1. Simplification of Articulated Mesh
Present by Guilin Liu

2. Motivation Explosion of digital 3D models Problem: large scale
1. reverse engineering: laser scanning
2. interactive software ….
Problem: large scale
Digital Michelangelo project:
1 billion polygons
Real-time application
real-time rendering, real-time interaction…

3. Simplification
Standard simplification
Assuming single, static shape

4. Simplification
Simplification trade-off

5. Simplification
Simplification associated with deformation

6. Simplification of Articulated Meshes
Input
Mesh models
Example poses
Output
Multi-resolution hierarchy:
Simplified vertices and their skin weights
Method
Minimize an error metric using quartic optimization method
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7. Previous work: static mesh
1. Vertex decimation[SZL92]

8. Previous work: static mesh
2. Vertex clustering method RB[93]
Cluster generation
Compute a representation
Mesh generation
Topology changes

9. Previous work: static mesh
3. edge collapse[Hop96, GH97]

10. Previous work: deformable
1. break-simplify-stitch[SF99]
Break into bones
Simplify bones individually
Stitch together

11. Previous work: deformable
2. static simplification-reinterpret[HP01]
Do simplification on static model
Reinterpret the simplification on deformable models

12. Previous work: deformable
3. Bagging method[MG03]
Compute simplification for all poses
Sum QEF error of all vertices for each pose
Use the QEF of vertices to govern the order of edge collapses

13. Previous work: deformable
4.improve method #3[DR05]
Improve by locally rotating the QEF using bone transformation and adding the QEF together
Allow QEF to position simplified vertices

14. Previous work: deformable
5.build multi-resolution hierarchy and search a closest simplification [SPB01,SP01]
Build multiply simplifications
For each pose of deformation, find a closest simplification that has best qualify for that pose

15. Method Input: one or more poses of the skeleton
Use edge collapses methods
Modify the quadratic error function

16. Method
Error function

17. Method Minimize error function Not quadratic, but quartic with α and v
Approach: split into two steps
Fix α, find optimal v --- quadratic!!!
Fix v, find optimal α ----quadratic!!!

18. Method Fix α, find optimal v
due to insufficient pose sampling or small number of bones. Lead to invertible matrix

19. Experiment results

20. Experiment results

21. Experiment results
masc.cs.gmu.edu

22. Experiment results
masc.cs.gmu.edu

23. Limitation & Discussion
The performance depends on how well the pose samplings are.
The skin weights comes from optimization solution.
Didn’t utilize the original skin weights information.
The skin weight and approximation position may influence each other.
Error accumulation
masc.cs.gmu.edu