2. Combining Laser Scans Yong Joo Kil 1, Boris Mederos 2, and Nina Amenta 1 1 Department of Computer Science, University of California at Davis 2 Instituto Nacional de Matematica Pura e Aplicada - IMPA IDAV Institute for Data Analysis and Visualization Visualization and Graphics Research Group

3. 2D Super Resolution A Fast Super-Resolution Reconstruction Algorithm, [Michael Elad, Yacov Hel-Or] Low Resolution ImagesSuper Resolution Image

4. Surface Super Resolution One Raw Scan Super resolved (100 scans) Photo

5. Improve 3D Acquisition Methods Better hardware –Costly Multiple scans + software –Refine output of current hardware –Cost effective –Smaller devices

6. Physical Setup xyxy z (viewing direction) Minolta Vivid 910

7. 3D Super Resolution Pipeline Input Scans Global Registration Super Resolution Super Registration Convergence No Yes Smoothing Super Resolution Mesh

8. Viewing direction axis z x y

9. Sample Points Low Resolution Sample Spacing Width Of one Scan

10. Super Resolution Sample Spacing q N(q) width/4

11. 2.5D Super Resolution

12. First Super Resolution Mesh (S 1 )

13. Super Resolution Method Input Scans Global Registration Super Resolution Super Registration Convergence No Yes Smoothing Super Resolution Mesh

14. Bilateral Filter

15. Super Resolution Method Input Scans Global Registration Super Resolution Super Registration Convergence No Yes Smoothing Super Resolution Mesh

16. Super Registration raw scan super resolution mesh

17. Second Super Resolution Mesh S 2

18. Super Resolution Method Input Scans Global Registration Super Resolution Super Registration Convergence No Yes Smoothing Super Resolution Mesh

19. Point Samples (1 st Model) Derived from Super-Resolution Reconstruction of Images - Static and Dynamic Paradigms [Michael Elad] Nyquist Sampling Theorem: Sample signal finely enough, then Reconstruct original signal perfectly. Band limited signal

20. Sampling at lower resolution Derived from Super-Resolution Reconstruction of Images - Static and Dynamic Paradigms [Michael Elad] That’s it!

21. Linear Model with Blur (2 nd Model) High- Resolution Image X Derived from Super-Resolution Reconstruction of Images - Static and Dynamic Paradigms [Michael Elad] C Blur 1 D 1 Decimation Low- Resolution Images Transformation F 1 Y 1 E 1 Noise + C N F N D N Y N E N +

22. The Model as One Equation Derived from Super-Resolution Reconstruction of Images - Static and Dynamic Paradigms [Michael Elad]

23. Model for 3D laser scan?

24. Pipeline : Laser Scanner Derived from Better Optical Triangulation through Spacetime Analysis, Curless and Levoy, 1995 laser beam Surface Peak reconstruction CCD sensor

25. Video sequence x y time

26. Non Linear functions

27. Simplification Assume –Points from Surface –Gaussian Noise

28. Point Sampling Model High- Resolution Image X C Blur k D k Decimation Low- Resolution Images Transformation F k x [ ELAD M., HEL-OR Y.: A fast super-resolution reconstruction algorithm for pure translational motion and common space invariant blur. IEEE Transactions on Image Processing 10,8 (2001) ] Solution Average Y k E k Gaussian Noise +

29. Simplification Solution –Register scans –Averaging Easy Inexpensive It works!

30. Close-up Scan of Parrot 146 Scans 4 times the original resolution.

31. Super resolve far & close objects? Derived from Better Optical Triangulation through Spacetime Analysis, Curless and Levoy, 1995 Surface CCD sensor

32. Super resolve small & large objects? One raw ScanSuper resolution (117 scans)

33. Is it worth taking more than one scan? One raw scan Super resolution PhotographSubdivion of (a)

34. Is it worth shifting? With Shifts (117scans)Without Shifts (117scans)

35. How many scans are enough?

36. Point Distribution

37. Tiling Artifact

38. Sampling Pattern Random xy shift + Rotation

39. Mayan Tablet (One Scan)

40. 39 Mayan Tablet (90 scans)

41. 40 Before & After

42. 41 Systematic Errors Super resolvedPhoto

43. 42 Parrot Model (6 views * 100 scans)

44. Future work 2.5D to 3D Resolving Systematic Errors Other Devices

45. Acknowledgements Kelcey Chen Geomagic Studios NSF CCF-0331736 Brazilian National Council of Technological and Scientific Development (CNPq)

46. 45 Extras

47. Interpolations

48. Nyquist frequency

49. 48 Data

51. 50 Solving this linear system is equivalent to an average. [ ELAD M., HEL-OR Y.: A fast super-resolution reconstruction algorithm for pure translational motion and common space invariant blur. IEEE Transactions on Image Processing 10,8 (2001) ] Mimize Diagonal Matrix Can be a permutation or displacement matrix Equivalent to

52. 51 Error between low res and super res.

53. 52 Error between low res and super res.

54. 53 Registeration result

55. 54 Before and After Registration

56. 55 Error between low res and super res.

57. 56 Least Squares Minimize: Solve by:, or Steepest Descent Iteration:,