To appear in the ACM SIGGRAPH Asia conference proceedings

Stretchable Cartoon Editing for Skeletal Captured Animations

Yann Savoye∗

INRIA Bordeaux University, France.

Figure 1: Laplacian Cartoon Skeleton Editing: Optimizing traditional skeletal animated structure with differential-aware bone stretchingeffects allows animators to efficiently re-use previously captured MoCap data in the context of cartoon productions. We increase Squash-and-Stretch effect on existing realistic BASKETBALL DUNK, DANCING, HORSE RUADE, KARATE KICK-OFF and JUMPING motion clips (fromleft to right hand side). Original and intermediate edited poses are displayed in transparency and resulting edited poses in superposition.

1 IntroductionIn this work, we describe a new and simple approach to re-useskeleton of animation with joint-based Laplacian-type regulariza-tion, in the context of exaggerated skeleton-based character anima-tion. Despite decades of research, interactive character animationsstill have a lack of flexibility and editability in order to re-use realvertebral motion. In further details, generation of expressive car-toon animation from real data, is a challenging key task for non-photorealistic animation. Hence, a major problem for artists in pro-duction is to enhance the expressiveness of classical motion clipsby direct manipulation of the underlying skeletal structure. Rela-tively small number of researchers present their approach for pro-cessing cartoon effects on motion data in [Kwon and Lee 2007;Davis and Kannappan 2002; Bregler et al. 2002]. However existingtechniques often avoid dealing with the potential of skeletal-basedoptimization, while preserving the joint coherence and connectivity.Besides, the majority of characters in cartoons have the flexibilityto stretch to extreme positions and squash to astounding shapes. Itcan also be noticed that squash-and-stretch is easier to realize intraditional animation rather than mocap-based computer generatedanimation. For this reason, Ratatouille a Pixar R©movie, did not usea rigid skeleton, while abandoning motion capture to reach such es-sential non-ultra realistic appeal.

2 Skeletal Graph LaplacianThe idea of the motion capture is to use sensor placed on the sub-ject, and to collect data that describes their motion while they areperforming motions. The pose of an articulated figure can be spec-ified by its joint configuration in addition to the position and rootorientation segment. Skeleton of animation S = (J ,B,M) iscomposed of a hierarchy of joints enriched with motion data, orga-nized in frames. S is made of a set J of n joints, a set B of bonesconnecting joints, and a set M of k motion frames. Two joints iand j are connected into a unique bone only if (i, j) ∈ B. Motiondata consist of bundle of signal defined as a continuous functionf (t). Compiled global rigid transformation matrix from capturedmotion data associated to the ith joint at the frame t is denoted byMt

i ∈ R4×4. The global location pti of the ith joint at the frame t is

then the homogeneous zero transformed by the sequence of trans-formation and can be written as: pt

i = Mti ·[~0 |1

]T. We define the

Differential Joint Coordinates δti of joint i at frame t as follows:

δti = pti −

∑j∈N(i)

1

di

((Mt

i −Mtj

)·[~0 |1

]T)∗ysavoye@siggraph.org

The degree of the joint i denoted by di is equal to the number ofjoints linked to i. The set of immediate adjacent joints to i is de-noted by N (i) = {j| (i, j) ∈ B}. In addition, the skeleton topol-ogy is represented as an open directed acyclic graph. So, we in-troduce the Skeletal Graph Laplacian LS by LS = D − A whereD is the diagonal matrix of joint degrees and A is the adjacencyjoint matrix. We denote by LS (.) the per-joint Uniform LaplacianOperator applied on the skeleton graph structure. The entries ofthe corresponding square symmetric n × n matrix LS are setup asfollows:

LS [i, j] =

1 if i = j−1/di if (i, j) ∈ B

0 otherwise

We focus on adding non-rigid effects to an existing captured skele-tal structure, while preserving its consistency and original connec-tivity. In our approach, we are referring to the well-known Lapla-cian shrinking effects (i.e. shearing and stretching distortion) in or-der to apply non-rigid warps over the rigid skeleton topology.

3 Cartoon Optimization AlgorithmOur algorithm takes an arbitrary input articulated motion signal andperturbates its Euler and Euclidean representations in such a waythat the output motion looks more cartoon-like. In order to hack therigidity, we prefer to deal with the skeletal structure as euclideanjoint coordinates. Our technique has two key components: spatio-temporal motion filtering and global joint location optimization. Atthe beginning of pre-optimization, we apply the cartoon animationfilter as suggested in the [Wang et al. 2006] in order to add: thefollow-through, exaggeration and anticipation effects on the motionsignal. The filtered motion signal f̃ (t) has interesting properties,especially on kinematic chains that are not explicitly edited auto-matically or hand-drawn specified. This filter involving a Laplacianof Gaussian (LoG), is defined as follows:

f̃ (t) = f (t)− f (t) ⊗ LoGTo continue, we reformulate the Squash-and-Stretch problem as askeletal adaptation optimization. Given the fact it is nearly impos-sible to get a plausible squash-and-stretch by working exclusivelyin Euler space with inverse kinematics, we prefer to optimize thewhole skeletal structure in term of global joint location of a pre-animated pose satisfying stretching constraints. The core algorithmof our technique relies on Skeletal Graph Laplacian, with the aim toensure spatial relationship of joints under sparse differential-awarestretching features over the whole joint hierarchy. As a result, thedriving idea is to employ fast and accurate skeleton fitting process,guided by kinematic-free constraints in each frame.

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To appear in the ACM SIGGRAPH Asia conference proceedings

At each frame, the initial solution is the Euclidean parameters of theanimated pose, generated by forward kinematics. Thus, pose esti-mation recovers the pose by minimizing an objective function thatis a combination of penalty and data terms. Smoothness term isrequired for making the warp field regular. To control a cartoon de-sired pose, the user inputs the targeted global joint positions qt

l fora collection C of edited joints. We conserve the Laplacian coordi-nates δti for each joint i in the skeleton hierarchy. The reconstructedpositions p̂ of the skeleton joints in world space coordinates areobtained by solving the following quadratic minimization problemseparately from each euclidean dimension:

argminp̂t

(∑l∈C

∥∥qtl − p̂t

l

∥∥2 + n∑i=1

∥∥LS (p̂ti

)− δti

∥∥2)Global joint location is estimated by minimizing the sum of squareddifference between the data-driven pre-animated pose and inputfeatures cues. In order to avoid purely translation effect provokedby a single dragged-and-dropped joint, we fix by default the rootjoint, acting as skeleton gravity center. The root joint is generallylocated in a place where many bones come together. In our frame-work, bone elongation at frame t can also be automatically estab-lished along the bone direction for selected joint l having the kth

joint as parent with a time-dependent scaling factor αt:

qtl = pt

l ± αt · (ptl−pt

k)‖pt

l−pt

k‖

Energy terms can be equilibrated by a weighting system. Usingsuch refined constraint formulation united with Laplacian on thebone structure is motivated by the fact that Squash-and-Stretch canbe accomplished by differential scaling in Euclidean coordinatessystem. Hence, this minimization problem can be solved efficientlyin least-squares sense based on the succeeding expression:

A ·X′ = B

Moreover, the global location of joints can be therefore found bysolving in real-time the very small sparse linear system using thisclosed form expression:

X′ =(ATA

)−1ATB

This sparse editing technique performs spatio-temporal numericaloptimization on MoCap data. As post-optimization step, we en-force temporal smoothness by penalizing inter-keyframe deviation.Our edited motion signal is consequently simply filtered using iter-ative smoothing convolution. A better solution is to diffuse editedexaggeration across time over the joint trajectories using temporalLaplacian solver with Dirichlet boundary conditions.

4 Results and DiscussionTo demonstrate the robustness and usefulness of our techniques, wehave implemented this advanced reproducible pipeline using onlyC++ and OPENGL. As shown on the accompanying video (pro-duced real-time and performed by a non-professional artist), just asingle editing feature is sufficient to adapt the whole skeletal posein coherent manner, as shown in Figure 2. Moreover, results haveshown that the proposed technique is robust enough to probably beused in low-budget productions, especially for processing sportymotion clips, as illustrated in Figure 1. We have tested the robust-ness of our method on a corpus composed of more than forty motionclips with success. In addition, we developed a simple interactiontechnique coupled with depth first search to handle the closest joint.

Even if human perception system tends to focus on kinematic pa-rameters rather than on structural clues, real-life creatures actuallyelongate and stretch due to the elasticity of tendons and muscles.Consequently, breaking the rigidity of the underlying armature addsa pleasant realism to cartoon rubber-like effects. The resulting ani-mated structure looks more pleasant while remains rigid in motion.

Our technique can be widely used in more complete 2D or 3D ani-mation systems to easily achieve non-rigid, rigged-and-skinned an-imation, cartoon shape control and elastic skin deformation fromMoCap data. Our method offers the potential ability to controlstretchable effect while allowing smooth behavior of skeletally-guided skin deformation, as far as the rigging function is smooth.

Figure 2: A single editing feature is sufficient to produce pleasantcartoon gait style over the whole skeletal pose in coherent mannerfor a horse ruade (top row) and a karate kick-off (bottom row).

5 Conclusion and Future WorkWe have introduced a novel, accurate, robust, easy to use, cutting-edge skeletal editing and interaction techniques that allow anima-tors to manipulate arbitrary animation with real-time control. Vio-lating physics of rigid motion allows us to obtain cartoon-like ef-fect, independently of the skin layer. Spatial coherence of joints ispreserved by differential-aware scaling represented by a quadraticenergy function leading to a new Skeletal Poisson Solver. The use-fulness and flexibility of our Laplacian approach is fully demon-strated to emphasize effective high-quality skeletal-based anima-tion pose. In the context of filmmaking, our pipeline reduces theamount of time needed to animate superbly well-articulated expres-sive character. More importantly, this contribution makes complexinteractions with animation more accessible to non-professionals,and offers real-time motion processing for video games as well.Notwithstanding, there is a large range of innovations to make in-teractive cartoon characters move naturally under exaggerated cues.For instance, selecting automatically good joint candidates for car-toon editing is an opened and unsolved problem for researchers. Aninteresting alternative idea is to incorporate as-kinematic-as possi-ble attenuation to enforce the original kinematic curvature.

ReferencesBREGLER, C., LOEB, L., CHUANG, E., AND DESHPANDE, H. 2002.

Turning to the masters: motion capturing cartoons. In Proceedings ofthe 29th annual conference on Computer graphics and interactive tech-niques, ACM, New York, NY, USA, SIGGRAPH ’02, 399–407.

DAVIS, J. W., AND KANNAPPAN, V. S. 2002. Expressive features formovement exaggeration. In ACM SIGGRAPH 2002 conference abstractsand applications, ACM, New York, NY, USA, SIGGRAPH ’02, 182–182.

KWON, J.-Y., AND LEE, I.-K. 2007. Rubber-like exaggeration for char-acter animation. In Proceedings of the 15th Pacific Conference on Com-puter Graphics and Applications, IEEE Computer Society, Washington,DC, USA, 18–26.

WANG, J., DRUCKER, S., AGRAWALA, M., AND COHEN, M. F. 2006.The cartoon animation filter. ACM Transactions on Graphics (Proceed-ings of SIGGRAPH 2006) 23, 3 (July), 1169–1173.

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