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Visibility-Guided Simplification
Eugene Zhang and Greg Turk
GVU Center, College of Computing
Georgia Institute of Technology
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Introduction
Problem:– Use visibility information to guide simplification.
Why useful:
Courtesy of Nooruddin and Turk
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Introduction
Solution:– Define a surface visibility measure.– Classify surface regions (mesh triangles) based on
this measure.– Allow higher geometric errors in low visibility regions
during simplification.
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Outline
Conclusion and Future Work
Visibility-Guided Simplification
Visibility Measure Definition Visibility Measure Calculation
Previous Work in Visibility and Simplification.
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Previous Work
Visibility calculation.– Visible surface determination.
• [Sutherland et al 74], [Catmull ‘74], [Myers ‘75], [Fuchs et al ‘80]
• [Appel ‘68], [Weiler & Atherton ‘77], [Whitted ‘80]
– Aspect Graph.• [Koenderink & Van Doorn ‘76], [Gigus et al ‘90]
– Interior/Exterior classification.• [Nooruddin & Turk ‘00]
– Texture Mapping with the help of visibility• [Sheffer & Hart ’02] (This conference)
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Previous Work
Mesh simplification based on edge collapse.– Progressive Meshes. [Hoppe ‘96]
– Geometry-Based Simplification. ([Ronfard & Rossignac ‘96], [Garland & Heckbert ‘97]).
– Image-Driven Simplification. [Lindstrom & Turk ‘00]
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Outline
Previous Work in Visibility and Simplification. Visibility Measure Definition Visibility Measure Calculation Visibility-Guided Simplification Conclusion and Future Work
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Visibility Function
Object M
Camera Space S
F(p, c1)=1
F(p, c3)=1
F(p, c2)=0
c1p
c2
c3
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Visibility Measure
V(p) measures the hard-to-see property of p.c: (camera position)
p: (point on model)
N(p):
surface normal
R(c): ray
viewing angle
Visibility Function
normalization factor
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Visibility Measure
Visibility Measure:
0 --- 1/3 --- 2/3 ---1
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Visibility Measure
The overall visibility of model M,
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Outline
Previous Work in Visibility and Simplification. Visibility Measure Definition Visibility Measure Calculation Visibility-Guided Simplification Conclusion and Future Work
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Visibility Measure Calculation
Difficulty: exact visibility calculation is computationally expensive.
Our Solution:– Find a dense set of viewpoints in S (subdivided
octahedron).– F(t,v)=1 iff part of triangle t is visible from viewpoint v. – Use hardware rendering to quickly compute F(t, v) for
all t and v.
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Visibility Measure Calculation
Algorithm for computing F(t, v) using hardware rendering– From each viewpoint v in S
• Mark F(t,v)=0 for each triangle in M• render M using color encoding of triangle ID’s. • read the color buffer. • set F(t,v)=1 if and only if color code of t is present
in the color buffer from v.
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Visibility Measure Calculation
Potential pitfalls:– When triangle is too large, F(t, v) is far from being constant.– When visible triangle is too small or sliver-shaped, the scan
conversion algorithm will likely miss it. (fall into “cracks”).
Solutions:– Subdivision based on edge length and a given
resolution.– Use depth information to help identify visible triangles
that fall into “cracks”.
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Visibility Measure Calculation (Results)
Visibility Measure: 0 --- 1/3 --- 2/3 ---1
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Visibility Measure Calculation
Camera space issues:– How many cameras are sufficient?– Does it matter where we place them?
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Visibility Measure Calculation
6 25818 4096Camera Positions
Surface Visibility
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Visibility Measure Calculation
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Outline
Previous Work in Visibility and Simplification. Visibility Measure Definition Visibility Measure Calculation Visibility-Guided Simplification Conclusion and Future Work
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Mesh Simplification
Edge collapse simplification. Key: what error measure to use.
– Geometry-based: e.g., Quadric ([Garland & Heckbert ‘97]).
– Perception-driven: e.g., Image-driven ([Lindstrom & Turk ‘00]).
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Visibility-Guided Simplification
Quadric Measure Eq(e)– T = 1-ring neighborhood of edge e.– triangle t in T is on plane
– Then
– Higher Eq(e) means higher Curvature.
ev v
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Visibility-Guided Simplification
Evaluating of Quadric Measure is fast
– or
– where
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Visibility-Guided Simplification
Our algorithm:– Edge collapse scheme.– Error metric = Quadric measure + Visibility measure.– New vertex location determined by Quadric measure.
Advantages:– Allow higher geometric errors for difficult-to-see
regions.– Have comparable speed as the quadric measure.
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Visibility-Guided Simplification
Visibility-Guided Measure:
– or
– where
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Visibility-Guided Simplification
Quadric based 15,000
Visibility Guided 15,000
Original 1,169,608
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Visibility-Guided Simplification
Quadric based 15,000
Visibility Guided 15,000
Original 1,688,933
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Visibility-Guided Simplification
Quadric based
Visibility Guided
Original Quadric based
Visibility Guided
Original
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Visibility-Guided Simplification
Quadric based 10,000
Visibility Guided 10,000
Original 140,113
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Visibility-Guided Simplification
Visual fidelity of the simplified models are measured in terms of image-based error between rendered images from 20 viewpoints ([Lindstrom & Turk ‘00]).
Geometric Errors are measured using Metro ([Cignoni et al ‘98]).
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Visibility-Guided Simplification
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Visibility-Guided Simplification
Quadric based 20,000
Visibility Guided 20,000
Original 1,087,416
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Visibility-Guided Simplification
Average image difference: red=higher error
Quadric based Visibility Guided
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Visibility-Guided Simplification
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Visibility-Guided Simplification
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Conclusion
Defined a surface visibility measure. Proposed an algorithm to efficiently and
accurately calculate this measure. Combined this measure with the Quadric
measure for mesh simplification– better visual fidelity– similar speed
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Future Work
More accurate algorithm for visibility function calculation.– e.g., change output type from binary to continuous.
Out-of-core calculation for larger models. Visibility-guided mesh parameterization. Visibility-guided shape matching.
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Thanks to
Geometric Models
Will Schroeder Ken Martin
Bill Lorensen Bruce Teeter
Terry Yoo
Mark Levoy and the Stanford Graphics Group
Mesh Simplification Code
Michael Garland
Excellent Suggestions
Anonymous reviewers
Sponsor
NSF (ACI 0083836)