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

2. 2 Introduction Problem: –Use visibility information to guide simplification. Why useful : Courtesy of Nooruddin and Turk

3. 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. 4 Outline Conclusion and Future Work Visibility-Guided Simplification Visibility Measure Definition Visibility Measure Calculation Previous Work in Visibility and Simplification.

5. 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. 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. 7 Outline Previous Work in Visibility and Simplification. Visibility Measure Definition Visibility Measure Calculation Visibility-Guided Simplification Conclusion and Future Work

8. 8 Visibility Function Object M Camera Space S F(p, c 1 )=1 F(p, c 3 )=1 F(p, c 2 )=0 c1c1 p c2c2 c3c3

9. 9 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

10. 10 Visibility Measure Visibility Measure: 0 --- 1/3 --- 2/3 ---1

11. 11 Visibility Measure The overall visibility of model M,

12. 12 Outline Previous Work in Visibility and Simplification. Visibility Measure Definition Visibility Measure Calculation Visibility-Guided Simplification Conclusion and Future Work

13. 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. 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 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.

15. 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”.

16. 16 Visibility Measure Calculation (Results) Visibility Measure: 0 --- 1/3 --- 2/3 ---1

17. 17 Visibility Measure Calculation Camera space issues: –How many cameras are sufficient? –Does it matter where we place them?

18. 18 Visibility Measure Calculation 6258184096 Camera Positions Surface Visibility

19. 19 Visibility Measure Calculation

20. 20 Outline Previous Work in Visibility and Simplification. Visibility Measure Definition Visibility Measure Calculation Visibility-Guided Simplification Conclusion and Future Work

21. 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]).

22. 22 Visibility-Guided Simplification Quadric Measure E q (e) –T = 1-ring neighborhood of edge e. –triangle t in T is on plane –Then –Higher E q (e) means higher Curvature. e vv

23. 23 Visibility-Guided Simplification Evaluating of Quadric Measure is fast –or –where

24. 24 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. 25 Visibility-Guided Simplification Visibility-Guided Measure: –or –where

26. 26 Visibility-Guided Simplification Quadric based 15,000 Visibility Guided 15,000 Original 1,169,608

27. 27 Visibility-Guided Simplification Quadric based 15,000 Visibility Guided 15,000 Original 1,688,933

28. 28 Visibility-Guided Simplification Quadric based Visibility Guided Original Quadric based Visibility Guided Original

29. 29 Visibility-Guided Simplification Quadric based 10,000 Visibility Guided 10,000 Original 140,113

30. 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. 31 Visibility-Guided Simplification

32. 32 Visibility-Guided Simplification Quadric based 20,000 Visibility Guided 20,000 Original 1,087,416

33. 33 Visibility-Guided Simplification Average image difference: red=higher error Quadric based Visibility Guided

34. 34 Visibility-Guided Simplification

35. 35 Visibility-Guided Simplification

36. 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. 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. 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)