Inverse Kinematics for Reduced Deformable Models

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Inverse Kinematics for Reduced Deformable Models
Kevin G. Der Robert W. Sumner1 Jovan Popovic Kevin G. Der Robert W. Sumner1 Jovan Popovic
Computer Science and Artificial Intelligence Laboratory Massachusetts Institute of Technology 1ETH Zürich
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Our Goal Interaction

• mesh manipulation
• direct, intuitive control
• speed

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Related Work

• mesh editing
• Zorin et al. 1997, Kobbelt et al. 1998, Sorkine
  2005
• Mesh-based inverse kinematics
• Sumner et al. 2005
• Skinning mesh animations
• James and Twigg 2005

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Our Method

• Examples

Mesh
Reduced Deformable Model
decouple deformation complexity from geometric
complexity!
Inverse Kinematics

• - completely automated animation pipeline

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Reduced Deformable Model
Examples
Reduced Deformable Model
James and Twigg 2005

• expresses deformations compactly
• automatically constructed

Control parameters
Skinning weights (Using mean-shift
clustering)

• non-rigid
• no hierarchy

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RDM Mesh Reconstruction
Control parameters Skinning weights
different values estimate each example
x before deformation v after deformation
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Inverse Kinematics

• find a semantically proper shape

• obtain natural poses by blending examples

Blending function.

• blend in which domain?
• vertex positions ?
• control parameters ?

Desired
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Deformation Gradients

• simple 3x3 transformation matrices
• describe deformation of each example

deformation function
Skinning equation.
Vertex deformation gradient.
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Deformation Gradients
flattened control matrices
constant matrix
flattened deformation gradients of vertices

• for each example have t ? get f

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Shape Blending

• combine example deformation gradients

Blending function.

• recover the control parameters given deformation
  gradients

Has closed form solution.
solving for reduced basis! but still slow
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Proxy Vertices

• evaluating deformation gradients at every vertex
  is undesirable
• summarize using a few vertices

same deformation gradient!
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Inverse Kinematics

• Find best natural pose that meets user
  constraints

When theres only a few constraints
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Results
Solving time for interaction
seconds
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Results
Solving time for interaction
Mesh Vertices Example Ct Pxy Total Solve MIK Efull(Eproxy)
Horse 8431 12 33 195 0.019 0.007 0.424 3.01(3.00)
Human 12500 10 42 471 0.031 0.013 0.675 6.01(5.95)
Mouse 13188 26 48 278 0.037 0.019 1.351 1.63(1.73)
Dragon 15560 7 72 380 0.046 0.023 0.590 0.96(0.97)
Gorilla 25436 27 28 198 0.045 0.013 2.962 4.38(4.33)
Elephant 42321 11 23 210 0.058 0.008 1.928 5.38(5.46)
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Conclusion

• interactive control of reduced deformable models

• future work
• error correction for new poses
• model transfer between meshes
• other reduced deformable models