The document presents a method for recovering the shape of transparent objects by leveraging time-of-flight (ToF) distortion caused by the refractive index. Utilizing a modified ToF camera, it discusses the challenges and contributions related to 3D reconstruction, integrating parameters like known refractive index and reference 3D points for accurate depth estimation. Experimental results demonstrate the effectiveness of this approach with specific mean errors for various transparent materials.

1. Recovering Transparent Shape
from Time-of-Flight Distortion
(CVPR2016)
1
K. Tanaka Y. Mukaigawa H. Kubo Y. Matsushita Y. Yagi

2. Transparent Objects
• Invisible, but distorted background can be seen.
• 3D reconstruction of transparent material is challenging.
3
Sensor
Estimated point
by triangulation
BackgroundReference
Distorted

3. Time-of-Flight (ToF) Camera
• Depth sensor based on time delay of light
• Kinect v2, Project Tango, etc.
4
time
Light signal
Observation
𝑡Δ
𝑑 =
𝑐𝑡Δ
2
(speed of light x time delay)

4. Time of Flight Distortion
• Speed of light slows down depending on refractive index.
• Depth becomes longer ( = ToF Distortion).
• We use this distortion for transparent shape recovery.
5
c
c
c

5. Contributions
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1. ToF distortion can be used for transparent shape recovery.
2. Easy multi-path mitigation using retroreflective sheet.
c
c
c

6. Problem Setting
Input
• Known refractive index
• 1 distorted ToF depth
• 2 references (3D points)
7
r
f
b
r
t
v v
r
s
Output
• 3D points of both surfaces
• Surface normals

7. Parameters and Candidate Shapes
• Candidate shapes
• Front surface is on camera ray at distance 𝑡
• Back surface is on reference ray at distance 𝑠
• Many candidates. (2 degree of freedom)
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ToF camera
𝑡
Glass object
Display or
known pattern
𝑠

8. Candidate Shape using ToF Distortion
• Candidate shapes
• Front surface is on camera ray at distance 𝑡
• Back surface is on reference ray at distance 𝑠
• such that 𝑠 + 𝑡 + 𝜂 = 𝑙 𝑇𝑜𝐹 : ToF distortion
• One degree of freedom
9
ToF camera
𝑡
Glass object
Display or
known pattern
𝑠

9. Surface Normal Consistency
• Surface normal is unique
Refractive normal
Geometric normal
• They should coincide.
10
ToF camera
𝑡
Glass object
Display or
known pattern
𝑠
𝑛 =
sin 𝜃1
sin 𝜃2
Refractive normal
camera ray
Geometric normal

10. Real world experiment setup
• modified Kinect v2 and LCD panel
11
Kinect v2
(IR Lens changed)
LCD panel
Linear stage
Target object

11. Results and evaluations
• Target materials and estimated results
• Evaluation
• Fit estimated points to ground-truth CAD model by ICP
12
Cube Wedge prism Schmidt prism
Object Mean error Std. dev.
Cube 0.188 mm 0.458 mm
Wedge 0.226 mm 1.137 mm
Schmidt 0.381 mm 1.398 mm

12. Summary
Input
• 1 distorted ToF depth
• 2 references (3D points)
• Known refractive index
13
r
f
b
r
t
v v
r
s
Output
• 3D points of both surfaces
• Surface normals

13. Time-of-Flight as alternative imager
• Light-in-flight [Gkioulekas+2015]
• Parameter tunable ToF camera (Texas instruments)
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14. Imaging, Analyzing using ToF Camera
• Recently Emerging Topic
[Heide+2013], [Kadambi+2013], [Naik+2013], [Godbaz+2013], [Freedman+2014],
[Lin+2014], [O’Toole+2014], [Gupta+2015], [Heide+2015], [Xiao+2015],
[Kadambi+2015], [Peters+2015], [Tadano+2015], and more!
• CVPR 2016
• 1 oral, 2 posters (including ours)
[Kadambi et al.], [Su et al.]
• SIGGRAPH 2016
• 2 technical papers.
[Shrestha et al.], [Kadambi et al.]
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We will continue working on ToF camera