what does motion reveal about transparency ?
DESCRIPTION
What Does Motion Reveal About Transparency ?. Moshe Ben-Ezra and Shree K. Nayar Columbia University ICCV Conference October 2003, Nice, France. This work was supported by an NSF ITR Award IIS-00-85864. Transparency is Very Challenging. Existence of a transparent object. - PowerPoint PPT PresentationTRANSCRIPT
What Does Motion Reveal About Transparency ?
Moshe Ben-Ezra and Shree K. NayarColumbia University
ICCV ConferenceOctober 2003, Nice, France
This work was supported by an NSF ITR Award IIS-00-85864
Transparency is Very Challenging
• Existence of a transparent object.• Finding its shape and pose
Real and Virtual Features
Lambertian
V1 V2
F`
V2
V1 F
Specular
F
F`
V1 V2
Transparent
Environmental Matting*
* Zongker, el al. SIGGRAPH 99,
Alternatingpattern Object Camera
• Does not recover shape and pose.• Requires controlled environment.
Shape from Polarization in Highlight*
* Saito et al. CVPR’99.
Object
CameraLight
RotatingPolarizer
• Limited to a single interface at the object’s surface.• Requires controlled environment.
N
Shape from Refraction and Motion*
* H. Murase. PAMI, 1992
Camera
Water
• Single interface only.
Fixed Pattern
Motion is Key to Transparency
Transparent Shape From Motion
Given: Views
1,,222
,
n
ne
eene zyxzyxs
And a Parametric Model (such as super-ellipse)
Recover:Shape: Values of parameters (e, n)Pose: Rotation R, Translation T
General analytic solution does not exist.
Transparency From Motion
Reversed rays are parallel to each other regardless ofthe complexity of their paths
Distantfeature
Approach: Initialization
Image Plane
Image Plane
Approach: Initial Guess
Approach: Refine
Error Function
(0,0,1)
r1,1 .. r1,n
r2,1 .. r2,n
j iji rzTRff
Feature Ray ,1 ,cosvar,,
• - Object’s shape parameter vector• R,T - Object’s pose
Simulation SetupParallel rays
from features
Transparentobject
Cameraside rays
Example (Simulation)
Single Parameter. Newton-Raphson optimization
Initial GuessSymmetric Superellipse (n=e)
Evaluation (Simulation)
GT
Both init
Pos res
Sphere
Ground Truth
Initial Guess
ComputedResult
ShapeError
GT
Both Init
Both Res
Lens
GT
Both Init
Both Res
Cube
GT
Both Init
Both Res
Water Pipe
mm15013.0:t mm
8003.0:f
25.00001.0:emm
160064.0:d
Real Experiment: Sphere
Features
Initial Guess
Setup: Initial Guess
Initial Guess: Diameter: 8 inch
Setup: Result
Ground Truth: Diameter: 3 inch. Computed: 3.18 inch
Result
Real Test: Water Filled Pipe
Features
Initial Guess
Setup: Initial Guess
Initial guess: Diameter: 200.0mm Thickness: 20.0mm
Setup: Result
Ground Truth: Diameter: 117.0mm Thickness: 3.0mmComputed: Diameter: 116.1mm Thickness: 2.3mm
Result
Real Test: Superquadric
Features
Initial Guess
Result
Ground truth: e = ? Computed: e = 0.18
Summary
Shape and poseparameters
Multiple interfaces
No Segmentationrequired
Parameterizations of Interest
• Polynomials: modeling surfaces, lenses
• CAD models: shape of industrial objects
• Dynamic models: time dependent parameters
Assumptions
• Camera parameters are known.
• Features are far* and are trackable.
• A proper model and a hypothesis (an initial guess) are given.
* One possible assumption.
Real Tests Setup
Implementation
• Features were manually selected and tracked (9 views).
• Captured rays, a model, refraction index and a hypothesis were given as inputs.
• Shape and pose were recovered using simple gradient decent (with derivatives).
The Physics of TransparencyFirst Interface:
μ1→ μ2
Second Interface: μ2 →μ1
3
11
3
N1
N2
2 2
3211 sinsin :Refraction
2
111 sin
:reflection internal Total
2
21
221
,21
R :Reflection
Parametric Shape Examples
Super-Ellipse2 parameters
Spherical Harmonics8 parameters
No analytic solution