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Simplification of Articulated Mesh. Present by Guilin Liu. Motivation. 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

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Simplification of articulated mesh

Simplification of Articulated Mesh

Present by Guilin Liu


Motivation
Motivation

  • 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…


Simplification
Simplification

  • Standard simplification

    • Assuming single, static shape


Simplification1
Simplification

  • Simplification trade-off


Simplification2
Simplification

  • Simplification associated with deformation


Simplification of articulated meshes

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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


Previous work static mesh
Previous work: static mesh

  • 1. Vertex decimation[SZL92]


Previous work static mesh1
Previous work: static mesh

  • 2. Vertex clustering method RB[93]

    • Cluster generation

    • Compute a representation

    • Mesh generation

    • Topology changes


Previous work static mesh2
Previous work: static mesh

3. edge collapse[Hop96, GH97]


Previous work deformable
Previous work: deformable

  • 1. break-simplify-stitch[SF99]

    • Break into bones

    • Simplify bones individually

    • Stitch together


Previous work deformable1
Previous work: deformable

  • 2. static simplification-reinterpret[HP01]

    • Do simplification on static model

    • Reinterpret the simplification on deformable models


Previous work deformable2
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 deformable3
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 deformable4
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


Method
Method

  • Input:

    • one or more poses of the skeleton

  • Use edge collapses methods

  • Modify the quadratic error function


Method1
Method

  • Error function


Method2
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!!!


Method3
Method

  • Fix α, find optimal v

    • due to insufficient pose sampling or small number of bones. Lead to invertible matrix






Limitation discussion
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


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