visibility in point clouds philip dutré - parag tole program of computer graphics cornell...
TRANSCRIPT
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Visibility in Point Clouds
Philip Dutré - Parag Tole
Program of Computer Graphics
Cornell University
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Motivation
points as modeling and rendering primitives
finding new ways to evaluate (and approximate) the visibility function
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General Idea
Sample original surfaces (polygons) to construct set of oriented points
Evaluate visibility between any two points in the scene using only this point cloud
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General Idea
Use it for shading only, NOT for primary visibility
eye
visibility = 0 or 1?
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General Idea
Exact visibility: 0 or 1
Approximate visibility: numerical value between 0 and 1 “confidence” that 2 points are mutually visible use as numerical value in shading calculations
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Generate oriented surface points
Scene geometry Surface sampling Oriented points
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Intersection heuristic
Find closest point x to query line pq
Approximate original surface by surface element Sx
position Sx : probability density dns(Sx)
Check whether Sx intersects pq
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Intersection heuristic
p
q
y
x
Sx
p
x
q
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Intersection heuristic
Probability y belongs to Sx :
Visibility value:
)()(
)()(),(
x
xSySx
xxx SdSdnsySp
),(),( ySp1pqxvis x
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Intersection heuristic
Use C closest points to query line pq
C
1ii pqxvispqvis ),()(
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Use only ‘valid’ points
p
q
x1
p
q
x2
x3
> threshold distance
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Validation
Sx = square with length L
dns(Sx):
NAL /
dns Sx
rxy
L-------
0
0 .2
0 .4
0 .6
0 .8
1
0 0 .2 0 .4 0 .6 0 .8 1
r x y
L-------
p Sx y
d 0=
d 5=
d 10=
d 3=
0
0 . 2
0 . 4
0 . 6
0 . 8
1
0 0 . 2 0 . 4 0 . 6 0 . 8 1
d 1=
d 3=
d 5=
d 10=
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Validation
Use vis(pq) as probability to determine whether pq is visible
compare to exact visibility of pq
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Validation
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5 6 7 8 9 100
0.2
0.4
0.6
0.8
1
5000 10000 15000 20000 25000 30000 35000 40000 45000 50000
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1 2 3 4 5 6 7 8 9 10
a. Size of square - fL b. Number of points in cloud N
c. Number of closest points C d. Power d
visible
invisible
total
visible
invisible
total
visible
invisible
total
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
0 10 20 30 40 50 60 70 80 90 100
visible
invisible
total
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Validation
size of Sx doesn’t really matter
Power d indicates a stepping function? true for this validation not true for shading
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Direct Illumination
use continuous value of vis(pq)
reference - 97min. 10,000 points - 50m. 20,000 points - 59m.
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Global Illumination
Bidirectional path tracing
Generate & store light paths
Rendering: generate eye path & connect to selected light paths
Use continuous visibility value with separate point cloud
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Global Illumination
reference - 37m. 20,000 points - 229m. 100,000 points - 334m.
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Some trivial extensions
Use point cloud for primary visibility (reprojection)
Light paths + point cloud = same set
Separate clouds for each object (e.g. LDIs, points as modeling primitives)
TR: http://www.graphics.cornell.edu/pubs/2000/DTG00.html
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Open Questions
“Polygons are so 10 days ago, but points are hot!!!”
Is exact visibility always necessary?
Do we need the same model representations for display & shading?
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Conclusion
TR: http://www.graphics.cornell.edu/pubs/ 2000/DTG00.html
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