スライド 1 - 広島市立大学
Download
Report
Transcript スライド 1 - 広島市立大学
Ikeuchi Laboratory
The University of Tokyo
Japan
Polarization-based Shape Estimation
of Transparent Objects
for Digitizing Cultural Assets
Daisuke Miyazaki
Katsushi Ikeuchi
The University of Tokyo
International Symposium on the CREST Digital Archiving Project
Introduction(1/3)
Polarization raytracing(7)
Shape estimation(6)
Experiment(5)
Conclusion(2)
Objective
Estimate 3D shape of transparent object
Analyze the polarization phenomena
Polarization analysis
Real transparent object
Virtual transparent object
International Symposium on the CREST Digital Archiving Project
Introduction(2/3)
Polarization raytracing(7)
Shape estimation(6)
Experiment(5)
Conclusion(2)
Application fields
Modeling cultural assets
3D catalog in web site
Manufacturing robot
Object recognition to recycle
International Symposium on the CREST Digital Archiving Project
Introduction(3/3)
Polarization raytracing(7)
Shape estimation(6)
Experiment(5)
Conclusion(2)
Methods developed in this project
Previous project
Miyazaki et al. 2004
Miyazaki et al. 2002
Today’s talk
International Symposium on the CREST Digital Archiving Project
Introduction(3)
Polarization raytracing(1/7)
Shape estimation(6)
Experiment(5)
Conclusion(2)
Polarization
Light = wave oscillates
Oscillates in certain direction polarization
DOP = degree of polarization
Incident
Reflected
Air
Object
Light
Unpolarized
(DOP 0)
Polarizer
Perfectly polarized
(DOP 1)
Transmitted
Partially polarized
(DOP 0~1)
International Symposium on the CREST Digital Archiving Project
Introduction(3)
Polarization raytracing(2/7)
Shape estimation(6)
Experiment(5)
Conclusion(2)
Reflection and transmission
Light
Unpolarized
Normal Depends
upon
Partially polarized
Air
Object
Partially polarized
International Symposium on the CREST Digital Archiving Project
Introduction(3)
Polarization raytracing(3/7)
Shape estimation(6)
Experiment(5)
Conclusion(2)
Tracing the light rays
Calculate reflection and transmission
International Symposium on the CREST Digital Archiving Project
Introduction(3)
Polarization raytracing(4/7)
Shape estimation(6)
Experiment(5)
Conclusion(2)
Polarization raytracing
Ray tracing
Ray tracing
Calculate intensity
Calculate polarization
Conventional raytracing
Polarization raytracing
International Symposium on the CREST Digital Archiving Project
Introduction(3)
Polarization raytracing(5/7)
Shape estimation(6)
Experiment(5)
Conclusion(2)
Mueller calculus
Conventional raytracing
Intensity: Scalar
Reflectivity&transmissivity: Scalar
Polarization raytracing
Polarization state: 4D vector
Reflection&transmisstion matrix: 4x4 matrix
International Symposium on the CREST Digital Archiving Project
Introduction(3)
Polarization raytracing(6/7)
Shape estimation(6)
Experiment(5)
Conclusion(2)
Example of Mueller calculus
Conventional raytracing
Reflected intensity reflectivity incident intensity
Scalar Scalar Scalar
Polarization raytracing
Reflection vector reflection matrix incidence vector
International Symposium on the CREST Digital Archiving Project
Introduction(3)
Polarization raytracing(7/7)
Shape estimation(6)
Experiment(5)
Conclusion(2)
Example of matrices
Reflection
ж(R|| + R ^
зз
зз
з (R|| - R ^
R = ззз
зз
0
зз
зз
0
и
з
Transmission
) 2 (R||
- R^
)2
0
) 2 (R||
+ R^
)2
0
0
R||R ^
0
0
Rotation
0
1
0 cos 2
C
0 sin 2
0
0
ц
ч
ч
ч
ч
0 ч
ч
ч
ч
ч
0 ч
ч
ч
ч
ч
ч
R||R ^ ш
ч
ч
ч
0
T|| T 2
T|| T 2
T
0
0
T T
T T
||
2
0
||
2
0
0
T||T
0
0
0
0
T||T
0
Phase shift
0
sin 2 0
cos 2 0
0
1
0
1
0
D
0
0
0
0
1
0
0
cos
0 sin
0
0
sin
cos
International Symposium on the CREST Digital Archiving Project
Introduction(3)
Polarization raytracing(7)
Shape estimation(1/6)
Shape estimation
Initial shape
Experiment(5)
Conclusion(2)
Iterative computation
with updating the shape
2
min
Input DOP
(degree of polarization)
Caculated DOP with
polarization raytracing
Final shape
International Symposium on the CREST Digital Archiving Project
Introduction(3)
Polarization raytracing(7)
Shape estimation(2/6)
Experiment(5)
Conclusion(2)
Error function
min
dxdy
Input
Calculated
p Hx q Hy
IE IR
min
I
I R H x p H y q dxdy
2
E
Relationship between
normal & height
2
2
Calculate height and normal
International Symposium on the CREST Digital Archiving Project
Introduction(3)
Polarization raytracing(7)
Shape estimation(3/6)
Experiment(5)
Conclusion(2)
Calculate normal from shape
Set initial height H properly
Calculate gradient p&q by differentiating height H
p = Hx
q = Hy
International Symposium on the CREST Digital Archiving Project
Introduction(3)
Polarization raytracing(7)
Update normal
Shape estimation(4/6)
Experiment(5)
p p 1E
q q 2E
Conclusion(2)
E I E I R
2
Input DOP
Calculated DOP
Light ray
Change
normal
Error
Object
Ray changes
Ray changes
International Symposium on the CREST Digital Archiving Project
Introduction(3)
Polarization raytracing(7)
Shape estimation(5/6)
Experiment(5)
Conclusion(2)
Calculate height from normal
Updated normal
Relaxation method
1
H H px q y
4
Calculated height
International Symposium on the CREST Digital Archiving Project
Introduction(3)
Polarization raytracing(7)
Shape estimation(6/6)
Experiment(5)
Conclusion(2)
Algorithm overview
Initial height
Normal from
height
Minimize
2
Input
Calc.
Update normal
Output height
Stop when
2
Input
Height from
normal
Calc.
is small enough
International Symposium on the CREST Digital Archiving Project
Introduction(3)
Polarization raytracing(7)
Shape estimation(6)
Experiment(1/5)
Conclusion(2)
Experimental setup
Monochrome camera
Camera adapter
Computer
IR/UV cut-off filter
Linear polarizer
Geodesic dome
Plastic sphere
40W lamp
Polarizer controller
Transparent object inside
International Symposium on the CREST Digital Archiving Project
Introduction(3)
Polarization raytracing(7)
Shape estimation(6)
Experiment(2/5)
Conclusion(2)
Simulational result
25 loop
Initial
Initial
20 loop
Frontal shape(estimated)
Frontal shape(truth)
Rear shape(known)
Refractive index 1.5
& Illumination (known)
International Symposium on the CREST Digital Archiving Project
Introduction(3)
Polarization raytracing(7)
Shape estimation(6)
Experiment(3/5)
Conclusion(2)
Experimental result
Acrylic hemisphere
Refractive index 1.5
Diameter 30mm
3000
Initial
(previous method)
Error(height):2.8mm
Error(normal):14
Initial
(previous method)
2
I
I
dxdy
E
R
1500
0
25
Error/loop
50
50 loop
Error(height):0.61mm
Error(normal):7.0
10 loop
International Symposium on the CREST Digital Archiving Project
Introduction(3)
Polarization raytracing(7)
Shape estimation(6)
Experiment(4/5)
Conclusion(2)
Experimental result
Initial
Acrylic object
Diameter(base)24mm
Refractive index 1.5
5 loop
50 loop
Error(height)
0.24mm
International Symposium on the CREST Digital Archiving Project
Introduction(3)
Polarization raytracing(7)
Shape estimation(6)
Experiment(5/5)
Conclusion(2)
Experimental result
Glass(refractive index 1.5)
10 loop
Initial(previous method)
International Symposium on the CREST Digital Archiving Project
Introduction(3)
Polarization raytracing(7)
Shape estimation(6)
Experiment(5)
Conclusion(1/2)
Summary
Polarization raytracing
Iteration
Initial shape
Calculated polarization data
2
min
Input polarization data
Object
Shape
International Symposium on the CREST Digital Archiving Project
Introduction(3)
Polarization raytracing(7)
Shape estimation(6)
Experiment(5)
Conclusion(2/2)
Future work for another project
Realtime measurement
Commercial product
?
Estimating refractive index
Modeling cultural assets
International Symposium on the CREST Digital Archiving Project
Ikeuchi Laboratory
The University of Tokyo
Japan
Thank you
Supported by
Japan Science and Technology Agency
Special thanks to
Interfaculty Initiative in Information Studies, The University of Tokyo
International Symposium on the CREST Digital Archiving Project
Ikeuchi Laboratory
The University of Tokyo
Japan
© Daisuke Miyazaki 2005
All rights reserved.
http://www.cvl.iis.u-tokyo.ac.jp/
Daisuke Miyazaki, Katsushi Ikeuchi, "Polarization-based
Shape Estimation of Transparent Objects for Digitizing
Cultural Assets," in Proceedings of International Symposium
on the CREST Digital Archiving Project, pp. 34-41, Tokyo,
Japan, 2005.03
International Symposium on the CREST Digital Archiving Project