sd models: super-deformed character models

Pacific Graphics 2012C. Bregler, P. Sander, and M. Wimmer(Guest Editors)

Volume 31 (2012), Number 7

SD Models: Super-Deformed Character Models

Liang-Tsen Shen, Sheng-Jie Luo, Chun-Kai Huang, Bing-Yu Chen

National Taiwan University

Figure 1: The SD models generated by our method. Upper row: the input models. Lower row: the SD style results. The modelsfrom left to right are: baseball cap boy, wolf, armadillo, dinosaur, dog, and lion.

Abstract

Super-deformed, SD, is a specific artistic style for Japanese manga and anime which exaggerates characters in thegoal of appearing cute and funny. The SD style characters are widely used, and can be seen in many anime, CGmovies, or games. However, to create an SD model often requires professional skills and considerable time andeffort. In this paper, we present a novel technique to generate an SD style counterpart of a normal 3D charactermodel. Our approach uses an optimization guided by a number of constraints that can capture the properties ofthe SD style. Users can also customize the results by specifying a small set of parameters related to the bodyproportions and the emphasis of the signature characteristics. With our technique, even a novel user can generatevisually pleasing SD models in seconds.

Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometryand Object Modeling—Curve, surface, solid, and object representations

1. Introduction

Super-deformed, a.k.a. SD or Chibi, is a specific style ofJapanese manga and anime which exaggerates charactersin the goal of appearing cute and funny. As shown in Fig-ure 2, the SD characters are usually drawn or designed indistorted body proportions to resemble small babies, typi-cally with chubby bodies, stubby limbs and oversized heads.The SD style can be seen everywhere in Japanese culture,from anime, manga to advertising. It is also used to manu-facture character figures and mascots. In many video games

and CG movies, the characters are sometimes designed inSD style for comedic effect. Therefore, designing a super-deformed counterpart (i.e., SD style) of a normal charactermodel is a common and important task for visual artists andgraphic designers.

To date the SD style is not formally and clearly defined,but it often consists of a number of characteristics. First, thehead length (and also width) of an SD character is normallyone-half to one-third of the character’s height. In contrast,the average proportion of an adult is about one-seventh. Sec-

c© 2012 The Author(s)Computer Graphics Forum c© 2012 The Eurographics Association and Blackwell Publish-ing Ltd. Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ,UK and 350 Main Street, Malden, MA 02148, USA.

L.-T. Shen, S.-J. Luo, C.-K. Huang, B.-Y. Chen / SD Models: Super-Deformed Character Models

(a) (b)

Figure 2: A cartoon character “Hatsune Miku” (a) and itsSD version (b). c©Crypton Future Media

ond, the SD characters lack of the details of their normalcounterparts. That is, the details such as folds on a jacket areignored, and general shapes are favored. Third, the signaturecharacteristics are emphasized on the SD versions to makethem much more prominent. In fact, creating an SD modelusually takes a professional graphic designers considerabletime and effort to carefully study the character and employa bunch of editing operations in order to achieve a visuallypleasing result. In addition, the editing process usually re-quires a spatially-varying deformation through all the bodyparts rather than a simple scaling, and the time-consumingediting process cannot be reused for alternative design tasks.As a result, the creation of an SD character model is chal-lenging.

In this paper, we present a novel technique that gives usersthe ability to semi-automatically generate an SD version ofa normal 3D character model. Our approach uses an opti-mization guided by some constraints based on the proper-ties of the SD style. A model can be customized by speci-fying a small set of parameters related to the body propor-tions and the emphasis of the signature characteristics. Inaddition, users can annotate the signature characteristics bymarking a number of vertices. To achieve this, our systemfirst embeds a predefined skeleton into a given model. Basedon the skeleton, the model is deformed through an optimiza-tion such that the body proportions satisfy the user-specifiedparameters, the details are smoothed, and the user-annotatedsignature characteristics are emphasized. We constraint thebody proportions in the range to satisfy the SD style proper-ties, and thus it provides an intuitive and simple manner forusers to generate an SD model. Although it requires some in-teraction, in practice we have found it relatively efficient andsimple to generate an SD model with our technique. Further-more, our technique can achieve visually pleasing results inseconds, and allows users to interactively and iteratively cus-tomize their SD models.

The primary contribution in this paper is an optimizationapproach for generating an SD model of a normal characterthat respects the user-specified parameters and constraintswhile minimizing a set of energy terms that model the prop-

erties of the SD style. We demonstrate the effectiveness ofthis approach with a number of results.

2. Related Work

Mesh deformation. High quality mesh deformation isbecoming a prominent field in geometric modeling andcomputer graphics. In recent years, many shape deforma-tion techniques have been introduced. Surface-based defor-mation techniques [Ale03, LSCO∗04, SCOL∗04, ZHS∗05,HSL∗06] regard mesh deformation as an energy minimiza-tion problem. Laplacian coordinate constraints are oftenused to preserve mesh details and manipulate mesh deforma-tion [Ale03, LSCO∗04, SCOL∗04]. Huang et al. [HSL∗06]enables the volume and skeleton constrains. Detail preserva-tion can be achieved by multi-resolution techniques [BK03].It first decomposes a mesh into a low frequency mesh andhigh frequency details, and then manipulates the low fre-quency mesh only while adding the details back for show-ing final results. In skeleton-based deformation techniques,linear-blend skinning (LBS) [MTLT88,LCF00] is a standardtechnique for character animation. A skeleton is embeddedinto a target mesh, and the transformations of each bone areassigned by animators. The deformed mesh is then obtainedby linearly blending the bones’ transformations.

Geometry processing. Our technique operates on meshgeometry to produce SD models. Many existing geome-try processing methods relate to our technique, such asmesh simplification and mesh smoothing. Mesh simplifica-tion is used to reduce the number of vertices and faces ofa polygonal mesh while approximating its original shape[CMS97, LWC∗02, GH97, Lin00]. Mesh smoothing is usedto reduce the geometry details, and also can be adopted toenhance the geometry features. Laplacian smoothing is thesimplest method for mesh smoothing, which smooths themesh geometry by relocating every vertex to the average po-sition of its neighbors [Fie88]. Shontz and Vavasis [SV03]further improved the results by applying weighted Lapla-cian. Eigensatz et al. [ESP08] proposed a curvature-domaintechnique to edit the geometry. Although these geometryprocessing techniques are powerful for surface editing, theycannot be trivially applied to transfer the semantic geometrystyles.

Artistic stylization. SD style is a popular artistic stylein cartoon production. In practical, many techniques havebeen proposed to produce specific artistic styles. Non-photorealistic rendering techniques are used to either ren-der a 3D model to an artistic style 2D image [KMN∗99,DS00, GTDS10] or convert an image or video to artisticstyles [DS02, WOG06, BNTS07, QPWH08]. Furthermore,Gal et al. [GSP∗07] proposed a non-realistic modeling tech-nique to convert a 3D model to an artistic 3D collage. An-other technique takes drawings from different views as input,and combines them to generate a 2.5D cartoon which can beused to simulate a rotation in 3D [RID10].

c© 2012 The Author(s)c© 2012 The Eurographics Association and Blackwell Publishing Ltd.


3. SD Stylization

For stylizing a novel character model to generate an SDmodel, an optimization approach is designed with respect toa number of user-specified parameters related to body pro-portions, such as

• Head proportion (ρH ): the ratio of the character height tothe head length. It is usually constrained as ρH ∈ [1.5,5]in SD style.• Body-to-feet proportion (ρBF ): the ratio of the body

length to the feet length. The range ρBF ∈ [0.5,1.5] is usu-ally used in SD style design. By default, we maintain theoriginal proportion of the input character model, but wealso retain the feasibility for users to specify it.• Body-to-head width proportion (δBH ): the ratio of the

body width to the head length. Because the head of anSD model is usually bigger than its body, we constraintits range in δBH ∈ [0.3,1].

In addition, users can also annotate the signature char-acteristics by marking a set of vertices. Based on the user-specified constraints, the embedded skeleton is first de-formed. A set of energy functions are developed based ona careful study of the properties of the SD style, and aweighted least-square optimization procedure is adopted tostylize the input model.

In this section, we first describe the definition of the inputcharacter model and the embedded skeleton in Section 3.1,and then describe the deformation of the embedded skele-ton with respect to user-specified parameters in Section 3.2.Finally, the details of the mesh optimization and the energyformulations based on the deformed skeletal bones are de-scribed in Section 3.3.

3.1. Character Model and Embedded Skeleton

The input of our system is a character model’s triangularmesh which is represented as M = (K,V) with connectiv-ity K and vertices V, where V = {v1,v2, ...vn}, vi ∈ R3 de-notes the vertices’ positions of the input model M. Then,the input model M will be stylized to generate a SD modelM′ = (K,V′) which has the same connectivity K but differ-ent geometry V′ = {v′1,v′2, ...v′n}, such that the body propor-tions and the emphasized signature characteristics can sat-isfy the user-specified constraints.

To manipulate a character model, such as human or ani-mal, professional graphical designers usually tend to adjustits underlying skeleton. Based on the observation, we de-fine a number of skeleton templates with different topolo-gies and embed them into corresponding character modelsusing [BP07]. Formally, an embedded skeleton is defined asS = (J,B) with joints J and bones B = {B1,B2, ...Bk}. Eachbone is represented as a line segment B j = {(1− t)a j + tb j |t ∈ [0,1]}, where a j,b j ∈ J are two joints the bone B j con-nects to. Symmetric bones (e.g., the left upper and right up-per arms) are first refined to the same length by scaling them

to their average. In order to achieve semantic adjustment, thebones are pre-annotated with semantic labels such as head,neck, shoulder, body, hand, and feet (Figure 3). In addition,we also categorize these bones into two sets in advance ac-cording to their relevance to the character height. In Figure 3,the bones colored in red are related to the character height,but the green bones are not. These annotations and categoriesare used when deforming the character model.

3.2. Skeleton Deformation

We observed that body reshaping, such as body heightchange, heavily depends on the changes of the underlyingskeleton. Therefore, we first deform the skeleton S = (J,B)to S′ = (J′,B′) based on the user-specified parameters asso-ciated with body proportions. Specifically, the bones anno-tated as head are fixed, and the remaining bones are scaled totheir target lengths along their original directions accordingto the head proportion (ρH ), body-to-feet proportion (ρBF ),and body-to-head width proportion (δBH ). Let BB, BS, andBF be the sets of bones annotated as body, shoulder, and feet,respectively, and B′B, B′S, and B′F be the corresponding setsof bones after being deformed. The deformed joint positionsJ′ are decided by solving the following equations:

ρH =L(B′H )+L(B′N)+∑B′i∈B′B

L(B′i )+2|B′F |

∑B′j∈B′FL(B′j)

L(B′H )

ρBF =∑B′j∈B′B

L(B′j)2|B′F |

∑B′i∈B′FL(B′i )

δBH =∑B′i∈B′S

L(B′i )

L(B′H ),

(1)

subjects toL(B′H) = L(BH)

L(B′N)L(BN)

=∑B′i∈B′B

L(B′i )+2|B′F |

∑B′j∈B′FL(B′j)

∑Bi∈BBL(Bi)+

2|BF |

∑B j∈BFL(B j)

L(B′i )L(Bi)

=L(B′j)L(B j)

,∀Bi,B j ∈ Bx,x ∈ {B,S,F},

(2)

where L(·) refers to the length of a bone, and BH and BN arethe bones annotated as head and neck, respectively.

3.3. Mesh Deformation

After obtaining the deformed skeleton B′ under the user-specified parameters in the previous section. In this section,we introduce our novel SD stylization approach which reli-ably deform the input character model to an SD style one.The deformation of a character body shape requires the re-sizing of each body part either along their underlying skele-ton axes (e.g., to increase or decrease height) or along theirorthogonal directions (e.g., to gain or lose weight). As a re-sult, our technique is based on the skeleton-aware model de-formation which adjusts each body part according to its cor-responding skeletal bones. The deformation process is for-mulated as an optimization to compute the optimal deformedmesh geometry V′. We then describe the deformation con-straints in details.



Head

Feet Feet

Body

Hand Hand

Shoulder Neck

Head

Feet

Body

Feet Feet

Shoulder Neck

(a) (b)

Figure 3: The skeleton templates for (a) humans and (b)quadruped animals with semantic annotations.

3.3.1. Body Proportion Constraint

The body proportion constraint is designed to deform amodel with respect to the deformations of its skeletalbones. A well-known standard real-time skeleton deforma-tion method is linear blend skinning (LBS), also calledskeletal subspace deformation [MTLT88, LCF00]. Specif-ically, given a closed mesh M and its embedded skeletonB, each skeletal bone B j ∈ B is assigned an affine transfor-mation TB j , which is then propagated to all vertices vi ∈ Von the mesh M with linearly blending. Hence, the skeleton-driven vertices v∗i are computed as:

v∗i = ∑B j∈B

ωB j (vi)TB j (vi), (3)

where ωB j (v) is the weight of the bone B j for the vertex v.The classic LBS equation works well for animating a char-acter model. However, to generate an SD model whose bodyproportions are usually distorted, the scaling of bones wouldresult in overly stretching the vertices located beyond an endpoint of a bone (i.e., joint), which has been well describedin [JBPS11]. Therefore, we adopt a modified LBS functionto resolve this problem.

The transformation of each bone can be decomposed intotranslation, scaling, and rotation operators. Because the de-formed skeletal bones obtained from the previous section donot perform any rotation, the rotation part can be discarded.Hence, the modified equation becomes:

v∗i = ∑B j∈B

ωB j (vi){aj′+(vi−aj)+

(vi− pro jB j (vi))(R j−1)+ eB j (vi)sB j},(4)

where aj′ is the transformed position of the joint aj (one of

the end points of bone B j), sB j = (||bj′−aj

′||||bj−aj|| − 1)(bj− aj)

is the stretch vector at the bone B j, projB j(·) refers to the

v i *

p i H

r H

o

proj ( )

proj ( )

Bj

Bj

v i * v i *

v k *

v k *

r j

p i j

p k j

(a) (b)

Figure 4: Each body part of an SD model could be fitted toa basic primitive, such as (a) the head is fitted to a sphereand (b) the limb is fitted to a capsule shape, respectively.

projection of a vertex to its nearest point on the bone B j,R j is the ratio of the deformed shoulder length to the origi-nal value for all bones excluding the head bone (i.e., R j = 1when B j = BH ), ωB j (vi) is computed using the heat equi-librium method presented in [BP07], and eB j (vi) is the jointweight defined as:

eB j (vi) =||projB j

(vi)−aj||||bj−aj||

. (5)

Notice that users can specify and emphasize the signaturecharacteristics by marking some vertices. This kind of op-eration can be achieved by modifying their joint weightseB j (vi) (Eq.(5)), and we will describe this in more detailsin Section 3.3.4.

Hence, the body proportion energy is formulated by mea-suring the squared distance between the deformed geometryv′i and the skeleton-driven geometry v∗i obtained from Eq.(4)as:

Ep =n

∑i=1||v′i−v∗i ||2. (6)

3.3.2. Primitive Fitting Constraint

As mentioned before, general shapes such as sphere or cylin-der are usually used to illustrate SD models. Therefore, eachbody part could be resembled by a specific 3D primitive forextreme SD illustration. For example, we can fit the charac-ter’s head to a sphere centered at the midpoint of the headbone. As shown in Figure 4 (a), we first project each trans-formed vertex v∗i on the sphere to obtain the projected pointpH

i , and then minimize the distance between them. To pre-vent the vertices of other body parts from being fitted to thesphere, the distance is weighted by the bone weight ωBH (vi)of the head bone to the vertex vi. Hence, the energy is de-fined as:

E f H =n

∑i=1

ωBH (vi)||v′i−pHi ||2, (7)

where pHi = o′+(v∗i − o′) rH

||v∗i −o′|| , o′ is the center of thedeformed head bone, and rH refers to the radius of the



(a) (b) (c)

Figure 5: The comparison of deforming a character model(a) without (b) and with (c) the primitive fitting constraint.

sphere, which can be found using least square fitting andyield 1

∑ni=1 ωBH (vi)

∑ni=1 ωBH (vi)||v∗i − o′||. Besides, users are

also allowed to provide the sphere radius for customization.

Furthermore, the limbs of a character can be fitted to acapsule shape as illustrated in Figure 4 (b). In this case,we connect each deformed vertex v∗i to its nearest pointprojB′j (v

∗i ) on the deformed bone B′j, and find the intersected

point p ji on the capsule surface. Hence, the energy is defined

as:

E f L(B j) =n

∑i=1

ωB j (vi)||v′i−p ji ||

2, (8)

where B j is the underlying bone of the limbs, p ji =

projB′j (v∗i ) + (v∗i − projB′j (v

∗i ))

r j||v∗i −projB′j

(v∗i )||, and the ra-

dius r j can be found with similar method described above.

Figure 5 shows a comparison of the results with and with-out the head primitive fitting constraint. In Figure 5 (c), thehead of the character becomes more circular and cuter thanthe result shown in Figure 5 (b).

3.3.3. Detail Smoothing Constraint

The SD model usually lacks of details. Therefore, the de-tail smoothing constraint is designed to smooth the sur-face details. Here we operate on the Laplacian coordinates[SCOL∗04] which uses a set of differentials to describe themesh geometry. To reduce the details of the geometry, weminimize the Laplacian through the mesh surface. Users arealso allowed to specify the important features that should bepreserved by painting on the surface to alter the importancesof the vertices. Formally, the energy is defined as:

Es =n

∑i=1

ρvi ||v′i−

1|N (v′i)|

∑v′j∈N (v′i )

v′j||2, (9)

where ρvi refers to the importance of the vertex vi, whichcan be manually specified by users, and N (vi) is the one-ring neighborhoods of the vertex vi.

3.3.4. Signature Characteristic Constraint

The signature characteristics of a character are critical andshould be preserved or emphasized during the deformation.However, they are usually related to semantic meanings, and

a j b j a j ^ b j

v p v q

v r

proj ( ) v q Bj

B j

proj ( ) v p Bj proj ( ) v r Bj

^

Figure 6: The illustration of computing the joint weight forthe marked signature characteristic.

are not easy to be analyzed via low-level features. Instead,our approach allows users to annotate the signature charac-teristics by marking a number of vertices, and emphasizethem either along their underlying skeleton axes or alongtheir orthogonal directions.

Emphasizing along Skeleton Axes. Emphasizing the char-acteristics along their underlying skeleton axes results in theelongation of the body parts, which highly relates to thescaling factor of the skeletal bones. As discussed in Sec-tion 3.3.1, the propagation of each bone’s scaling to verticescan be controlled via the joint weights eB j (vi). As a result,rather than developing a new energy function, we modifythe computation of the joint weights of Eq.(5), such thatthe propagation satisfies the user-specified constraints. Fig-ure 6 illustrates the setup of the joint weight computation.The red region indicates the user-annotated portion to em-phasize along the bone B j. We first project the marked ver-tices whose ωB j (v)> 0 to the bone B j, and find a j and b j asthe nearest points to the joints a j and b j, respectively. Thejoint weight of each vertex is computed according to its pro-jected point on the bone B j, that is, the projected point may

locate on a ja j (the green vertex vq), a jb j (the red vertex vp),

or b jb j (the blue vertex vr). Formally, we define D1 as thedistance between a j and a j , D2 represents the distance be-tween a j and b j, and D(vi) refers to the distance betweena j and the projected point projB j

(vi) of the vertex vi on thebone B j. The modified joint weight of a vertex vi to the boneB j is then defined as:

eB j (vi) =

D(vi)+||projB j

(vi)−a j||S

||b j−a j||+||b j−a j||S, i f D1 6 D(vi)6 D2

D(vi)

||b j−a j||+||b j−a j||S, i f D(vi)< D1

D(vi)+||b j−a j||S||b j−a j||+||b j−a j||S

, i f D(vi)> D2

(10)where S is the stretch factor provided by the users. Specif-ically, Eq.(10) assures that the stretch of the marked areaswould not result in that of other areas. Figure 7 shows the il-lustration of stretching the annotated area using the originaland modified weights, respectively.

Emphasizing along Skeleton Orthogonal Directions. Em-phasizing the characteristics along the orthogonal directionsof the underlying skeleton axes results in the amplificationof the body parts. To achieve this, users can provide an en-larging factor SE to indicate how much the marked portion



Annotated area (stretch to 3x)

L

0.3L 0.5L 0.2L

(a)Annotated area

0

1 0.3 0.8

Annotated area

0

1 0.15

0.9

e B j original

e B j modified (S = 2) 0

1

e B j

position

position

e B j

2L

0.3L 1.5L 0.2L

2L

0.6L 1L 0.4L

stretch

stretch

Stretched annotated area

Stretched annotated area

(b) (c)

Figure 7: The example of stretching the annotated areawith the original and modified joint weights. (a) The orig-inal mesh and annotated area. (b) The original (upper) andmodified (lower) joint weights. (c) The results of stretching.

should be emphasized, and the factor are used to control thedistance between each marked vertex to the skeleton. Fig-ure 8 demonstrates the relationship between a marked vertexvi and a bone B j, as well as that between the deformed ver-tex v′i and bone B′j . We hope that after the deformation, thedeformed vertex v′i can be adjusted according to the user-specified factor SE while maintaining its parameters to allbones. Hence, we can obtain the deformed vertex positionassociated with the bone B j as:

vB ji = a′j + tB j (vi)(b′j−a′j)

+R j(SE r j(vi)+1)(vi−projB j(vi)),

(11)

where tB j (vi) refers to the parameter of the parametric rep-resentation of projB j

(vi) = a j + (b j − a j)tB j (vi), and R jis the ratio of the deformed shoulder length to the origi-nal one for all bones excluding the head bone (i.e., R j = 1when B j = BH ). For the bone B j, we calculate r j(vi) forthe marked vertices vi as follows. If the bone weights of B jfor the marked vertices are all equal to zero, then we setr j(vi) = 0. Otherwise, as illustrated in Figure 9, we definer j(vi) = (d j(vi)− dmin

j )/(dmaxj − dmin

j ), where d j(vi) de-notes the distance between vi and the bone B j, and dmin

j anddmax

j refer to the distance between the nearest and farthestmarked vertices and B j, respectively. Therefore, the energyfunction is defined for the marked vertices as:

Ea =m

∑i=0

∑B j∈B

ωB j (vi)||v′i−vB ji ||

2, (12)

where m is the number of marked vertices, and ωB j (vi) is theweight of the bone B j for the vertex vi.

B j

v i

a j

b j

proj ( ) v i Bj

t ( ) Bj v i

B j

a j

b j

proj ( ) Bj

v i '

v i '

'

'

'

t ( ) Bj v i

(a) (b)

Figure 8: The illustration of emphasizing along skeleton or-thogonal directions, which shows the. relationship betweena vertex vi / v′i and a bone B j / B′j in the original / deformedmesh (a) / (b).

v i

B j a j b j

d min j

d max j d ( ) j v i

Figure 9: Illustration of the distance definitions used to cal-culate r j(vi).

3.3.5. Total Energy and Optimization

The total energy for the deformation is a weighted sum ofthe constraint energies defined in the previous sections:

E = wpEp +w f HE f H +w f L ∑Bk∈BL

E f L(Bk)+wsEs +waEa.

(13)Clearly, it is impossible to satisfy these constraints for an ar-bitrary character because they conflict with each other. Ourmethod spreads the conflicts according to these weights andobtains the compromised solution by a global optimization.Larger weight of a constraint makes the solution closer to theconstraint. We visually experimented and examined the SDstylization results with different relative weights, and foundthat a wide range of weights can work well. The results pre-sented in this paper are generated with wp = 1, w f H = 0.3,w f L = 0.2, ws = 10, and wa = 1.

The total energy is a least-square function and is linear, soit can be optimized with a linear system and solved by theTAUCS [Tol03] library. Notice that none of the constraintshould be satisfied absolutely, because any constraint alonedoes not illustrate the properties of the SD style completely.

4. Results and Discussion

In this section, we demonstrate the results of our system on anumber of examples. Our system can generate different SDmodels by specifying different parameters such as head pro-portion (ρH ), body-to-feet proportion (ρBF ), and body-to-head width proportion (δBH ). Figure 10 demonstrates someresults generated with different ρH and δBH . The head of



(a) (b) (c) (d) (e)

Figure 10: Some results of the curly hair girl model gen-erated with different head proportions (ρH ) and body-to-head width proportions (δBH ). (a) Input model. (b) ρH = 1.5,δBH = 0.2. (c) ρH = 2, δBH = 0.4. (d) ρH = 2.5, δBH = 0.55.(e) ρH = 3 and δBH = 0.65.

(a) (b) (c) (d)

Figure 11: Some results of the robot model generated withdifferent body-to-feet proportions (ρBF ). (a) Input model. (b)ρBF = 0.3. (c) ρBF = 1. (d) ρBF = 3.

the character model would look bigger with lower ρH andlower δBH . Figure 11 demonstrates some results generatedwith different ρBF . The body of the character model wouldbe longer with higher ρBF .

Our technique also allows users to emphasize signaturecharacteristics by marking some vertices. Figure 12 showsthe emphasis of the giraffe’s neck by stretching it along thebone axis. The result with emphasis would exaggerate thesignature characteristics of the giraffe. Figure 13 shows theemphasis of the camel’s hump by enlarging it. Our techniquecan be used to customize the SD models by passing abovementioned factors.

We also compare our results with those generated by anaïve body part uniform scaling method and the artist manu-ally crafted models as shown in Figure 14. Figure 14 (a) arethe input models, with the naïve scaling method (Figure 14(b)), the results are not satisfying because each part under-goes a uniform scaling, so the limbs and body would be toothin. We also asked two professional graphical designers tomanually craft the SD models (Figure 14 (c)) for compar-ison, which are very exquisite, but each model takes abouttwo and half days to produce. Although our method can-not achieve the professionally tuned details, it still can pro-

(a) (b) (c)

Figure 12: The comparison of deforming the giraffe model(a) without (b) and with (c) emphasizing its neck (red area).The stretch factor used in (c) is 1.0.

(a) (b) (c)

Figure 13: The comparison of deforming the camel model(a) without (b) and with (c) emphasizing its hump (red area).The enlarging factor used in (c) is 0.5.

duce satisfying results (Figure 14 (d)) efficiently. Figure 15demonstrates more SD results generated by our system.

Performance. Table 1 shows the model information used inthis paper and the performance measured on a desktop PCequipped with an Intel i7 3.50GHz CPU and 16GB RAM.The optimization time is proportional to the number of ver-tices, and it usually takes only seconds to obtain the result.

User study. To evaluate the quality of our generated SDmodels, we conducted a user study with 47 subjects and 12input models. The goal is to verify that (1) if the SD counter-parts are cuter than the original model? and (2) which headproportion is cuter? For each model, we generated 5 SDcounterparts with randomly selected five head proportionsbetween 1.5 ∼ 5 (interval is 0.5). The 5 SD models and theoriginal one were shown to the participants in a random or-der. The participants were asked to rate each model on howcute the character is (1[Negative]...5[Positive]). In total, wereceived 282 ratings for each input model. For the first ques-tion, the Wilcoxon rank sum test was used to test the null hy-pothesis that the rating medians of the original models andtheir SD counterparts are nearly identical. The Z statistics is−7.087 with p-value = 0. It indicates with a high statisticalconfidence that the null hypothesis is rejected and the ratingof the original models are smaller than the SD ones. Thus,our SD models are cuter than the original ones. For the sec-ond question, the similar method was used to test betweenany two head proportions. The result of the Wilcoxon ranksum test showed that the participants prefer the head pro-



(a) Input models (b) Uniform scaling (c) Artist hand crafted (d) Our method

Figure 14: The comparison of our results with those generated by a naïve uniform scaling method and the artist hand craftedmodels. Upper row: Milton. Lower row: Proton.

Model # of Vertex Optimization Timedog 1,480 0.749sdog2 4,070 2.122swolf 4,712 2.48slion 5,000 2.527sMilton 7,097 3.588sProton 7,433 3.746sgiraffe 9,239 4.945scamel 9,757 4.898sbaseball cap boy 13,336 7.852sodd guy 13,336 7.597srobot 13,336 7.675scurly hair girl 13,336 7.48sMario 15,002 8.705sLuigi 15,002 8.595sarmadillo 25,273 16.287sdinosaur 27,146 15.646s

Table 1: Timing of several models presented in this paper.

portions ρH ∈ [3.5,4.5], and ρH = 2 was the worst rankedresults.

Limitation and future work. Though our method can ob-tain several good results, there are still some limitations.First, the dependence on correctly embedded skeleton canbe one of them. Second, our method does not take modelself-intersections and vertex sampling density issues intoaccount, though considering self-conflicts and combiningadaptive remeshing techniques could resolve the issues. Fi-nally, our method does not consider the texture coordinatesof the input model. Although some cases can still get goodresults (Figure 16 (b)), the structural texture would be visu-

Figure 15: The SD results generated with our method. Thecases from left to right are: Mario, Luigi, dog2, and odd guy.

ally distorted on some SD models (Figure 16 (d)). There-fore, two research directions are worthy of future explo-ration. First, exploring the method of handling texture co-ordinates such that the texture would not be distorted is oneof them. Second, the combination of image abstraction tech-niques and SD texture stylization to produce vivid SD resultscan be another one.

5. Conclusion

We have presented an optimization-based technique that en-ables users to semi-automatically generate a character modelwith the SD style. Our technique supports the customiza-tion of the stylized result by specifying a small set of seman-tic parameters that are directly associated with the characterbody proportions. In addition, the users can also mark the



(a) (b) (c) (d)

Figure 16: The SD results with textures. (b) is an acceptabletextured SD result of (a), but (d) is a failure case due to itsstructural texture as shown in (c).

signature characteristics, and emphasize them to exagger-ate the model. The applications of the proposed techniqueare manifold. First, it can be used to transfer an existingCG movie to SD style, which could provide a new moviewatching experience. Second, it can be efficiently adaptedto customize a 3D character in video games for players. Inaddition, it can be used to manufacture the SD figures of anormal character.

Acknowledgments: We thank the anonymous reviewers fortheir thoughtful suggestions, and also thank Digimax forproviding high quality character models, (Figure 14 and Fig-ure 16), and the artist hand crafted results shown in Fig-ure 14. The models of “baseball cap boy” (Figure 1), “oddguy” (Figure 15), “curly hair girl” (Figure 10), and “robot”(Figure 11) are initially provided by SolidWorks. Figure 2(a) is the cartoon character “Hatsune Miku” copyrighted byCrypton Future Media. We also thank Sei Imai for designingits SD version (Figure 2 (b)). This research was supported inpart by the National Science Council of Taiwan under grantNSC101-2221-E-002-200-MY2.

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