A Powell Optimization Approach for Example-Based ... - JP Lewis

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to character skinning at present. A nice reviewof SSD is given in [1]. SSD is widely used ingames, virtual reality and other realtime applicationsdue to its ease of implementation and lowcost of computing. It provides the relation betweencharacters and their underlying skeletons.Normally this relation is defined in the rest pose,and determines how characters move accordingto their skeletons thereafter. Sometimes, artistswill edit the geometry of characters in the restpose to fine-tune animations. This approach isnot commonly applied, however, since editing inthe rest pose will influence most other poses. Onthe other hand SSD is also notorious for artifactsat rotating elbows and extreme poses. For thoseapplications that require visual fidelity, such asmovies, SSD serves only as a basic framework,on which lots of more complicated deformationapproaches are built as a compensation.Example based skinning methods such asPose Space Deformation (PSD) are candidatesfor correcting SSD limitations. Example geometricmodels paired with underlying skeletonsin different poses are provided by artists withcarefully sculpting and posing. PSD smoothlyinterpolates these meshes in pose space and producesvisually attractive animations. However,although PSD may be used as a compensationto the underlying SSD, and the animator specifiesthe PSD examples after the SSD has beenperformed, it is generally believed that the examplesare best interpolated in the rest pose, beforethe SSD has been applied. Therefore theaction of the SSD and any other deformationsmust be “inverted” in order to push the examplecompensation before these operations. BesidesSSD, other skinning approaches such as rigidskinning, Free Form Deformation etc. can alsobe applied. Our goal is to incorporate examplebasedskinning into a system having a variety ofother skinning and deformation operations, andto be able to invert these operations regardlessof their nature.Since SSD is the most representative in thefamily of basic skinning, we will discuss howit performs in the inverse operation of PSDscheme. For a simplified condition where onlyone joint rotation and two example poses areconsidered, we demonstrate this inverse strategyhas a better performance than the same frameworkwithout it.The rest of this paper is organized as follows.After a review of related work, we willstudy details of SSD and PSD respectively inthe third section. Then discussion of the inverseoperation is presented in the fourth section includingits implementation and reasons why thisapproach will improve the quality of deformation.In the fifth section, we propose a unifiedskinning framework by applying minimizationtheory with respect to other basic skinningschemes. Conclusion and some discussions offuture work are presented in the last section.2 Related WorkBesides the geometric solutions mentioned inthe previous section, physical modelling and animationis another field providing realistic charactersimulations. Given physical principles,this category can generate more believable animationeffects compared to its geometric counterpart.But they are seldom applied to interactiveapplications because of the high cost ofcomputing and complicated algorithms. Thispaper is mainly dedicated to geometric solutions.Pose Space Deformation [1] combines shapeblending and Skeleton Subspace Deformationby formulating a scattered data interpolationproblem over sculpted (or otherwise obtained)example poses. Character geometries in problematicposes will be re-sculpted by animatorsand then resulting displacement (referredas delta values in this paper) from the originalgeometries will be stored as “scattered data”for interpolation phase. The interpolation isperformed in the pose space which consists ofskeleton joints, or other potentially abstract controllers.Their values such as rotation degreescan be chosen as coordinates of the abstractpose space. After a model is posed and resculptedin different example poses, a multidimensionallinear system is built by implementingan interpolation scheme using Radial BasisFunctions (RBF), and the output of this systemis the weights of each example pose. The finalanimation can be synthesized by linearly blendingRBF functions with the solved weights.Related research efforts have improved thespeed and power of example-based skinning. [2]2
incorporate linear elements into RBF to produceconstant changes between examples. [3] precomputeprincipal components of the deformationinfluences for individual kinematic jointsinstead of storing displacements for key poses,thereby enabling realtime rendering large nonlinearfinite element models of human hands.[4] introduce weighted pose space deformationfor deforming realistic models of human hand.The latest work [5] identifies statistically relevantbones and approximates bone transformsfrom example mesh animations.Using established terminology from statisticalmodeling, these example-based approachescan be considered as non-parametric skin deformationmethods. The data needed for thesemethods grows with the number of examples,but arbitrary deformations can be approximatedas a result. Simpler parametric skinning approaches(of which SSD is the prototype) havea fixed number of parameters; these have alsoseen some development in recent years [6], [7].Skinning using free form lattices [8], [9] orNURBS curves [10] instead of skeletons to drivecharacter surface are also common practices inthe entertainment production. Our frameworkimplements existing PSD theory and the distinctionis that we insert an optimization moduleinto the PSD pipeline by applying a unified inverseapproach assuming the knowledge of basicskinning is unavailable.2.1 Our ContributionWe provide detailed reasons why and how theinverse operation can improve the results. For asimplified case, we show that the direction of deformedvertices from inverse skinning is a linearfunction of joint rotation, while in the forwardapproach, that direction is kept as a constant.This demonstration provides for the first time aclear theoretical reason why inverse operation isrequired.We formulate editing geometry in rest poseas an optimization problem and propose a unifiedframework which can be implemented onhigh-end commercial packages while allowingany proprietary skinning operators to be incorporated.3 Skeleton Sub-SpaceDeformation(a).65432100 1 2 3 4 5 6 7 8(b).Figure 1: (a). Skeleton Subspace Deformation; (b). RadialBasis InterpolationSkeleton Subspace Deformation (SSD) is abasic algorithm that is used to define how thecharacter surface deforms following movementsof its underlying skeletons. The main idea is introducedby [11], and is also known as soft skinning,linear blending or Single Weight Enveloping(SWE). Due to its simplicity and efficiency,SSD is widely applied to interactive applicationssuch as games and virtual reality, and it is implementedin most commercial animation packages.A skeleton should be rigged to a character surfacebeforehand, roughly based on the anatomyof the character and kinetic rules. The posein which the skeleton is rigged normally is referredto as the rest pose. The basic relationshipbetween surfaces and skeletons is definedat the rest pose, and all motions of the characterwill be influenced thereafter. If SSD isadopted to define this relation, each vertex orcontrol point of the character surface is providedwith a list of joints, that will influence it, alongwith the weight indicating the amount of influence.When the character is animated, the positionof a vertex in the animated pose is the resultof weighted linear blending of its transformationby each associated joint. We formulate SSD as:v p = SSD p (v r M)= ∑ ω k T pk v r (1)k=1For a vertex in rest pose v r , its transformed positionin pose p is v p . T pk means the kth joint’stransformation from rest pose to pose p. Readerscan find details on how to compute T pk in [1].ω k is the corresponding weight. This weight isusually a function of distance between v r and itsassociated joints, and is defined when we applySSD to the rigged character. Figure 1 (a). is a3
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