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Semantic Deformation
Ilya Baran, Daniel Vlasic, Eitan Grinspun, Jovan Popovi
SIGGRAPH 2009
Reading group presentation (and nothing at all to do with the
real guys who did this at MIT) twak
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Animation is Expensive
Artist time is expensive
Job is thankless, unrewarding etc...
Common solution is outsourcing
Large mocap libraries exist with lots of movementdata that we could reuse
But how to apply that mocap data to differentmodels?
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Skeletal Retargeting
Vertices are mapped to a weighed set of frames Animation only moves frames
Splice many small animation clips
a skeletal model may not be able to capture the fullsubtlety of the poses
Example-based control of human motion, Hsu et al., 2004
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Deformation Transfer
Mesh Modification Using Deformation Gradients, Robert W. Sumner 2005
Literal mapping from target to source instead ofsemantic correspondence
Arbitrary vertices in input and output model
User specified correspondence map
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Semantic Deformation Transfer
Given a set of pose correspondences between two meshes...
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...and an arbitrary pose as input...
...what's the output?
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Method
Create a space that can be manipulated via standard
linear algebra techniques, so we can apply these
techniques to targeting meshes.
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Projection - just find the weights!
[x1, x2 ...xn][w
w2...wn
]=[ p]x, p are given and projected poses
w are weights
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The End
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Shape Space
"For semantic deformation transfer to work, the shape
space must satisfy two requirements: linearinterpolation between points in the shape space mustproduce blended poses without artifacts, and projection
of a pose onto a subspace of the space must produce
the most similar pose in the subspace to the original."
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Why not an existing space?
All likely points inspace shouldcorrespond to
desirable
deformations ofthe model
Matrix animation and polar decomposition, Ken Shoemake & Tom Duff, 1992
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Three techniques
Matrix logarithms
Deformation Gradients Linear Rotation-invariant Coordinates
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Neat trick to find rotation matrix:
Q0=
Q i1=Q iQ iT
2
Can parameterize to interpolate Q between tworotations. But still doesn't help we need one matrixwe can linearly interpolate
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Matrix Logarithms
exp
iw
i
log Q
Provide a mapping between the group of 3Drotation SO(3) and the Lie algebra so(3) of skew-symmetric 3x3 matricies
so(3) allows linear interpolation
Mesh-Based Inverse Kinematics, Sumner et al., 2005
A Mathematical Introduction to Robotic Manipulation, Murray, 2002
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K= V V
1
Deformation transfer for triangle meshes, Sumner et al. 2004
V=[ v2 v1, v3 v1, v4 v1]
V=[vv, vv, v4v1]
KV=
v1
v2
v3
v4
vv2
v
v3
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Linear Rotation Invariant Coordinates
Linear rotation-invariant coordinates for meshes, Lipman et al., 2005
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Rotation invariant mesh representation
Each vertex encodes the location of it's neighbors
Cylindrical coordinates
Solve a pair of linear systems to reconstruct
Absolute Frame Orientations
Vertex Positions
Here's a video from a similar technique
Free-Form Motion processing, Kircher & Garland. , 2008
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Properties of LRI
LRI accumulates noise over the mesh
Much faster than other non-linear techniques
Linear interpolation fails if polar coordinates stored
naively
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Putting it all together
Now we want to combine these techniques to create alinear space with the desired properties.
It's got to be rotation invariant (for arbitrary inputmeshes)...
...so we store the differences between a set of differentcoordinate systems.
And we want semantic correspondence...
...so we'll use deformation coordinates relative to patchesdefined on the input and target models.
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Output Mesh
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Reconstruction
Recover patch frames from adjacencies
GiG j Gi , j
Solve for G's
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Recovering Verts
Deformation Gradients from G's and S's Not vertex positions, so solve minimizing distance
from base pose
(f's are faces, j's are vertex indexes, v' arereconstructed and tildes are rest poses)
f
j
v ij1'vi j
'Qf Sf v i jv ij
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Patches!
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Criticism
...we expect to end up with...a crocodile swing dancingas if it were an adult human. Admittedly, this
faithfulness to the original motion is not always
artistically desirable. However, we prefer to relegatethe difficult creative decisions (How do crocodilesdance?) to the user's selection of an initial motion.
Retargetting motion to new characters, Gleicher, 1998
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Engineered accumulation of other people's work
Feet don't stick to floor
Skeletons have hardware support, deformation gradientsdon't
Needs to have a good set of base poses and theircorrelating transform
Doesn't show re-encoding the base pose?
Assumes topology invariant (people don't grow anotherarm)
No exploitation of temporal similarities
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