketize the distribution units when performing
hierarchical space-filling curve traversals - Distribute units in each bucket in a round-robin
fashion
13Run-Time Rendering
- WTSP tree traversal
- User specifies time step and tolerances of both
spatial and temporal errors - Traverse octree skeleton and the binary time
trees for each encountered octree node - A sequence of data blocks is identified in
back-to-front order for rendering
14Run-Time Rendering
- Data block reconstruction
- Get low-pass filtered subblock from its parent
node - Decode high-pass filtered wavelet coefficients
- Perform inverse 3D wavelet transform
- Reduce reconstruction time from O(c1ho c2hoht)
to O(c1ko c2kokt), where - c1 time to perform an inverse 3D wavelet
transform - c2 time to perform an inverse 1D wavelet
transform - ho the height of the octree
- ht the height of the time tree
- ko of levels in an octree node group
- kt of levels in a time tree node group
15Run-Time Rendering
- Parallel Volume Rendering
- Each processor renders the data blocks identified
by the WTSP tree traversal and assigned to it
during the data distribution stage - Cache reconstructed data for subsequent frames
- Screen tiles partition
- Image composition
16Results
- Data sets and wavelet transforms
data (type) RMI (byte)
range (threshold) 0, 255 (0)
volume (size) 1024 1024 960 32 (30 GB)
block (size) 64 64 32 (128 KB)
tree depth 6 (octree) and 6 (time tree)
wavelet transform Haar with lifting (both space and time)
data (type) SPOT (float)
range (threshold) 0.0, 10.109 (0.005)
volume (size) 512 512 256 30 (7.5 GB)
block (size) 32 32 16 (64 KB)
tree depth 6 (octree) and 6 (time tree)
wavelet transform Daubechies 4 (space) and Haar (time)
17Results
- Testing environment
- A PC cluster consisting of 32 2.4 GHz Pentium 4
processors connected by Dolphin networks - Performance
- Software raycasting
- 96.53 parallel CPU utilization, or a speedup of
30.89 times for 32 processors
18Results
- Data distribution with EVERY-K scheme (ko 2, kt
2)
RMI data set
SPOT data set
19Results
RMI data set
SPOT data set
20Results
- The timing result with 5122 output image
resolution
data set RMI SPOT
(se, te, t) (50, 10, 29) (0.05, 0.01, 23)
number of blocks 6,218 4,840
wavelet reconstruction 15.637s 4.253s
software raycasting 10.810s 2.715s
image composition 0.118s 0.070s
overhead 3.093s 1.719s
total time 29.658s 8.757s
difference time 2.043s 0.241s
21Results
- Rendering of RMI data set at selected time steps
1st 536
8th 743
15th 1,317
32th 1,625
22Results
- Rendering of SPOT data set at selected time steps
1st 2,558
12th 2,743
21th 2,392
30th 2,461
23Results
- Multiresolution volume rendering
RMI data set, 11th time step
SPOT data set, 5th time step
24Conclusion Future Work
- Multiresolution volume rendering framework for
large-scale time-varying data visualization - Hierarchical WTSP tree data representation
- Data partition and distribution scheme
- Parallel volume rendering algorithm
- Future work
- Utilize graphics hardware for wavelet
reconstruction and rendering speedup - Incorporate optimal feature-preserving wavelet
transforms for feature detection
25Acknowledgements
- Funding agencies
- NSF ITR grant ACI-0325934
- NSF Career Award CCF-0346883
- DOE Early Career Principal Investigator Award
DE-FG02-03ER25572 - Data sets
- Mark Duchaineau _at_ LLNL
- John Clyne _at_ NCAR
- Testing environment
- Jack Dongarra and Clay England _at_ UTK
- Don Stredney and Dennis Sessanna _at_ OSC