1. 3D Object Reconstruction Using Multiple Linear Light Sources in Image Scanner Advisor ：趙春棠 Chun-Tang Chao Master ：鍾明軒 Ming-Hsuan Chung 01

2. Outline  ABSTRACT  INTRODUCTION Image scanner Photometric models  Purpose  Materials and Methods 3D shape estimation using two groups of two light sources Surface normal vectors and color estimation Specular components estimation  EXPERIMENTAL RESULTS Shape estimation by two groups of two light sources Specular estimation by multiple light sources Shape and specular estimation for complex object  CONCLUSION  FUTURE WORKS  REFERENCES 02

3. Abstract Discusses a 3D shape measurement device based on an image scanner. Shape reconstruction method using the image scanner is one of the photometric stereo method applied to multiple linear light sources. 03

4. INTRODUCTION The reflectance intensity on the object surface depends on the object shape, color, specular components and so on. It is difficult to estimate these components directly from only one image intensity, therefore the photometric stereo method which uses some images have been developed. Employ the iterative process in which the shape, color and specular reflection components are estimated alternatively. Propose new method to estimate object shape, color and specular components at each point on a surface using several images taken by light sources located at different positions. In experiments, by using synthetic scanned images we discuss optimal position and number of light sources to estimate object shape and specular components. 04

5. INTRODUCTION Image scanner  Figure01. Image scanner 05

6. INTRODUCTION  Figure02. Arrangement of K 1  Figure03. Arrangement of K 2 Image scanner 06

7. INTRODUCTION  Charge-coupled Device Image scanner 07

8. INTRODUCTION Photometric models  Equation 01. The illuminant intensity is attenuated according to the distance from the light source  Equation 02. The Lambertian reflectance property on the object surface 08

9. INTRODUCTION  Equation 03. Torrance-Sparrow’s model  Equation 04. Cosθ (x, y) in Torrance-Sparrow’s model  Figure4. Vectors of specular reflection  Equation 05. γ (i) (x, y) in Torrance-Sparrow’s model 09 Photometric models

10. INTRODUCTION  Equation 08. The photometric model of the reflectance intensity  Equation 09. The photometric model of the reflectance intensity considering only the Lambertian reflection in our method. 10 Photometric models

11. Purpose A method to recover object shape, color and reflectance properties from scanned images taken by an image scanner. These devices are usually very expensive for the general person to use it. The calibration operation and the treatment is troublesome. It can be also used as a low cost and easy operating shape scanner. 11

12. Materials and Methods  Figure05. Outline of method 12

13. Materials and Methods 3D shape estimation using two groups of two light sources  Figure06. Arrangement of two light source(a)_Same direction from a point on the object surface  Equation 10. The ratio of these photometric models is derived as a equation only for z. 13

14. Materials and Methods  Figure06. Arrangement of two light source(b)_Two groups of light sources  Equation 11. The ratio of these photometric models is derived as a equation only for z. 14 3D shape estimation using two groups of two light sources

15. Materials and Methods Surface normal vectors and color estimation  Equation 12. The surface normal vector (n x, n y, n z ) and color (the Lambertian albedos) ρ(c) (c = {r, g, b}) at (x, y) on the object surface are estimated by minimizing  Equation 13. The surface normal vector (N) and the direction of light source (Li) is smaller than a threshold angle (t2) 15

16. Materials and Methods  Equation 14. The specular reflection P S(ic) (x, y)  Equation 15. Equation is a linear equation about log ρ s(c) and 1/σ 2 (c) 16 Surface normal vectors and color estimation

17. Materials and Methods  Equation 16. The linear least squares  Equation 17. Include only the Lambertian reflection (no specular reflection) 17 Surface normal vectors and color estimation

18. Materials and Methods  Equation 18. The surface normal vector (N) and the direction of light source (Li) is smaller than a threshold angle (t2) 3D shape estimation using two groups of two light sources 18

19. EXPERIMENTAL RESULTS Shape estimation by two groups of two light sources  Figure08. Input scanned images  Table01. ALBEDO VALUES ON VIRTUAL HEMISPHERE 19

20. EXPERIMENTAL RESULTS  Figure07. Arrangement of light sources in shape estimation 20 Shape estimation by two groups of two light sources

21. EXPERIMENTAL RESULTS  Figure09. Estimated shapes 21 Shape estimation by two groups of two light sources

22. EXPERIMENTAL RESULTS  Figure10. Cross-section view of estimated shapes 22 Shape estimation by two groups of two light sources

23. EXPERIMENTAL RESULTS  Figure11. RMS errors of height z 23 Shape estimation by two groups of two light sources

24. EXPERIMENTAL RESULTS Specular estimation by multiple light sources  Figure12. Arrangement of light sources in specular estimation 24

25. EXPERIMENTAL RESULTS  Figure13. Finally estimated shapes 25 Specular estimation by multiple light sources

26. EXPERIMENTAL RESULTS  Figure14(a). Finally estimated shapes components 20 light sources 26 Specular estimation by multiple light sources

27. EXPERIMENTAL RESULTS  Figure14(b). Finally estimated shapes components 10 light sources 27 Specular estimation by multiple light sources

28. EXPERIMENTAL RESULTS  Figure14(c). Finally estimated shapes components 6 light sources 28 Specular estimation by multiple light sources

29. EXPERIMENTAL RESULTS Shape and specular estimation for complex object  Figure15. Part of input scanned images of complex object 29

30. EXPERIMENTAL RESULTS  Figure16. Estimated shapes of complex object 30 Shape and specular estimation for complex object

31. EXPERIMENTAL RESULTS  Figure17. Estimated specular components of complex object 31 Shape and specular estimation for complex object

32. CONCLUSION Discuss the method to measure the 3D shape, color and specular reflections of the object from scanned images using the image scanner. Propose the shape estimation method using two groups of two light sources located in same direction. The surface normal vectors, color and specular components estimation method using several light sources located on a circular path. 32

33. FUTURE WORKS Discuss the method to estimate specular components accurately using active moving light sources Examine the effectiveness of the proposed method using the actual scanner 33

34. REFERENCES [1] H.Ukida and K.Konishi, “3D Shape Reconstruction Using Three Light Sources in Image Scanner,” IEICE Trans. on Inf. & Syst., Vol.E84-D, No.12, pp.1713–1721, Dec. 2001. [2] R.J.Woodham, “Photometric Method for Determining Surface Orientation from Multiple Images,” Optical Engineering, Vol.19, No.1, pp.139– 144, 1980. [3] H. Ukida, Y.Tanimoto, T.Sano and H.Yamamoto, “3D shape, color and specular estimation using an image scanner with multiple illuminations,” Measurement Science and Technology, Vol.20, 104014, 10pp, 2009. [4] H. Ukida, Y.Tanimoto, T.Sano and H.Yamamoto, “3D Object Shape and Reflectance Property Reconstruction Using Image Scanner,” 2009 IEEE InternationalWorkshop on Imaging System and Techniques Proceedings, May 2009. [5] K.E.Torrance and E.M.Sparrow, “Theory for off-specular reflection from roughened surfaces,” In Journal of Optical Society of America, Vol.57, No.9, pp.1105–1114, 1967. 34