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Combining Laser Scans Yong Joo Kil 1 , Boris Mederos 2 , and Nina Amenta 1

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

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Combining Laser Scans Yong Joo Kil 1 , Boris Mederos 2 , and Nina Amenta 1

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  1. Combining Laser Scans Yong Joo Kil1, Boris Mederos2, and Nina Amenta1 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

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

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

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

  5. xy Physical Setup Minolta Vivid 910 z (viewing direction)

  6. 3D Super Resolution Pipeline Global Registration Input Scans Super Resolution Smoothing Super Resolution Mesh Yes Convergence No Super Registration

  7. Viewing direction axis z x y

  8. Sample PointsLow Resolution Sample Spacing Width Of one Scan

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

  10. 2.5D Super Resolution

  11. First Super Resolution Mesh (S1)

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

  13. Bilateral Filter

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

  15. Super Registration super resolution mesh raw scan

  16. Second Super Resolution Mesh S2

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

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

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

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

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

  22. Model for 3D laser scan?

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

  24. Video sequence x y time

  25. Non Linear functions

  26. Simplification • Assume • Points from Surface • Gaussian Noise

  27. + k E Point Sampling Model Low- Resolution Images High- Resolution Image X Gaussian Noise Transformation Blur Decimation x Y F D C k k k k Solution 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) ]

  28. Simplification • Solution • Register scans • Averaging • Easy • Inexpensive • It works!

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

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

  31. Super resolve small & large objects? One raw Scan Super resolution (117 scans)

  32. Is it worth taking more than one scan? One raw scan Super resolution Subdivion of (a) Photograph

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

  34. How many scans are enough?

  35. Point Distribution

  36. Tiling Artifact

  37. Sampling Pattern Random xy shift + Rotation

  38. Mayan Tablet (One Scan)

  39. Mayan Tablet (90 scans)

  40. Before & After

  41. Systematic Errors Super resolved Photo

  42. Parrot Model (6 views * 100 scans)

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

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

  45. Extras

  46. Interpolations

  47. Nyquist frequency

  48. Data

  49. 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 Can be a permutation or displacement matrix Equivalent to Diagonal Matrix

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