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PSICHIATRIA FORENSE - Estratto del documento

Slide, Psicologia Forense

Invia: 5 giugno 2013
Estratto
Pose Space Deformation

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Pose Space Deformation




“Pose Space Deformation: A Unified Approach to Shape Interpolation and Skeleton-Driven Deformation” J. P. Lewis, Matt Cordner, Nickson Fong

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Paper Outline
     

1. Introduction 2. Background 3. Deformation as Scattered Interpolation 4. Pose Space Deformation 5. Applications and Discussion 6. Conclusion

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Key Goals of a Skinning System


“The algorithm should handle the general problem of skeleton-influenced deformation rather than treating each area of anatomy as a special case. New creature topologies should be accommodated without programming or considerable setup efforts.”

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Key Goals of a Skinning System


“It should be possible to specify arbitrary desired deformations at arbitrary points in the parameter space, with smooth interpolation of the deformation between these points.”

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Key Goals of a Skinning System


“The system should allow direct manipulation of the desired deformations”

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Key Goals of a Skinning System


“The locality of deformation should be controllable, both spatially and in the skeleton’s configuration space (pose space).”

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Key Goals of a Skinning System


“In addition, we target a conventional animatorcontrolled work process rather than an approach based on automatic simulation. As such we require that animators be able to visualize the interaction of a reasonably high-resolution model with an environment in real time. Real time synthesis is also required for applications such as avatars and computer games”

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Paper Outline (section 2)


2. Background  2.1 Surface Deformation Models  2.2 Multi-Layered and Physically Inspired Models  2.3 Common Practice  2.3.1 Shape Interpolation

S 0 + ∑k =1 wk (S k − S 0 )


⇒ v′ = v base + ∑ φi ⋅ (v i − v base ) ⇒ v′′ = ∑ wi Wi ⋅ B i−1 ⋅ v


2.3.2 Skeleton-Subspace Deformation
δ kk
0 −1 0 k p

p = ∑w L L L p
 

2.3.3 Unified Approaches 2.4 Kinematic or Physical Simulation?
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Key Technology


Scattered Data Interpolation Using Radial Basis Functions

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Key Technology




Scattered Data Interpolation Using Radial Basis Functions Huh?

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Interpolation
    

Interpolation vs. Extrapolation Linear Interpolation vs. Higher Order Structured vs. Scattered 1-Dimensional vs. Multi-Dimensional Interpolation vs. Approximation

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Interpolation Techniques
 



Splines (cubic, B-splines, NURBS…) Series (polynomial, Fourier, radial basis functions, wavelets…) Rational functions Exact solution, minimization, fitting, approximation



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Radial Basis Functions
 

What is a radial basis function? How do we use them to interpolate data?

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What is an RBF?


 



A radial basis function (RBF) is simply a function based on a scalar radius: _(r) We can use it as a spherically symmetric function based on the distance from a point In 3D space, for example, you can think of a field emanating from a point that is symmetric in every direction (like a gravitational field of a planet) The value of that field is based entirely on the distance from the point (i.e., the radius)
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Radial Basis Functions


If we placed a RBF at location xk in space, and we want to know the value of the field at location x, we just compute: _(|x-xk|)



This works with an x of any number of dimensions

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Radial Basis Functions
 



What function should we use for _(r) ? Well, technically, we could use any function we want We will choose to use a Gaussian:

−r  ψ (r ) = exp 2   2σ   

2

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Gaussian RBF


Why use a Gaussian RBF?
    



We want a function that has a localized influence that drops off to 0 at a distanc
e We want to be able to adjust the range of influence (that’s what _ is for) We want a smooth
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