• Contour Tracking • Surface Rendering • Di t V l R d iDirect … · I D color x λe τ λdλ...
Transcript of • Contour Tracking • Surface Rendering • Di t V l R d iDirect … · I D color x λe τ λdλ...
What we will cover
• Contour Trackingg• Surface Rendering
Di t V l R d i• Direct Volume Rendering• Isosurface Renderingg• Optimizing DVR
d• Pre-Integrated DVR
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I Q lit D dImage Quality Depends on
Sampling RateOTF a ianceOTF varianceOTF*Sampling Rate
2Really nothing?
R I iRay-Integration
Discrete approximation of volume rendering integral will converge against correct result forintegral will converge against correct result for ray sampling interval > 0
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Hi h F TFHigh-Frequency TFs
High frequencies in the transfer function T increase i d li t
High frequencies in the transfer function T increase i d li trequired sampling raterequired sampling rate
T(s) T(s(x))s(x)
x s x
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x s x
Hi h F TFHigh-Frequency TFs
T(s)
s
64 data slices 10 times more slices
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Hi h F TFHigh-Frequency TFs
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PP I t t d V l R d iI t t d V l R d iPP I t t d V l R d iI t t d V l R d iPrePre--Integrated Volume RenderingIntegrated Volume RenderingPrePre--Integrated Volume RenderingIntegrated Volume Rendering
Idea: Pre-Integrated Classificationslab by slab rendering– slab-by-slab rendering
slice-by-slice slab-by-slab
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d l fPre-Integrated Classification
pre-integrate all possible combinations in the TF
front slice
back slice combinations in the TFslice slice
sf sbstore integral g
into table
d ss sb
dAssume constant
sampling distance d
sbsf
8sf
p g
PP I t t d V l R d iI t t d V l R d iPP I t t d V l R d iI t t d V l R d iPrePre--Integrated Volume RenderingIntegrated Volume RenderingPrePre--Integrated Volume RenderingIntegrated Volume Rendering
project slice
sf sbsf sb
front back
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front slice
back slice
PrePre--Integrated Volume RenderingIntegrated Volume RenderingPrePre--Integrated Volume RenderingIntegrated Volume Rendering
f t h i t l d d fetch integral from dependent texture
adapt texture coordinatesfor projected slice
sf sbsbf b
slice
sf
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slice
P i t t d T f F tiPre-integrated Transfer Function
DImage Plane
D0
λλ λτ dexcolorDID
∫ −= ),0())(()0(
( ) λD
∫ ∫ ⎞⎛
λλ dexcolorDI ∫= 0))((),0(
( ) λλλκλλ
ddxsxscD
∫ ∫ ⎟⎠⎞⎜
⎝⎛ (−)=
0 0')))'((exp )((~
11sampled density
P i d T f F iPre-integrated Transfer Function
( )( )( ) by exp eApproximat0
⎟⎠⎞⎜
⎝⎛ ′′− ∫
λλλκ dxs
( )( ) )1()))((exp)))(((exp/
1
/
1
/
1i
d
i
d
i
d
i
didxsddixs ακκλλλ
∏∏∑===
−=−=⎟⎠
⎞⎜⎝
⎛×−
ddixsddixs αi ))) ((()))) (((exp(1 where κκ ≈−−≈
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i d f iPre-integrated Transfer Function
( )( )( ) ( )( )( ) λλλκλλ
ddxsxscDID
⎟⎠⎞⎜
⎝⎛ ′′−= ∫∫ 00
exp~),0( ( )( )( ) ( )( )( )⎠⎝ ∫∫ 00
p)(
( )ds(x(id))c~C~ ≈By approximating color
∑ ∏−
≈n i
CnI1
)1(~)0( α
( )ds(x(id))c Cy pp g
∑ ∏= =
−≈i
jj
iCnI0 0
)1(),0( α
'' ~)(~~Back-to-front compositing
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'1
' )1( +−+= iiii CCC α
Pre-integrated Transfer Function
))))(((exp(1),,()1(
λλκαα dxsdssdi
bfi ∫+
−−== ))))(((p(),,(idbfi ∫
∫ +−−−≈1
0) ))1((exp(1 ωωωκ ddss bf∫0
∫ +−=1
0))1((~~
bfi sscC ωω∫0ωωωωκ
ωddddss bf )' )')'1((exp(
0∫ +−−×
We can get ∑ ∏−
−≈n
j
i
iCnI0
1
0
)1(~),0( α
14with pre-computed color and opacity values = =i j0 0
The approximated opacity of pp p ythe i-th segment
α α-=
))))(((()1(
λλ ddi
∫+
sf sb0 sf sb0
))))(((exp(1)(
λλκα dxsidi ∫−−=
∫ +−−−≈1
)))1((exp(1 ωωωκ ddss bf∫ +0
)))1((exp(1 ωωωκ ddss bf
⎟⎟⎞
⎜⎜⎛−−= ∫
sdssd b )(exp1 κ
( ) ( )( )⎟⎞⎜⎛
⎟⎟⎠
⎜⎜⎝ −−−= ∫s
fb
d
dssss f
)(exp1 κ
∫s
d)()(h15
( ) ( )( )⎟⎟⎠
⎞⎜⎜⎝
⎛−
−−−= fb
fb
sTsTss
dexp1 ∫= dsssT0
)()( where, κ
The approximated color of ppthe i-th segment
∫ +−=1
0))1((~~
bfi sscC ωωω
dddd )')')'1((( ∫ +Self-attenuation within segment
N l t th lf tt ti
ωωωωκ ddddss bf )')')'1((exp(0∫ +−−×
Neglect the self-attenuation
ωωω ddsscC bfi ))1((~~ 1
∫ +−≈
)(~sdsscd b= ∫
bfi ))((0∫
))()((
sfb
sKsKd
ss a
=
− ∫
∫=s
dsscsK )(~)(where16
))()(( fbfb
sKsKss
−−
= ∫= dsscsK0
)()( where,
12 bit I H dli12-bit Image Handling
2D Pre-integration Table with fixed d12bits per S S– 12bits per Sf, Sb
– Construct Pre-integrated Table requires too much time and spacemuch time and space
MBytebitBGR 648),,,(22 : tableLookup 1212 =××× α
( )= bfi dss ,,ααsb( )
( ) ( )( )⎟⎟⎞
⎜⎜⎛
−−−≈ fb
bfi
sTsTdexp1
,,sb
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( ) ( )( )⎟⎠
⎜⎝ − fb
fb ssp
sf
Pre-integrated classification
2D Pre-integration Table with a fixed d⎞⎛( ) ( ) ( )( )⎟⎟⎠
⎞⎜⎜⎝
⎛−
−−≈−=− fb
fbbfi sTsT
ssddss exp,,11 αα
⎠⎝ f
fb
bbss
ss
sdsd − ∑∑ ⎟⎟⎞
⎜⎜⎛−=⎟
⎟⎞
⎜⎜⎛−= )(exp)(exp κκ fb
ff
s
ssssfb
sdsss ==
∑∑ ⎟⎟⎠
⎜⎜⎝−=⎟
⎟⎠
⎜⎜⎝ −−= )(exp)(exp κκ
fb
b
f
sss
ss
ds−
=∏ −= ))(exp( κ
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f
(s)ddsds cytransparen)(1))(exp( =−≈− κκNote thatNote that
Opacity ComputationTransparency = 0.4 0.5 0.6 0.4
A B C D length=4
S=100 101 102 103
Opacity of a material with four blocks
104
(x)406050401
(o) 4.06.05.04.014 ×××−=
×××−=
α
α?)(ABCDα(x) 4.06.05.04.01 ×××−=α
( ) ?)1,104,100(,, ααα == dss bfi When d=1( )f
(x) 4.06.05.04.01 ×××−=α?=α
19(o) 4.06.05.04.01 4 ×××−=α
100 104
?=α
1D P I i T bl1D Pre-Integration Table
Instead of integral function, we use arithmetic average term for the fast generation of TablegUse 1D table with extra operation but less memory
KBytesbitBGR 168),,,(2:tableLookup 12 =×× α
b
sss
dsdss ∏ ))(exp(1)( κα
KBytesbitBGR 168),,,(2:tableLookup α
fb
f
ss
ssbf dsdss −
=∏ −−= ))(exp(1),,( κα
∑ −−≈bs
ds ))(exp(11 κ∑=
−−
−≈fssfb
dsss
))(exp(1 κ
20T=0.4 0.6 0.3 0.2 4/)2.03.06.04.0(1 +++−=α
PP I d V l R d iI d V l R d iPP I d V l R d iI d V l R d iPrePre--Integrated Volume RenderingIntegrated Volume RenderingPrePre--Integrated Volume RenderingIntegrated Volume Rendering
Pre-Classification
Post-Classification
Pre-Integrated-Classification
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PP I t t d V l R d iI t t d V l R d iPP I t t d V l R d iI t t d V l R d iPrePre--Integrated Volume RenderingIntegrated Volume RenderingPrePre--Integrated Volume RenderingIntegrated Volume Rendering
128 slicespre-
lassifi ation
128 slicespost-
lassifi ationclassification classification
128 slicespre-integrated
284 slicespost-
classification
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classification
PrePre--Integrated Volume RenderingIntegrated Volume RenderingPrePre--Integrated Volume RenderingIntegrated Volume Rendering
Texture-based (2D/3D)Pre-computed ray-segment lookupDependent texture
Especially suited for:Low resolution volume dataLow resolution volume dataNon-linear transfer functions
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d l d id l d id l d id l d iPrePre--Integrated Volume RenderingIntegrated Volume RenderingPrePre--Integrated Volume RenderingIntegrated Volume Rendering
Reduce compositing time by larger re-sampling intervalintervalNeed to re-compute the pre-integrated table whenever OTF is changedwhenever OTF is changed.Brings blurring effectsMore compositing voxels (20 30%)More compositing voxels (20-30%)
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