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Seminar WS 08/09 Surface Reconstruction Dr. Peer Stelldinger S Surface f Reconstruction Digitalisierung Surface Reconstruction: Dr. Peer Stelldinger WS 2008/2009 p. 2 Digitalisierung Abtastung Rekonstruktion Anwendung Anwendung

slide-1
SLIDE 1

Seminar WS 08/09 Surface Reconstruction

  • Dr. Peer Stelldinger

S f Surface Reconstruction

slide-2
SLIDE 2

Digitalisierung

  • p. 2

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

slide-3
SLIDE 3

Digitalisierung

Abtastung Rekonstruktion Anwendung Anwendung

  • p. 3

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

slide-4
SLIDE 4

Rekonstruktion

Bedienungen an die Abtastung Bedienungen an die Abtastung B i f h Beweisverfahren Methode

  • p. 4

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

slide-5
SLIDE 5

Surface Reconstruction

  • Computational Geometry

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 5
slide-6
SLIDE 6

Surface Reconstruction

  • Computational Geometry
  • Surface Fitting

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 6
slide-7
SLIDE 7

Surface Reconstruction

  • Computational Geometry
  • Surface Fitting
  • Implicit Function Fitting

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 7
slide-8
SLIDE 8

Computational Geometry

  • Voronoi Diagrams, Delaunay Triangulations and

Alpha Shapes

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 8
slide-9
SLIDE 9

Computational Geometry

  • Voronoi Diagrams, Delaunay Triangulations and

Alpha Shapes

  • Flow Shapes
  • Flow Shapes

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 9
slide-10
SLIDE 10

Computational Geometry

  • Voronoi Diagrams, Delaunay Triangulations and

Alpha Shapes

  • Flow Shapes
  • Flow Shapes
  • r-Regular Shape Reconstruction

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 10
slide-11
SLIDE 11

Computational Geometry

  • Voronoi Diagrams, Delaunay Triangulations and

Alpha Shapes

  • Flow Shapes
  • Flow Shapes
  • r-Regular Shape Reconstruction
  • One Triangle at a Time

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 11
slide-12
SLIDE 12

Computational Geometry

  • Voronoi Diagrams, Delaunay Triangulations and

Alpha Shapes

  • Flow Shapes
  • Flow Shapes
  • r-Regular Shape Reconstruction
  • One Triangle at a Time
  • Lower Dimensional Localized Delaunay

Triangulation

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 12
slide-13
SLIDE 13

Computational Geometry

  • Voronoi Diagrams, Delaunay Triangulations and

Alpha Shapes

  • Flow Shapes
  • Flow Shapes
  • r-Regular Shape Reconstruction
  • One Triangle at a Time
  • Lower Dimensional Localized Delaunay

Triangulation

  • Ball Pivoting

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 13
slide-14
SLIDE 14

Computational Geometry

  • Voronoi Diagrams, Delaunay Triangulations and

Alpha Shapes

  • Flow Shapes
  • Flow Shapes
  • r-Regular Shape Reconstruction
  • One Triangle at a Time
  • Lower Dimensional Localized Delaunay

Triangulation

  • Ball Pivoting
  • Crust

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 14
slide-15
SLIDE 15

Computational Geometry

  • Voronoi Diagrams, Delaunay Triangulations and

Alpha Shapes

  • Flow Shapes
  • Flow Shapes
  • r-Regular Shape Reconstruction
  • One Triangle at a Time
  • Lower Dimensional Localized Delaunay

Triangulation

  • Ball Pivoting
  • Crust
  • Power Crust

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 15
slide-16
SLIDE 16

Computational Geometry

  • Voronoi Diagrams, Delaunay Triangulations and

Alpha Shapes

  • Flow Shapes
  • Flow Shapes
  • r-Regular Shape Reconstruction
  • One Triangle at a Time
  • Lower Dimensional Localized Delaunay

Triangulation

  • Ball Pivoting
  • Crust
  • Power Crust
  • Cocone
  • Cocone

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 16
slide-17
SLIDE 17

Computational Geometry

  • Voronoi Diagrams, Delaunay Triangulations and

Alpha Shapes

  • Flow Shapes
  • Flow Shapes
  • r-Regular Shape Reconstruction
  • One Triangle at a Time
  • Lower Dimensional Localized Delaunay

Triangulation

  • Ball Pivoting
  • Crust
  • Power Crust
  • Cocone
  • Cocone
  • Homology of Submanifolds

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 17
slide-18
SLIDE 18

Computational Geometry

  • Voronoi Diagrams, Delaunay Triangulations and

Alpha Shapes

  • Flow Shapes
  • Flow Shapes
  • r-Regular Shape Reconstruction
  • One Triangle at a Time
  • Lower Dimensional Localized Delaunay

Triangulation

  • Ball Pivoting
  • Crust
  • Power Crust
  • Cocone
  • Cocone
  • Homology of Submanifolds
  • Lipschitz Surfaces

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 18
slide-19
SLIDE 19

Computational Geometry

  • Voronoi Diagrams, Delaunay Triangulations and

Alpha Shapes

  • Flow Shapes
  • Flow Shapes
  • r-Regular Shape Reconstruction
  • One Triangle at a Time
  • Lower Dimensional Localized Delaunay

Triangulation

  • Ball Pivoting
  • Crust
  • Power Crust
  • Cocone
  • Cocone
  • Homology of Submanifolds
  • Lipschitz Surfaces
  • r-Stable Reconstruction

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 19
slide-20
SLIDE 20

Surface Fitting

  • Adaptive Meshes

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 20
slide-21
SLIDE 21

Surface Fitting

  • Adaptive Meshes
  • Balloon Fitting

g

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 21
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SLIDE 22

Surface Fitting

  • Adaptive Meshes
  • Balloon Fitting

g

  • Surface Inferencing

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 22
slide-23
SLIDE 23

Surface Fitting

  • Adaptive Meshes
  • Balloon Fitting

g

  • Surface Inferencing
  • Moving Least Squares

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 23
slide-24
SLIDE 24

Implicit Function Fitting

  • Surfaces from Unorganized Points

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 24
slide-25
SLIDE 25

Implicit Function Fitting

  • Surfaces from Unorganized Points
  • Radial Basis Functions

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 25
slide-26
SLIDE 26

Implicit Function Fitting

  • Surfaces from Unorganized Points
  • Radial Basis Functions
  • Level Sets

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 26
slide-27
SLIDE 27

Implicit Function Fitting

  • Surfaces from Unorganized Points
  • Radial Basis Functions
  • Level Sets
  • FFT-Based Reconstruction

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 27
slide-28
SLIDE 28

References

  • Voronoi Diagrams, Delaunay Triangulations and Alpha Shapes

– “The Union of Balls and Its Dual Shape*”, 1995, H. Edelsbrunner – “Three-Dimensional Alpha Shapes”, 1995, H. Edelsbrunner, E.P. Mücke – “Introduction to Alpha Shape”, 2000, K. Fisher Introduction to Alpha Shape , 2000, K. Fisher

  • Flow Shapes

– „The Flow Complex: A Data Structure for Geometric Modeling“, 2003, J. Giesen, M. John – “Alpha-Shapes and Flow Shapes are Homotopy Equivalent”, 2003, T.K. Dey, J. Giesen, M. John

  • r-Regular Shape Reconstruction

– „r-Regular Shape Reconstruction from Unorganized Points“, 1997, D. Attali

  • One Triangle at a Time

– “Surface Reconstruction, One Triangle at a Time”, 2004, D. Freedman

  • Lower Dimensional Localized Delaunay Triangulation

– “Surface Reconstruction based on Lower Dimensional Localized Delaunay Triangulation”, 2000, M. Gopi, S. Krishman, C.T. Silva

  • Ball Pivoting

Th B ll Pi ti Al ith f S f R t ti ” 1997 F B di i J Mittl H R h i C Sil – „The Ball-Pivoting Algorithm for Surface Reconstruction”, 1997, F. Bernardini, J. Mittleman, H. Rushmeier, C. Silva,

  • G. Taubin
  • Crust

– „the Crust and the β-Skeleton: Combinatirial Curve Reconstruction“, 1998, N. Amenta, M. Bern, D. Eppstein – A New Voronoi-Based Surface Reconstruction Algorithm “ 1998 N Amenta M Bern M Kamvysselis „A New Voronoi Based Surface Reconstruction Algorithm , 1998, N. Amenta, M. Bern, M. Kamvysselis

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 28
slide-29
SLIDE 29

References

  • Power Crust

– „The Power Crust “, 2001, N. Amenta, S. Choi, R.K. Kolluri – „The Power Crust, Union of Balls, and the Medial Axis Transform“, 2001, N. Amenta, S. Choi, R.K. Kolluri „The Power Crust, Union of Balls, and the Medial Axis Transform , 2001, N. Amenta, S. Choi, R.K. Kolluri

  • Cocone

– „A Simple Algorithm for Homeomorphic Surface Reconstruction“, 2001, N. Amenta, S. Choi, T.K. Dey, N. Leekha – „ Tight Cocone : A Watertight Surface Reconstructor“, 2003, T.K. Dey, S. Goswami

  • Homology of Submanifolds

gy

– “Finding the Homology of Submanifolds with High Confidence from Random Samples”, 2004, P. Niyogi, S. Smale, S. Weinerger

  • Lipschitz Surfaces

– “Provably Good Sampling and Meshing of Lipschitz Surfaces”, 2006, J-D. Boissonnat, S. Oudot – “Guaranteed-Quality Mesh Generation for Curved Surfaces”, 1993, L.P. Chew

  • r-Stable Reconstruction

– “Topologically Correct 3D Surface Reconstruction and Segmentation from Noisy Samples”, 2008, P. Stelldunger

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 29
slide-30
SLIDE 30

References

  • Adaptive Meshes

– “Sampling and Reconstruction with Adaptive Meshes”, 1991, D. Terzopulos, M. Vasilescu

  • Balloon Fitting

– Description of Complex Objects from Multiple Range Images Using an Inflating Balloon Model“ 1995 Y Chen G „ Description of Complex Objects from Multiple Range Images Using an Inflating Balloon Model , 1995, Y. Chen, G. Medioni

  • Surface Inferencing

– „ Inference of Surfaces, 3D Curves, and Junctions From Sparse, Noisy, 3D Data“, 1997, G. Guy, G. Medioni – „ Inference of Integrated Surface, Curve, and Junction Descriptions, From Sparse 3D Data“, 1998

  • Moving Least Squares

– „Drawing Contours from Arbirtrary Data Points“, 1974 D.H. McLain – „Mesh-Independent Surface Interpolation“, 2003, D. Levin

  • Surfaces from Unorganized Points

– „ Surface Reconstruction from Unorganized Points“,1992, H. Hoppe, T. DeRose, T. Duchamp

  • Radial Basis Functions

– „Reconstruction and Representation of 3D Objects with Radial Basis Functions“, 2001, J.C. Carr, R.K. Beatson, J.B. Cherrie, T.J. Mitchel, W.R. Fright, B.C. McCallum, T.R. Evans

L l S t

  • Level Sets

– „Fast Surface Reconstruction Using the Level Set Method“, 2001, H.K. Zhao, S. Osher, R. Fedkiw – „Visualization, Analysis and Shape Reconstruction of Unorganized Data Sets“, 2002, H.K. Zhao, S. Osher

  • FFT-Based Reconstruction

Reconstruction of Solid Models from Oriented Point Sets“ 2005 M Kazhdan – „ Reconstruction of Solid Models from Oriented Point Sets , 2005, M. Kazhdan

WS 2008/2009

Surface Reconstruction: Dr. Peer Stelldinger

  • p. 30