Analytical Motion Blur
Rasterization with
Compression
1
Carl Johan Gribel
Michael Doggett1
1,2
Tomas Akenine-Möller
Lund University
2
Intel Corproration
1
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Motivation
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Motivation
•
•
Human visual system designed to detect motion
•
Motion blur aids the motion detection of the visual system
This fails when presented too few images, or too much
motion per image
- motion gets jumpy
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Talk outline
• Edge Equations and exact exposure intervals
- analytic inside-test
- visibility management
• Computing the time integral
- opaque/translucent resolve
• Compression
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Previous work
•
Accumulation buffer [HA90][WGER05][DWS88]
- expensive
- strobing artifacts
•
Stochastic [CCC87] [AMMH07][McGuire et al.
HPG2010]
- correct solution but slow convergence
•
Single sample analytical visibility [KB83]
Extended with stochastic shading by Sung et al. [SPW02]
- details missing for visibility computations
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Edge Equation primer for
static triangle
p1
(x0 , y0 )
p2
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p0
Edge Equation primer for
static triangle
p1
(x0 , y0 )
p2
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p0
Edge Equation primer for
static triangle
p1
(x0 , y0 )
e1 < 0
p2
3D homogeneous space:
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p0
e1 = (p2 × p0 ) · (x0 , y0 , 1)
Edge Equation primer for
static triangle
p1
e0 e2
e1
p2
3D homogeneous space:
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p0
e1 = (p2 × p0 ) · (x0 , y0 , 1)
Edge Equation primer for
moving triangle
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Edge Equation primer for
moving triangle
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Edge Equation primer for
moving triangle
r0
q0
p0 (t) = (1 − t)q0 + tr0
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t ∈ [0, 1]
Edge Equations
p1 (t)
(x0 , y0 )
p2 (t)
p0 (t)
e1 (t) = (p2 (t) × p0 (t)) · (x0 , y0 , 1)
= (((1 − t)q2 + tr2 ) × ((1 − t)q0 + tr0 )) · (x0 , y0 , 1)
2
= (f t + gt + h) · (x0 , y0 , 1)
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Edge Equations
p1 (t)
(x0 , y0 )
p2 (t)
p0 (t)
e1 (t) = (p2 (t) × p0 (t)) · (x0 , y0 , 1)
= (((1 − t)q2 + tr2 ) × ((1 − t)q0 + tr0 )) · (x0 , y0 , 1)
2
= (f t + gt + h) · (x0 , y0 , 1)
We also derive the analytical depth function d(t) ...
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t=0.0
depth function
t=1.0
0.33
1.0
t
t=0.0
t=1.0
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Rasterization
• For each pixel of bounding box, compute
2nd degree solutions
• Insert intervals into per-pixel list
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d
t
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d
t
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d
Resolve
to final pixel
color
t
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Opaque resolve
d
•
Sweep over time and keep track of overlapping
intervals
•
•
Pick colors of the closest intervals
Blend together for final color
t
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Opaque resolve
d
•
Sweep over time and keep track of overlapping
intervals
•
•
Pick colors of the closest intervals
Blend together for final color
t
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Opaque resolve
d
•
Sweep over time and keep track of overlapping
intervals
•
•
Pick colors of the closest intervals
Blend together for final color
t
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Translucent resolve
•
d
Sweep over time and keep track of overlapping
intervals
• Alpha-blend each subsection
• Blend together for final color
α = 1.0
{
{
α = 0.6
t
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Translucent resolve
•
d
Sweep over time and keep track of overlapping
intervals
• Alpha-blend each subsection
• Blend together for final color
α = 1.0
{
{
α = 0.6
t
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Translucent resolve
•
d
Sweep over time and keep track of overlapping
intervals
• Alpha-blend each subsection
• Blend together for final color
α = 1.0
{
{
α = 0.6
t
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Compression
• Will end up with lots of intervals
• But, can expect spatial & temporal coherency
• Proposal: merge similar intervals
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Compression:
Oracle function
O(∆i , ∆j )
• Metric for interval similarity
• Merge pairs of intervals deemed most similar
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d
∆i
∆j
t
O(∆i , ∆j ) =
s
h1 max(tj
−
e
ti , 0)+
h2 |¯
zi − zj |+
h3 |ki − kj |+
e
h4 (ti
−
s
ti
+
h5 (|ci −cj |)
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e
tj
−
s
tj )+
temporal proximity
d
∆i
∆j
t
O(∆i , ∆j ) =
s
h1 max(tj
−
e
ti , 0)+
h2 |¯
zi − zj |+
h3 |ki − kj |+
e
h4 (ti
−
s
ti
+
h5 (|ci −cj |)
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e
tj
−
s
tj )+
temporal proximity
depths
d
∆j
∆i
t
O(∆i , ∆j ) =
s
h1 max(tj
−
e
ti , 0)+
h2 |¯
zi − zj |+
h3 |ki − kj |+
e
h4 (ti
−
s
ti
+
h5 (|ci −cj |)
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e
tj
−
s
tj )+
temporal proximity
depths
slope
d
∆i
∆j
t
O(∆i , ∆j ) =
s
h1 max(tj
−
e
ti , 0)+
temporal proximity
depths
slope
e
tj
temporal coverage
h2 |¯
zi − zj |+
h3 |ki − kj |+
e
h4 (ti
−
s
ti
+
h5 (|ci −cj |)
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−
s
tj )+
d
∆i
∆j
t
O(∆i , ∆j ) =
s
h1 max(tj
−
e
ti , 0)+
temporal proximity
depths
slope
e
tj
temporal coverage
color norm
h2 |¯
zi − zj |+
h3 |ki − kj |+
e
h4 (ti
−
s
ti
+
h5 (|ci −cj |)
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−
s
tj )+
d
∆i
∆j
t
O(∆i , ∆j ) =
s
h1 max(tj
−
e
ti , 0)+
temporal proximity
depths
slope
e
tj
temporal coverage
color norm
h2 |¯
zi − zj |+
h3 |ki − kj |+
e
h4 (ti
−
s
ti
+
h5 (|ci −cj |)
weights
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−
s
tj )+
Interval merging
•
•
•
Merge interval pair with lowest Oracle value
Combine temporal coverage
Blend attributes
d
d
t
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t
Compression with occlusion
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39 intervals
8 intervals
77 intervals
8 intervals
Results
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GT
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4 spp
16 spp
Analytical
Compression: 8
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Compression: 8
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Ground Truth
Stochastic 12 spp
Analytical, compression 8
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Compression
Rates
GT
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Rate 4
Rate 6
Rate 8
Rate 10
Compression: 64
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Compression: 64
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Algorithm summary
•
Time-dependent edge equations to compute
exact exposure intervals
•
Visibility management by using a linear
approximation of a cubic rational depth
function
•
Blur translucent geometry by performing alphablending extended in time
•
We propose a compression algorithm to
address fixed memory requirements
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Future work
• GPU implementation (in progress)
• Motion blurred shadows (in progress)
• Apply decoupled shading
• Analytical spatial anti-aliasing
• Higher order motion
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Danke !
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Danke !
* No bunnies were harmed during the research
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Compression failure case
Fast moving fence
24 spp
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Analytical 16 intervals
256 spp
Depth approximation
error
108
Relative depth error histogram
107
106
105
104
103
102
101
100
0.001%
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0.01%
0.1%
1%
10%
100%