PSICHIATRIA FORENSE - Estratto del documento

Slide, Psicologia Forense

Descrizione: Slides di Psichiatria Forense

Pose Space Deformation Pose Space Deformation   “Pose Space Deformation: A Unified Approach to Shape Interpolation and Skeleton-Driven Deformation” J. P. Lewis, Matt Cordner, Nickson Fong Paper Outline       1. Introduction 2. Background 3. Deformation as Scattered Interpolation 4. Pose Space Deformation 5. Applications and Discussion 6. Conclusion 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.” 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.” Key Goals of a Skinning System  “The system should allow direct manipulation of the desired deformations” Key Goals of a Skinning System  “The locality of deformation should be controllable, both spatially and in the skeleton’s configuration space (pose space).” 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” 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

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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? Key Technology  Scattered Data Interpolation Using Radial Basis Functions Key Technology   Scattered Data Interpolation Using Radial Basis Functions Huh? Interpolation      Interpolation vs. Extrapolation Linear Interpolation vs. Higher Order Structured vs. Scattered 1-Dimensional vs. Multi-Dimensional Interpolation vs. Approximation Interpolation Techniques    Splines (cubic, B-splines, NURBS…) Series (polynomial, Fourier, radial basis functions, wavelets…) Rational functions Exact solution, minimization, fitting, approximation  Radial Basis Functions   What is a radial basis function? How do we use them to interpolate data? 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) 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 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 Gaussian RBF  Why use a Gaussian RBF?       We want a function that has a localized influence that drops off to 0 at a distanc

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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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