Inverse Polarization Raytracing:

1
Inverse Polarization Raytracing Estimating
Surface Shapes of Transparent Objects
Daisuke Miyazaki, Katsushi Ikeuchi Institute of
Industrial Science, The University of Tokyo
Objective
Polarization
Raytracing
Purpose
Surface normal
Estimate the 3D surface shape of transparent
objects
Reflected light
Incident light
Partially polarized
Input
Unpolarized
q1
q1
3 or more images of transparent object with
different angle of the polarizer
Calculate polarization
Material 1
Calculate intensity
Raytracing
Raytracing
Material 2
q2
Partially polarized
Output
Scalar
Scalar
Scalar
One piece of height map of the frontal surface of
transparent object
Transmitted light
Conventional raytracing
Polarization raytracing
Error
Algorithm
Cost function
Calc height
min
dxdy
Input
Calc.
Relationship between normal height
Input
Calc.
Calc normal
Update the surface normal in order to minimize
the error
Stop if error is small
Output height
Initial height
Calculate height and normal
Setup
Results
Monochrome camera
Camera adapter
Initial
Computer
IR/UV cut-off filter
Real object
Real object diameter 30mm
Linear polarizer
Initial previous method
20 iteration
Geodesic dome
Error(height)2.8mm Error(normal)14deg
Initial previous method
Front shape (estimated)
Plastic sphere
10 iteration
Front shape (truth)
40W lamp
Back shape (given)
Transparent object inside
Polarizer controller
50 iteration
Error(height)0.61mm Error(normal)7.0deg
Refractive index Illumination (given)
"Cocoon"
10 iteration
Rendering example
This research was supported in part by Ministry
of Education, Culture, Sports, Science and
Technology under the Leading Project,
"Development of High Fidelity Digitization
Software for Large-Scale and Intangible Cultural
Assets." Daisuke Miyazaki was supported by the
Japan Society for the Promotion of Science.
1 Daisuke Miyazaki, Katsushi Ikeuchi, "Inverse
Polarization Raytrading Estimating Surface
Shapes of Transparent Objects," in Proceedings of
International Conference on Computer Vision and
Pattern Recognition, San Diego, CA USA, June
2005. 2 ????, ????, "???????????????????????????
?," ??????????? D-II, 2005?8?.