Transcript My PhD Thesis Work (University of Washington, ‘91-’94)  With: Tony DeRose (Computer Science) Tom Duchamp (Mathematics) John McDonald (Statistics) Werner Stuetzle (Statistics) ... 

My PhD Thesis Work
(University of Washington, ‘91-’94)

With:
Tony DeRose (Computer Science)
Tom Duchamp (Mathematics)
John McDonald
(Statistics)
Werner Stuetzle
(Statistics)
...

3D Scanning
computer-aided design (CAD)
digital
model
physical
object
reverse engineering/
3D scanning
shape
color
surface
reconstruction
material
Why 3D scanning?
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Digital models for many objects don’t exist.
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Traditional design (using clay)
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reverse engineering (Boeing 737X)
archiving
virtual environments
car industry
computer animation
3D faxing!
Surface reconstruction
points
P
surface
S
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reverse engineering
traditional design (wood,clay)
virtual environments
Previous work
surface topological type
simple
arbitrary
[Schumaker93], …
[Hoppe-etal92,93],
[Turk-Levoy94], ...
implicit
[Sclaroff-Pentland91],
...
[Moore-Warren91],
[Bajaj-etal95]
subdivision
-
[Hoppe-etal94]
B-spline
[Schmitt-etal86],
[Forsey-Bartels95],...
[Krishnamurthy-Levoy]
[Eck-Hoppe96],…
smooth surfaces
meshes
Surface reconstruction problem
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Given: points P sampled from
unknown surface U
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Goal: reconstruct a surface S approximating U
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accurate (w.r.t. P, and U!)
concise
Why is this difficult?
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Points P
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Surface S
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unorganized
noisy
arbitrary, unknown topological type
sharp features
Algorithm must infer:
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topology, geometry, and sharp features
3-Phase reconstruction method
points
[SIGGRAPH92]
Goals:
phase 1
Find initial surface of correct
topological type.
initial mesh
[SIGGRAPH93]
phase 2
Improve its accuracy and
conciseness.
optimized mesh
[SIGGRAPH94]
phase 3
Find piecewise smooth surface.
Detect sharp features automatically
optimized
subdivision surface
Example
1
13,000 points
3
2
Phase 1: Initial surface estimation
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U
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)? + + + + +
+ + ++
+
+
– – – ++
+ –– –
+
–
–
d(p)?
–
–
+
+
–
+
+
+ + + +
+ +
S
P
Estimate d from P
Extract Z(d)
Phase 1 (cont’d)
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How to estimate d?
compute tangent planes
orient them consistently
Phase 1 (cont’d)
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How to extract Z(d)?
run “marching cubes”
Phase 2: Mesh optimization
2
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Input: data points P, initial mesh Minitial
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Output: optimized mesh M, minimizing
E(M) = Edistance + Ecomplexity
Phase 2 (cont’d)
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Optimization over:
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the number of vertices
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their connectivity
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their positions
 consider any mesh of the same topological type as Minitial
Phase 2 (cont’d)
Nested optimization:
 optimize connectivity
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for fixed connectivity, optimize geometry
Greedy approach:
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consider local perturbations
accept if DE(M)<0
edge collapse
edge split
edge swap
Phase 2: Results
using 31,000 points
from Digibotics, Inc.
using 13,000 points
using 182,000 points
from Technical Arts Co.
Phase 3: Piecewise smooth surface
3
piecewise planar  piecewise smooth surface
Subdivision surfaces
[Loop87]
M0
[Hoppe-etal94]
tagged control mesh
M1
M2
S=M
Phase 3 (cont’d)
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Generalize phase 2 optimization:
edge collapse
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edge split
edge swap
Again, apply perturbation if DE(M)<0
edge tag
Phase 3: Results
Related work
volumetric repr. (Curless&Levoy)
phase 1
alpha shapes (Edelsbrunner)
initial mesh
phase 2
optimized mesh
phase 3
optimized
subdivision surface
NURBS surface
(Krishnamurthy&Levoy)
(Eck&Hoppe)
CAD models (Sequin)