semantic deformation

8/14/2019 Semantic Deformation

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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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semantic deformation

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