flat refractive geometry
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. Prior Art- a Single Viewpoint Model. Just a magnification effect:. B. Skerry and H. Hall, ‘02 Webster, ‘98 - PowerPoint PPT PresentationTRANSCRIPT
Flat Refractive Geometry
Tali Treibitz, Yoav Y. Schechner Technion, Israel
Hanumant SinghWoods Hole Oceanographic Institute
Into Water Through Flat Window/192
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
/193
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
/194
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
Effective Viewpoint
Treibitz, Schechner & Singh, Flat Refractive Geometry
5
interface
n
apparent viewpoint?
apparent viewpoint?
Single Viewpoint? No!
Treibitz, Schechner & Singh, Flat Refractive Geometry
physical lens position
6
Other non-single viewpoint systems:
Grossberg & Nayar, IJCV’05
Sturm et al., Imaging beyond the pinhole camera,’06
Swaminathan et al., IJCV’06
Peleg et al., PAMI’01
Zomet et al., PAMI’03
Pajdla, IJCV’02
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
Treibitz, Schechner & Singh, Flat Refractive Geometry
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