Visibility-Guided Simplification

1
Visibility-Guided Simplification

• Eugene Zhang and Greg Turk
• GVU Center, College of Computing
• Georgia Institute of Technology

2
Introduction

• Problem
• Use visibility information to guide
  simplification.

• Why useful

3
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.

4
Outline

• Previous Work in Visibility and Simplification.

• Visibility Measure Definition
• Visibility Measure Calculation

• Visibility-Guided Simplification

• Conclusion and Future Work

5
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)

6
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

7
Outline

• Previous Work in Visibility and Simplification.
• Visibility Measure Definition
• Visibility Measure Calculation
• Visibility-Guided Simplification
• Conclusion and Future Work

8
Visibility Function
Camera Space S
Object M
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Visibility Measure

• V(p) measures the hard-to-see property of p.

c (camera position)
R(c) ray
N(p) surface normal
p (point on model)
10
Visibility Measure
Visibility Measure 0 --- 1/3 --- 2/3 ---1
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Visibility Measure

• The overall visibility of model M,

12
Outline

• Previous Work in Visibility and Simplification.
• Visibility Measure Definition
• Visibility Measure Calculation
• Visibility-Guided Simplification
• Conclusion and Future Work

13
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.

14
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 IDs.
• 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.

15
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?

18
Visibility Measure Calculation
6
258
18
4096
Camera Positions
Surface Visibility
19
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

21
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.

v
v
e
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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.

25
Visibility-Guided Simplification

• Visibility-Guided Measure
• or
• where

26
Visibility-Guided Simplification
Quadric based 15,000
Original 1,169,608
Visibility Guided 15,000
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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
Original 140,113
Visibility Guided 10,000
30
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).

31
Visibility-Guided Simplification
32
Visibility-Guided Simplification
Quadric based 20,000
Original 1,087,416
Visibility Guided 20,000
33
Visibility-Guided Simplification
Quadric based
Visibility Guided
Average image difference redhigher error
34
Visibility-Guided Simplification
35
Visibility-Guided Simplification
36
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

37
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.

38
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)