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.

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Presentation transcript:

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

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

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

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

Physical Setup xyxy z (viewing direction) Minolta Vivid 910

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

Viewing direction axis z x y

Sample Points Low Resolution Sample Spacing Width Of one Scan

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

2.5D Super Resolution

First Super Resolution Mesh (S 1 )

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

Bilateral Filter

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

Super Registration raw scan super resolution mesh

Second Super Resolution Mesh S 2

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

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

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

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 +

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

Model for 3D laser scan?

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

Video sequence x y time

Non Linear functions

Simplification Assume –Points from Surface –Gaussian Noise

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 +

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

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

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

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

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

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

How many scans are enough?

Point Distribution

Tiling Artifact

Sampling Pattern Random xy shift + Rotation

Mayan Tablet (One Scan)

39 Mayan Tablet (90 scans)

40 Before & After

41 Systematic Errors Super resolvedPhoto

42 Parrot Model (6 views * 100 scans)

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

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

45 Extras

Interpolations

Nyquist frequency

48 Data

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

51 Error between low res and super res.

52 Error between low res and super res.

53 Registeration result

54 Before and After Registration

55 Error between low res and super res.

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