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 - PowerPoint PPT Presentation
Combining Laser Scans Combining Laser Scans Yong Joo Kil Yong Joo Kil 1 , Boris Mederos , Boris Mederos 2 , and Nina Amenta , and Nina Amenta 1 1 1 Department of Computer Science, University of Department of Computer Science, University of California at Davis California at Davis 2 Instituto Nacional de Matematica Pura e Aplicada - Instituto Nacional de Matematica Pura e Aplicada - IMPA IMPA IDAV IDAV Institute for Data Analysis and Visualizati Institute for Data Analysis and Visualizati Visualization and Graphics Research Group Visualization and Graphics Research Group
Transcript
Combining Laser ScansCombining Laser Scans
Yong Joo KilYong Joo Kil11, Boris Mederos, Boris Mederos22, and Nina Amenta, and Nina Amenta11
1 1 Department of Computer Science, University of California at DavisDepartment of Computer Science, University of California at Davis22 Instituto Nacional de Matematica Pura e Aplicada - IMPA Instituto Nacional de Matematica Pura e Aplicada - IMPA
IDAV IDAV Institute for Data Analysis and VisualizationInstitute for Data Analysis and VisualizationVisualization and Graphics Research GroupVisualization and Graphics Research Group
2D Super Resolution2D Super Resolution
A Fast Super-Resolution Reconstruction Algorithm, [Michael Elad, Yacov Hel-Or]
Low Resolution Images Super Resolution Image
Surface Super ResolutionSurface Super Resolution
One Raw Scan Super resolved (100 scans) Photo
Improve 3D Acquisition MethodsImprove 3D Acquisition Methods
• Better hardware– Costly
• Multiple scans + software– Refine output of current hardware – Cost effective– Smaller devices
Physical SetupPhysical Setup
xy
z (viewing
direction)
Minolta Vivid 910
3D Super Resolution Pipeline3D Super Resolution Pipeline
Super Resolution Sample SpacingSuper Resolution Sample Spacing
q
N(q)width/4
2.5D Super Resolution2.5D Super Resolution
First Super Resolution Mesh (S1)First Super Resolution Mesh (S1)
Super Resolution MethodSuper Resolution Method
Input Scans Global Registration
Super Resolution
Super Registration
Convergence
No
Yes
Smoothing Super Resolution Mesh
Bilateral FilterBilateral Filter
Super Resolution MethodSuper Resolution Method
Input Scans Global Registration
Super Resolution
Super Registration
Convergence
No
Yes
Smoothing Super Resolution Mesh
Super RegistrationSuper Registration
raw scan super resolution mesh
Second Super Resolution Mesh S2Second Super Resolution Mesh S2
Super Resolution MethodSuper Resolution Method
Input Scans Global Registration
Super Resolution
Super Registration
Convergence
No
Yes
Smoothing Super Resolution Mesh
Point Samples (1st Model)Point Samples (1st Model)
Derived from Super-Resolution Reconstruction of Images - Static and Dynamic Paradigms [Michael Elad]
Nyquist Sampling Theorem:Sample signal finely enough, thenReconstruct original signal perfectly.
Band limited signal
Sampling at lower resolutionSampling at lower resolution
Derived from Super-Resolution Reconstruction of Images - Static and Dynamic Paradigms [Michael Elad]
That’s it!
Linear Model with Blur (2nd Model)Linear Model with Blur (2nd Model)
Nkkkkkk EXY 1 FCD
High-ResolutionImage X
Derived from Super-Resolution Reconstruction of Images - Static and Dynamic Paradigms [Michael Elad]
C
Blur
1 D1
Decimation
Low-Resolution
Images
Transformation
F1
Y1E1
Noise
+
CNFN DN
YNEN+
Nkkkkkk EX 1Y FCD
The Model as One Equation
NNNNN E
E
E
X
Y
Y
Y
2
1
222
111
2
1
FCD
FCD
FCD
EX HY
Derived from Super-Resolution Reconstruction of Images - Static and Dynamic Paradigms [Michael Elad]
Model for 3D laser scan? Model for 3D laser scan?
Pipeline : Laser Scanner Pipeline : Laser Scanner
Derived from Better Optical Triangulation through Spacetime Analysis, Curless and Levoy, 1995
laser beam
SurfacePeak reconstructionCCD sensor
Video sequenceVideo sequencex
y
time
Non Linear functionsNon Linear functions
f ( ) =
g ( ) =
SimplificationSimplification
• Assume– Points from Surface– Gaussian Noise
Point Sampling ModelPoint Sampling Model
High-ResolutionImage X
C
Blur
k Dk
Decimation
Low-Resolution
ImagesTransformation
Fk 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
YkEk
Gaussian Noise
+
SimplificationSimplification
• Solution– Register scans– Averaging
• Easy
• Inexpensive
• It works!
Close-up Scan of ParrotClose-up Scan of Parrot• 146 Scans• 4 times the original resolution.
Super resolve far & close objects?Super resolve far & close objects?
Derived from Better Optical Triangulation through Spacetime Analysis, Curless and Levoy, 1995
SurfaceCCD sensor
Super resolve small & large objects?Super resolve small & large objects?
One raw Scan Super resolution (117 scans)
Is it worth taking more than one scan? Is it worth taking more than one scan?
One raw scan Super resolution PhotographSubdivion of (a)
Is it worth shifting?Is it worth shifting?
With Shifts (117scans) Without Shifts (117scans)
How many scans are enough?How many scans are enough?
Parrot Model (6 views * 100 scans)Parrot Model (6 views * 100 scans)
Future workFuture work
• 2.5D to 3D
• Resolving Systematic Errors
• Other Devices
AcknowledgementsAcknowledgements
• Kelcey Chen
• Geomagic Studios
• NSF CCF-0331736
• Brazilian National Council of Technological and Scientific Development (CNPq)
45
ExtrasExtras
InterpolationsInterpolations
Nyquist frequencyNyquist frequency
48
DataData
g-1( ) =
50
N
k 1kk
tk
tk FDDFR
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) ]
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) ]
2
1k ||Y||)( XFDX k
N
kk
kF
PRX
N
k 1k
tk
tk YDFP
Mimize
Diagonal MatrixDiagonal Matrix
Can be a permutation or displacement matrixCan be a permutation or displacement matrix
Equivalent to Equivalent to
51
Error between low res and super res.Error between low res and super res.
52
Error between low res and super res.Error between low res and super res.
53
Registeration resultRegisteration result
54
Before and After RegistrationBefore and After Registration
55
Error between low res and super res.Error between low res and super res.
