Shape Measurement of Transparent Objects using Polarization and Geometrical Characteristics

1. Shape Measurement of Transparent Objects using Polarization and Geometrical Characteristics Daisuke MiyazakiInstitute of Industrial Science,The University of Tokyo

2. Overview • Introduction • Theory • Algorithm • Result • Conclusion

3. Aim • Shape measurement of transparent objects • Easy setup • Automatic calculation • Polarization and Geometrical Characteristics

4. Location θ θ φ

5. Location Polarizerangle CCD normal polarizer Incidenceangle light Reflectionangle Incidenceplane θ θ Incidenceplaneorientation φ object location

6. θ θ φ Light intensity and polarization • CCD camera and polarizer • Rotate polarizer • Light intensity

7. Rotate polarizer θ θ φ unpolarized Light wave polarized

8. Rotate polarizer Polarizer angle = φ 45° 45° 45° 45°

9. Polarization and angle • Orientation: • Degree of polarization: n : refractive index (given)

10. ρ θ1 θB θ2 θ Φ１ Φ2 180° Two probable angles • θ: (θ1, θ2) • φ: (φ1,φ2) (θB: Brewster angle)

11. z n θ θ n n θ θ x φ θ φ φ y Surface normal • n⇔(θ,φ)=(elevation,azimuth angle) Put camera over object coordinates

12. Halfway summary • 4 possible surface normals(θ1,φ1), (θ1,φ2), (θ2,φ1), (θ2,φ2) • Choose the correct θ and φ • Choosing correct azimuth angle φ • Choosing correct elevation θ

13. Choosing correct φ • φ1,φ2: direction is directly oppositei.e. |φ1-φ2|=180° • Choose the correct azimuth angle φ φ2 φ1 Two φ at each pixel Obtaining data 2D image of object

14. Background area Objectarea y x 2D 1D 1D direction of 2D angle • Looking through lines parallel to y axis • 1D direction of 2D azimuth angle φ • Direction changing point

15. (x, y) φ φ φ φ φ φ φ φ 2 2 2 2 2 2 2 2 φ φ φ φ φ φ φ φ 1 1 1 1 1 1 1 1 (x, y+1) change do notchange change do notchange Detect changing point • The point where φ stride across the line parallel to x axis at adjacent pixels

16. Summary of choosing φ • Looking through lines parallel to y axis • Thinking of 1D direction of 2D angle φ • Detect direction changing points • Determine the angle of object boundary as outside direction • Change the direction at changing point

17. ρ θ1 θB θ2 θ Choosing correct θ • θ1,θ2: calculate from ρ • Choose the correct elevation θ

18. z Rotate the object θ1 θ2 y ρ ρ2 ρ1 θ θ1 θ2 Rotate object • Rotate object around x axis • Examine changes of polarization degree

19. ρ ρ θ θ θ θ B B Patterns of changes of ρ Distinguish by direction of φ Distinguish by changes of ρ Distinguish by changes of ρ

20. Algorithm of choosing θ ρ: increase ρ: decrease ρ: increase ρ: decrease If above method doesn’t work well: determine as same as adjacent pixel

21. Summary of choosing θ • Rotate object around x axis • Thinking of changes of ρ • Choose the correct θ by angle φ and changes of ρ • If we cannot choose θ by above, determine by adjacent pixel

22. Height from normal • n=(θ,φ): chosen • Object height is calculated by relaxation method: iterative shown below p, q: surface gradient (x and y component each)

23. CCD Camera Lightsource Polarizer Object Opticaldiffuser Experimental setup • Optical diffuser behaves as surface illuminant

24. Experimental result • Result of acrylic hemisphere object

25. Conclusion • Obtain polarization data by easy setup • Calculated 4 possible surface normal • Chose the correct surface normal (θ and φ) • Object surface height is calculated

26. (c) Daisuke Miyazaki 2000All rights reserved. http://www.cvl.iis.u-tokyo.ac.jp/ 宮崎大輔, 斉藤めぐみ, 佐藤洋一, 池内克史, "偏光特性と幾何特性を利用した透明物体の表面形状計測," 情報処理学会コンピュータビジョンとイメージメディア研究会, 2000-CVIM-123, pp.33-42, 東京, 2000年9月