Flat Refractive Geometry
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Flat Refractive Geometry Tali Treibitz, Yoav Y. Schechner Technion, Israel Hanumant Singh Woods Hole Oceanographic Institute
description
Flat Refractive Geometry. Tali Treibitz, Yoav Y. Schechner Technion, Israel Hanumant Singh Woods Hole Oceanographic Institute. /19 2. Into Water Through Flat Window. /19 3. Geometrical Applications. Size measurements. Underwater stereo. Harvey & Shortis. Brandou et al. /19 4. - PowerPoint PPT Presentation
Transcript of Flat Refractive Geometry
Flat Refractive Geometry
Tali Treibitz, Yoav Y. Schechner Technion, Israel
Hanumant SinghWoods Hole Oceanographic Institute
Into Water Through Flat Window/192
Geometrical Applications
Size measurements Underwater stereo
Harvey & Shortis
Brandou et al.
/193
Prior Art- a Single Viewpoint Model
Just a magnification effect:
B. Skerry and H. Hall, ‘02
Webster, ‘98
Lavest et al, ECCV ‘00
scubageek.com
Other diving and underwater photography literature
water airf n f
Treibitz, Schechner & Singh, Flat Refractive Geometry
/194
radial distortion, e.g.2 4
1 2( )distortedx x k r k r
in a water tank
Prior Art- a Single Viewpoint Model
Treibitz, Schechner & Singh, Flat Refractive Geometry
/195
3D distortion
Harvey & Sortis, MTS J. ’02
Bryant et al, ACRA ’00
Pessel et al., WSCG ’03
Kwon & Casebolt, Sports Biomechanics ‘06
Negahdaripour & Firoozfan, IEEE J. Oceanic Eng. ’05
interface
n
apparent viewpoint?
apparent viewpoint?
Single Viewpoint? No!
Treibitz, Schechner & Singh, Flat Refractive Geometry
physical lens position
Other non-single viewpoint systems:
Sturm et al., Imaging beyond the pinhole camera,’06
Swaminathan et al., IJCV’06
Grossberg & Nayar, IJCV’05
Pajdla, IJCV’02
Peleg et al., PAMI’01
/196
lens
Z
interface
A Radial
Distortion?
No!
r
1( )?g r
single viewpoint model error
Treibitz, Schechner & Singh, Flat Refractive Geometry
[
distortion cannot be corrected
visible objects are occluded
errors can
reach dozens
of pixels
/197
air
water
Treibitz, Schechner & Singh, Flat Refractive Geometry
/199
Prior Light Field Calibration: non-parametric
• General
• Used in Aquaria
• Requires a few frames
• Difficult outside the lab
Fuchs et al., EGSR ’08Kutulakos & Steger, IJCV ’07Narashiman et al., ICCV ’05
Grossberg & Nayar, IJCV ’05Sturm & Ramalingam, ECCV ’04Zongker et al., SIGGRAPH ’99
/1910
lens
d̂
f̂
Parameter Fitting
known size
[
known distance
measured projection
Treibitz, Schechner & Singh, Flat Refractive Geometry
knowns
/1911
Our Calibration Method
worldw i 2 2
i( / ) 1
zdr r
f fn r n
2 2model w,1 w,2 w,1 w,2 1 2( ) ( ) 2 cos | |s r r r r
Known inputs: s=247.5mm
s=247.5mm
s=192.5mm
model knowns sConstraint:
size , distance worldzknownsAn underwater experiment
w,1 1,r w,2 2,r
x
/1912
Result- a Ray Map
SessionCalibration Distance
df
137cm7.4cm26.4mm
248cm7.9cm24.3mm
378cm4.2cm58mm
Applications:
Stereo
Measurements
Geometrical applications Imaging System
/1913
7
12
17
22
27
1 2 3 4 5 6 7 8
Experiment #
Siz
e [
cm]
Size Measurement From Known Distances
Treibitz, Schechner & Singh, Flat Refractive Geometry
* not at the calibration distances
11.5cm
20.5
cm
14cm
28cm
26cm single vi
ewpoint
underesti
mationground truth
our method
/1914
Rays in the Imaging System
iris
Treibitz, Schechner & Singh, Flat Refractive Geometry
/1915
Rays in the Imaging System
iris
a caustic surface
Treibitz, Schechner & Singh, Flat Refractive Geometry
/1916
d
d
0.9d
lens
interfacea camera with a full FOV of 100° in air
Treibitz, Schechner & Singh, Flat Refractive Geometry
Caustics of the Flat Interface System/1917
Caustics of the Flat Interface System
3
ii 2
1.52
ii 2
1( ) 1
1( ) 1 1
rR r d
n f
rZ r dn
n f
0 d
A closed-form solution:
Treibitz, Schechner & Singh, Flat Refractive Geometry
n
f
ir
d
the system has a single viewpoint
/1918
Flat Refractive Geometry• Non-single viewpoint system
• Old models significant errors
• Correct physics-based model & caustics
• Calibration of true geometry: accurate, practical, in-situ
Tali Treibitz, Yoav Y. Schechner & Hanumant Singh
