lecture 18: single-view modeling, part 2
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CS4670 / 5670 : Computer Vision. Noah Snavely. Lecture 18: Single-view modeling, Part 2. Announcements. Project 3 due this Thursday by 11:59pm Demos on Friday (?) Project 3 artifacts due this Friday by 11:59pm Take-home prelim out Friday, due Wednesday 10/24 by the beginning of class - PowerPoint PPT PresentationTRANSCRIPT
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Lecture 18: Single-view modeling, Part 2
CS4670 / 5670 : Computer VisionNoah Snavely
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Announcements
• Project 3 due this Thursday by 11:59pm– Demos on Friday (?)
• Project 3 artifacts due this Friday by 11:59pm
• Take-home prelim out Friday, due Wednesday 10/24 by the beginning of class– Please don’t post on Piazza about the prelim, just
email the staff
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Quiz from last time
• How do you compute the image-space line l passing through two points p and q?
• How do you compute the image-space point p at the intersection of two lines l and m?
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Comparing heightsVanishingVanishing
PointPoint
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Measuring height
1
2
3
4
55.4
2.8
3.3
Camera heightHow high is the camera?
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Measuring height without a ruler
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C
Measuring height without a ruler
ground plane
Compute Z from image measurements• Need more than vanishing points to do this
Z
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The cross ratio• A Projective Invariant– Something that does not change under projective
transformations (including perspective projection)
P1
P2
P3
P4
1423
2413
PPPP
PPPP
The cross-ratio of 4 collinear points
Can permute the point ordering• 4! = 24 different orders (but only 6 distinct values)
This is the fundamental invariant of projective geometry
1i
i
i
i Z
Y
X
P
3421
2431
PPPP
PPPP
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vZ
r
t
b
tvbr
rvbt
Z
Z
image cross ratio
Measuring height
B (bottom of object)
T (top of object)
R (reference point)
ground plane
HC
TBR
RBT
scene cross ratio
1
Z
Y
X
P
1
y
x
pscene points represented as image points as
R
H
R
H
R
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Measuring height
RH
vz
r
b
t
R
H
Z
Z
tvbr
rvbt
image cross ratio
H
b0
t0
vvx vy
vanishing line (horizon)
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vz
r
b
t0
vx vy
vanishing line (horizon)
v
t0
m0
What if the point on the ground plane b0 is not known?• Here the guy is standing on the box, height of box is known• Use one side of the box to help find b0 as shown above
b0
t1
b1
Measuring height
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3D Modeling from a photograph
St. Jerome in his Study, H. Steenwick
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3D Modeling from a photograph
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3D Modeling from a photograph
Flagellation, Piero della Francesca
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3D Modeling from a photograph
video by Antonio Criminisi
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3D Modeling from a photograph