My PhD Thesis Work

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My PhD Thesis Work
(University of Washington, 91-94)

• With
• Tony DeRose (Computer Science)
• Tom Duchamp (Mathematics)
• John McDonald (Statistics)
• Werner Stuetzle (Statistics)
• ...

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3D Scanning
computer-aided design (CAD)
digital model
physical object
reverse engineering/ 3D scanning
shape
color
material
surface reconstruction
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Why 3D scanning?

• Digital models for many objects dont exist.
• reverse engineering (Boeing 737X)
• archiving
• virtual environments
• Traditional design (using clay)
• car industry
• computer animation
• 3D faxing!

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Surface reconstruction
pointsP
surface S

• reverse engineering
• traditional design (wood,clay)
• virtual environments

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Previous work
surface topological type
simple
arbitrary
meshes
Schumaker93,
Hoppe-etal92,93, Turk-Levoy94, ...
implicit
Sclaroff-Pentland91, ...
Moore-Warren91, Bajaj-etal95
subdivision
-
Hoppe-etal94
smooth surfaces
B-spline
Schmitt-etal86, Forsey-Bartels95,...
Krishnamurthy-LevoyEck-Hoppe96,
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Surface reconstruction problem

• Given points P sampled from unknown surface
  U
• Goal reconstruct a surface S approximating U
• accurate (w.r.t. P, and U!)
• concise

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Why is this difficult?

• Points P
• unorganized
• noisy
• Surface S
• arbitrary, unknown topological type
• sharp features
• Algorithm must infer
• topology, geometry, and sharp features

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3-Phase reconstruction method
points
Goals
Find initial surface of correct topological
type.
phase 1
SIGGRAPH92
initial mesh
Improve its accuracy and conciseness.
phase 2
SIGGRAPH93
optimized mesh
Find piecewise smooth surface.
phase 3
SIGGRAPH94
Detect sharp features automatically
optimizedsubdivision surface
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Example
1
2
13,000 points
3
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Phase 1 Initial surface estimation

• If U were known, it would satisfy U Z(d)
  p d(p)0 ,where d(p) is the signed distance
  of p to U

d(p)?







U













d(p)?













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S
P
Estimate d from P
Extract Z(d)
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Phase 1 (contd)

• How to estimate d?

compute tangent planes
orient them consistently
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Phase 1 (contd)

• How to extract Z(d)?

run marching cubes
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Phase 2 Mesh optimization
2

• Input data points P, initial mesh Minitial
• Output optimized mesh M, minimizing
  E(M) Edistance Ecomplexity

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Phase 2 (contd)

• Optimization over

• the number of vertices

• their connectivity

• their positions

Þ consider any mesh of the same topological type
as Minitial
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Phase 2 (contd)

• Nested optimization
• optimize connectivity
• for fixed connectivity, optimize geometry

• Greedy approach
• consider local perturbations
• accept if DE(M)lt0

edge collapse
edge swap
edge split
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Phase 2 Results
using 31,000 points from Digibotics, Inc.
using 13,000 points
using 182,000 points
from Technical Arts Co.
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Phase 3 Piecewise smooth surface
3

• piecewise planar Þ piecewise smooth surface

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Subdivision surfaces
Loop87
M0
M1
M2
SM
Hoppe-etal94
tagged control mesh
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Phase 3 (contd)

• Generalize phase 2 optimization

edge collapse
edge swap
edge split
edge tag

• Again, apply perturbation if DE(M)lt0

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Phase 3 Results
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Related work
volumetric repr. (CurlessLevoy)
phase 1
alpha shapes (Edelsbrunner)
initial mesh
phase 2
optimized mesh
NURBS surface (KrishnamurthyLevoy)
(EckHoppe)
phase 3
optimizedsubdivision surface
CAD models (Sequin)