Visibility-Guided Simplification Eugene Zhang and Greg Turk GVU Center, College of Computing Georgia Institute of Technology

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 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


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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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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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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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Camera space issues:– How many cameras are sufficient?– Does it matter where we place them?

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6 25818 4096Camera Positions

Surface Visibility

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Outline


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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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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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Evaluating of Quadric Measure is fast

– or

– where

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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 Measure:

– or

– where

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Quadric based 15,000

Visibility Guided 15,000

Original 1,169,608

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Original 1,688,933

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Quadric based

Visibility Guided

Original Quadric based

Visibility Guided

Original

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Original 140,113

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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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Original 1,087,416

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Average image difference: red=higher error

Quadric based Visibility Guided

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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)

Documents

Visibility-Guided Simplification Eugene Zhang and Greg Turk GVU Center, College of Computing Georgia Institute of Technology