AFastVolumeRenderingAlgorithm forTimevaryingFieldsusinga - - PowerPoint PPT Presentation

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a fast volume rendering algorithm for time varying fields
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AFastVolumeRenderingAlgorithm forTimevaryingFieldsusinga - - PowerPoint PPT Presentation

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AFastVolumeRenderingAlgorithm forTimevaryingFieldsusinga TimespacePar<<oning(TSP)Tree HanWeiShen,LingJenChiang, KwanLiuMa Vis1999

slide-1
SLIDE 1

A
Fast
Volume
Rendering
Algorithm
 for
Time‐varying
Fields
using
a
 Time‐space
Par<<oning
(TSP)
Tree



Han‐Wei
Shen,
Ling‐Jen
Chiang,
 Kwan‐Liu
Ma
 Vis
1999


slide-2
SLIDE 2

How
do
we
deal
with
large
dataset?


  • Subdivision


– Break
big
pieces
into
smaller
ones


slide-3
SLIDE 3

SpaEal
Subdivision


  • Hierarchy
‐‐
Octree


bricks


slide-4
SLIDE 4

Add
Time…


  • One
Octree
per
Emestep
?







t
=
0





















t
=
1





















t
=
2
…


slide-5
SLIDE 5

Add
a
Dimension…


  • 4D
tree
Octree
(8‐tree)
‐>
16
tree
?


…

slide-6
SLIDE 6

Time‐Space
ParEEon
Tree


  • Two
Level
Hierarchical
Subdivision

  • 1st
level
SpaEal
subdivision
‐‐
Octree


bricks


slide-7
SLIDE 7

Time‐Space
ParEEon
Tree


  • Temporal
Subdivision


T=

0





1




2






3


[0,3]
 [0,1]
 [2,3]


4
<me
steps


slide-8
SLIDE 8

Rendering


  • Image
composiEon
remains
the
same
as
an


Octree


slide-9
SLIDE 9

Temporal
Coherence


  • Images
in
the
octree
nodes
are
cached
for


nodes
with
high
temporal
coherence


T=

0





1




2






3


[0,3]
 [0,1]
 [2,3]


T
=
1


slide-10
SLIDE 10

Time‐Varying
Volume
Rendering


  • Approximate
reconstrucEon
from
the
TSP
tree


E
=
0.05
(3.4%
image
diff.)


 E
=
0.05
(3.4%
image
diff.)


 Error
=
0

 11.2
speedup


slide-11
SLIDE 11

Results


  • Shock
wave:
1024
x
128
x
128
,
40
Eme
steps

  • Minimum
brick
size
32
x
32
x
32


  • Temporal
error
tolerance
=
0.02



Time
Step

 #
Bricks
Loaded
 Percentage
 0
 


10
 20
 30
 561
 73
 75
 72
 100
%

 13.0
%

 13.3
%

 12.8%



slide-12
SLIDE 12

Summary


  • TSP
Tree
‐‐
Extend
Octree
to
include
temporal


informaEon


  • Render
with
standard
Octree
image


composiEon


  • Temporally
coherent
images
are
cached
to


reduce
loads


  • Allow
approximated
volume
rendering


animaEon
via
the
hierarchy


slide-13
SLIDE 13

Importance‐Driven
Time‐Varying
 Data
Visualiza<on


Chaoli
Wang,
Hongfeng
Yu,
and
 Kwan‐Liu
Ma
 Vis
2008


slide-14
SLIDE 14

Importance
Driven
Volume
Rendering


  • Given
a
segmentaEon

  • Emphasis
important
segments
(works
for
medical


data)


  • How
about
Eme
varying
data?

slide-15
SLIDE 15

Time
Varying
ScienEfic
Data


  • No
temporal
segmentaEon

  • Measure
importance

  • Focus
on
analysis

  • How
to
capture
the
important
aspect
of
data?


– Importance
–
amount
of
change,
or
“unusualness”


  • How
to
uElize
the
importance
measure?


– Data
classificaEon
 – Abnormality
detecEon
 – Time
budget
allocaEon
 – Time
step
selecEon


slide-16
SLIDE 16

Importance


  • Consider
data
as
feature
vectors
[X,
Y]

  • Blockwise
importance
measurement

  • Entropy
based



– Mutual
InformaEon
 – CondiEonal
Entropy


slide-17
SLIDE 17
  • Consider
a
Eme
window
for
neighboring


blocks


  • Importance
of
a
data
block
Xj
at
Eme
step
t:

  • Importance
of
Eme
step
t:

slide-18
SLIDE 18

Examples


T I T I T I

Earthquake‐‐Regular
 Climate
‐‐
Periodic
 Vortex
–
Turbulence



slide-19
SLIDE 19

Cluster
the
Curves
(k
Means)


599
Eme
steps
 50
segments
 1200
Eme
steps
 120
segments
 90
Eme
steps
 90
segments


slide-20
SLIDE 20

Results
Highlights


  • Earthquake

slide-21
SLIDE 21

Time
BudgeEng


  • Allocate
rendering
Eme
base
on
importance

slide-22
SLIDE 22

Time
Step
SelecEon


  • Select
the
first
Eme
step

  • ParEEon
the
rest
of
Eme
steps
into
(K-1)
segments

  • In
each
Eme
segment,
select
one
Eme
step:

  • Maximize
the
joint
entropy

slide-23
SLIDE 23

Summary


  • Importance‐driven
data
analysis
and


visualizaEon


– QuanEfy
data
importance
using
Entropy
 – Cluster
the
importance
curves
 – Leverage
the
importance
in
visualizaEon