Simplification of Articulated Mesh

Present by Guilin Liu

Explosion of digital 3D models 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…

Motivation

Standard simplification Assuming single, static shape

Simplification

Simplification trade-off

Simplification

Simplification associated with deformation

Simplification

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Input Mesh models Example poses

Output Multi-resolution hierarchy:

Simplified vertices and their skin weights

Method Minimize an error metric using quartic

optimization method

Simplification of Articulated Meshes

1. Vertex decimation[SZL92]

Previous work: static mesh

2. Vertex clustering method RB[93] Cluster generation Compute a representation Mesh generation Topology changes

Previous work: static mesh

3. edge collapse[Hop96, GH97]

Previous work: static mesh

1. break-simplify-stitch[SF99] Break into bones Simplify bones individually Stitch together

Previous work: deformable

2. static simplification-reinterpret[HP01] Do simplification on static model Reinterpret the simplification on deformable

models

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

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

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

Previous work: deformable

Input: one or more poses of the skeleton

Use edge collapses methods Modify the quadratic error function

Method

Error function

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!!!

Method

Fix α, find optimal v due to insufficient pose sampling or small

number of bones. Lead to invertible matrix

Method

Experiment results

Experiment results

Experiment results

masc.cs.gmu.edu

Experiment results

masc.cs.gmu.edu

Limitation & Discussion

masc.cs.gmu.edu

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