SKELETON-BASED RIGID SKINNING

FOR CHARACTER ANIMATION

Andreas Vasilakis and Ioannis Fudos

Department of Computer Science, University of Ioannina, Ioannina, Greece

Keywords:

Skeletonization, Rigid skinnig, Character animation, Mesh generation.

Abstract:

Skeleton-based skinning is widely used for realistic animation of complex characters deﬁning mesh move-

ment as a function of the underlying skeleton. In this paper, we propose a new robust skeletal animation

framework for 3D articulated models. The contribution of this work is twofold. First, we present reﬁnement

techniques for improving skeletal representation based on local characteristics which are extracted using cen-

troids and principal axes of the character’s components. Then, we use rigid skinning deformations to achieve

realistic motion avoiding vertex weights. A novel method eliminates the artifacts caused by self-intersections,

providing sufﬁciently smooth skin deformation.

1 INTRODUCTION

In video games, crowd simulations, computer gener-

ated imagery ﬁlms and other applications of 3D com-

puter graphics, achieving skin motion of deformable

objects in a realistic-looking way is of utmost impor-

tance. Since, due to its versatility, skeletal animation

is one of the most popular techniques, we focus on

skin motion techniques for skeletal animation of ar-

ticulated objects.

In skeletal animation, a representation model con-

sists of at least two main layers: a highly detailed 3D

surface representing the character’s skin, and an un-

derlying skeleton which is a hierarchical tree structure

of joints connected with rigid links (bones) providing

a kinematic model of the character.

The process of extracting a skeleton is called

skeletonization. A skeleton acts as a special type of

deformer transferring its motion to the skin by as-

signing each skin vertex one (rigid skinning) or more

(linear blending skinning-LBS) joints as drivers. In

the former case, inherent ﬂaws arise caused by self-

intersections, especially in areas around joints. In the

latter case of LBS , each skin vertex is assigned mul-

tiple inﬂuences and blending weights for each joint.

This scheme provides more detailed control over the

results. However, the generated meshes exhibit vol-

ume loss as joints are rotated to extreme angles pro-

ducing non-natural deformations (also known as col-

lapsing joint and candy wrapper effects). Yet an-

other problem with LBS is that tuning the LBS ver-

tex weights tends to be a tedious and cumbersome

task (Lewis et al., 2000; Mohr and Gleicher, 2003;

James and Twigg, 2005). Despite these drawbacks,

variations of this method are widely used in interac-

tive computer graphics applications because they are

simple and easy to implement on GPUs.

Figure 1: Robust rigid skinning. From top left to bottom

right: the initial model; rotating the lower part; removing

points; adding points; construct a robust blending patch.

To address the above issues we present an integrated

skeleton-based rigid skinning framework for animat-

ing 3D solid modular articulated models. A visu-

ally satisfactory skeleton is extracted using centroids

and principal axes (Lien et al., 2006) of the compo-

302

Vasilakis A. and Fudos I.

SKELETON-BASED RIGID SKINNING FOR CHARACTER ANIMATION.

DOI: 10.5220/0001799803020308

In Proceedings of the Fourth International Conference on Computer Graphics Theory and Applications (VISIGRAPP 2009), page

ISBN: 978-989-8111-67-8

nents of a segmented object by performing a depth-

ﬁrst traversal of the skeleton hierarchy tree. We re-

ﬁne the produced skeleton segments with local and

neighbor features to derive better skeletal represen-

tations that are more appropriate for our application.

Then, we use classic rigid skinning by assigning each

skin vertex to an inﬂuence bone to achieve mesh an-

imation avoiding thus vertex weight estimation and

training pose set production costs. We introduce a

novel method to eliminate degeneracies and artifacts

from self-intersections, especially in areas near joints,

by performing alternative intuitive deformations. Fig-

ure 1 illustrates the entire process.

2 RELATED WORK

There is an abundance of research work in the litera-

ture that tackles the skeleton extraction and skinning

of 3D objects from different perspectives. We focus

on recent developments most closely related to ani-

mation.

Skeletonization algorithms may be classiﬁed

based on whether they work on the boundary surface

(geometric methods) or on the inner volume (volumet-

ric methods). Researchers have proposed geometric

based algorithms approximating MAT to overcome

some of its inefﬁciencies, however MAT based skele-

tons are still not well ﬁtted for animation applications.

Several methods (Liu et al., 2003; Ma et al., 2003)

generate skeletons by constructing discrete ﬁeld func-

tions by means of the object’s volume. Although ac-

curate, such methods are usually very time consuming

and they cannot be applied to animation since the vol-

umetric information needed is not usually part of the

animation model. Researchers also generate skeletons

based on mesh contraction (Au et al., 2008). (Katz

and Tal, 2003) extract a skeleton using a hierarchical

mesh decomposition algorithm. Finally, (Lien et al.,

2006) proposed an iterative approach that simultane-

ously generates hierarchical shape decomposition and

a corresponding set of multi-resolution skeletons.

Linear blend skinning (LBS) is the most widely

used technique for real-time animation due to its com-

putational efﬁciency and straightforward GPU imple-

mentation (Rhee et al., 2006). Recent skinning al-

gorithms are classiﬁed based on whether they use

(Geometric methods) or a training set of poses (Ex-

ample based methods) of input models. Geometric

methods revert to non-linear blending of rigid trans-

formations since deformation is inherently spherical.

Numerous proposed methods have replaced the lin-

ear blending domain with simple quaternion (Hejl,

2004), spherical blending (Kavan and

Z´ara, 2005) and

dual quaternion (Kavan et al., 2008). Example-based

methods remove artifacts by correcting LBS errors

with storage and computation cost increase (Lewis

et al., 2000; Wang and Phillips, 2002; Merry et al.,

2006). Our rigid skinning approach falls under Geo-

metric class of algorithms introducing a novel versa-

tile, robust and efﬁcient blending approach based on

rational quadratic Bezier patches.

3 SKELETONIZATION

We have built on techniques introduced by (Lien

et al., 2006) that produce reﬁned local skeletal morphs

from the components of modular models. A straight-

forward approach to build the skeleton of a compo-

nent is to connect the opening centroids. A boundary

of a componentconsists of the common joining points

of two adjacent components generated during a mesh

segmentation process. We denote the centroid of a

boundary as opening centroid. An improvement over

this method is to use the centroid or kernel centroid of

the component in addition to the opening centroids.

However, frequently they do not capture the compo-

nent shape accurately.

In (Lien et al., 2006) proposed to overcome failures

of previous methods by extracting a skeleton from

a component by connecting the opening centroids to

the principal axis. Our approach adapts this skeleton

extraction technique for use in our animation frame-

work. Let OC be the set of the opening centroids

of component C, OC = {oc

,... , oc

}. First, we

select the principal axis segment of the component’s

convexhull that resides within the interior of the com-

ponent. For even better results we have used as major

axis an axis parallel to the principal axis of the con-

vex hull that goes through the kernel centroid of the

component to ensure that skeleton segments have the

least possible intersection with the component’s bor-

der. We denote this major axis segment as pa. We

subdivide the pa in a number of uneven segments by

picking as link points the projections of the opening

centroids on pa (see Figure 2). Let P

(oc

) be the

projection of opening centroid oc

on pa. Our match-

ing algorithm uses a dynamic programming concept,

enhanced with new score functions which aim at max-

imizing the length of the utilized pa.

After grouping has been performed, we create

the set of skeleton edges. Beyond the standard con-

nections between the opening centroids and the link

points, we use extra skeleton edges based on the map-

ping result.

Our approach improves the principal axis orien-

tation by introducing two modiﬁcations, the ﬁrst is

SKELETON-BASED RIGID SKINNING FOR CHARACTER ANIMATION

303

(oc

) P

(oc

)

(oc

)

min

(oc

)

min

(oc

)

(

)

(

)

(

)

(

)

(oc

)

d(P

(oc

),P

(oc

))

d(P

(oc

),P

(oc

))

d(P

(oc

),P

(oc

))

con

Figure 2: Skeleton segments extracted by the grouping (sk

) and the connecting (sk

con

) algorithm.

based on local features and the second uses knowl-

edge inherited from the component hierarchy. Finally,

we propose to add four more joints which represent

the two ends of the other axes segments making the

skeletal representation more topologically expressive.

3.1 Grouping Algorithm

Our approach manages to minimize the total mapping

length and the cardinality of the set of link points

(score function F

), while at the same time maximizes

the used pa length (score function F

Let d(~p

, ~p

) be the euclidean distance between

point ~p

and point ~p

. For a set of opening cen-

troids, oc

= hoc

,... , oc

i, we compute their link

points on pa as the average of their projections by

(oc

) =

∑

k=i

(oc

)

|oc

(1)

∀ oc

∈ oc

, we evaluate its normalized variation as

V(oc

) =

d(oc

(oc

)) − d

min

(oc

)

max

(oc

) − d

min

(oc

)

(2)

where d

min

(oc

) = d(oc

(oc

)) and

max

(oc

) = max

1≤l≤|OC|

{d(oc

,oc

)}.

Moreover, we deﬁne the ratio of the pa length

which is vanished after grouping as the pa length

which is generated among the projections of these

opening centroids divided by the maximum used pa

length.

Deﬁnition 1. The normalized merging score function

for oc

group set is deﬁned as the average of the

total distance cost and the ratio of the not used pa

length,

(oc

) =

∑

k=i

|oc

d(P

(oc

),P

(oc

))

d(P

(oc

),P

(|OC|))

(3)

Deﬁnition 2. The normalized separating score func-

tion F

for groups G

= hoc

,... , oc

i and G

hoc

l+1

,... , oc

i is deﬁned as the average of the sums

of their total distance cost and the complement of the

ratio of pa length which is generated between these

groups,

) =

∑

V(oc

)

∑

V(oc

)

+ (1− gR

)

(4)

where gR

d(P

(oc

),P

(oc

l+1

))

d(P

(oc

),P

(|OC|))

3.2 Connecting Algorithm

The ﬁnal skeleton of the component contains line seg-

ments that connect opening centroids to link points

and line segments that interconnect link points. Open-

ing centroid grouping often generates skeletons that

do not capture important topological information.

Therefore, the connection algorithm works with the

following rules:

1. If all opening centroids are grouped to one link

point and this point is close to:

• pa’s centroid, we connect it with the pa’s end points

on both sides of its centroid.

• one of pa’s end points, we connect it with the pa’s

end point on the other side of pa’s centroid.

2. If opening centroids are connecting to more than

one link point and these points are close to:

• pa’s centroid, we connect the ﬁrst and the last link

points with the pa’s end points on both sides of pa’s

centroid, respectively.

• one of pa’s end points, we connect the ﬁrst or the last

link point with the pa’s end point on the other side

of pa’s centroid.

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304

Figure 3: Oriented bounding boxes and skeletons of “Human” components: (left) Original conﬁguration (right) After align-

ment.

3.3 Local Reﬁnement

To achieve optimal or satisfactory orientation results,

we approximately align principal directions along

some qualitative features through slight modiﬁcation.

The proposed algorithm performs weighted vector

alignment for each opening centroid. If the com-

ponent has more than one opening centroids, we

align with regards to the closest principal direction by

angle=

weight

, where α is the angle between the given

vector and its closest axis and weight w =

|OC|+1

ex-

cept from the opening centroid which lies at the root.

This is assigned an increased weight : 2∗ w, such that

∑

|OC|

i=1

= 1.

3.4 Hierarchical Reﬁnement

We extend the orientation improvements performed

individually on each component by performing opti-

mal ﬁtting of the local principal directions of neigh-

bor components. The algorithm starts from the chil-

dren of the root node of the skeleton tree perform-

ing the same process to their children until it reaches

the tree leaves. For each component, this process ﬁrst

aligns with regards to the parent’s principal direction

which is closer to the child’s principal axis. Subse-

quently, from the rest of the child’s and parent’s prin-

cipal directions we detect those that are closer and

aligns them. Note that ﬁtting two principal direc-

tions from different components, results in rotating

the other principal directions too.

4 ADVANCED RIGID SKINNING

We have developed a novel technique to address the

major ﬂaws from self-intersections in areas around

the joints providing sufﬁciently smooth skin defor-

mation. Brieﬂy, our approach ﬁrst removes the skin

vertices of the overlapping component parts and then

adds new vertices to ﬁll in the gap. Finally, for each

frame it constructs a blending mesh that produces a

smooth surface using a robust triangulation method.

4.1 Removing Vertices

The ﬁrst step of our technique is to detect which ver-

tices from each of the collided components are lo-

cated inside each other. A fast approximate test is to

use the oriented bounding box (OBB) since accurate

methods require a lot of computational resources. We

start from the boundary points to perform the fewer

tests since they have the highest probability to be in-

side the other component’s OBB and move through

their 1-ring of neighbors until we reach the points

which are in the outer side of the OBB. Two points

are 1-ring neighbors if they belong to the same facet.

4.2 Adding Vertices

Deﬁnition 3. There are three point sets that will use

to construct the blending mesh:

• Boundary is the set of boundary points that have not

been removed.

• Replaced is the point set that will replace the points that

have been removed.

• In-between is the point set which consists of the average

of the initial and ﬁnal positions of the opening points

which have been removed (O

i,initial

points).

We present two blending techniques; the ﬁrst one

called front blending patch construction uses only

the Boundary set and the second called rear blend-

ing patch construction uses both the Replaced and In-

between sets.

4.2.1 Front Blending Patch Construction - Fbps

The observation behind this process is that when we

rotate a component about an arbitrary axis, movement

SKELETON-BASED RIGID SKINNING FOR CHARACTER ANIMATION

305

of every point B ∈ Boundary will describe a circu-

lar arc. The task is to ﬁnd new points by interpolat-

ing from the point’s position (B

= q

−1

) before

the rotation q

to the point’s position after rotation

′

= q

−1

) q

(see Figure 4). We use fast linear

interpolation of quaternions (QLERP) since the inter-

polation along the shortest segment hardly causes any

observable skin defect (Kavan and

Z´ara, 2005).

4.2.2 Rear Blending Patch Construction - Rbps

We have to ﬁll in the gap in the area where we have

removed points from both components. The major

issue is that we only have the Replaced points from

each component without any correspondence between

them. So, we propose to use as extra point set,

called In-between points.

A grouping function is developed to create triplets

from each InB

∈ In-between and one point from

child’s and parent’s Replaced sets (R

points, re-

spectively). The feature of each triplet is that the

plane deﬁned by its points, has the minimum dihe-

dral angle with the plane deﬁned by the joint position

and the kernel centroids of the participating compo-

nents (plane PL). Then, we construct blending arcs

given the triplet as control points using a Rational

Bezier representation (Fudos and Hoffmann, 1996).

The tangent vectors at R

deﬁned as the projec-

tions on PL of the vectors going from the joint posi-

tion to child’s and parent’s kernel centroids, respec-

tively. To prevent the generated meshes from exhibit-

ing volume loss as joints rotate to extreme angles we

replace InB

point with V

. We deﬁne V

as the aver-

age of the InB

point and the intersection of their tan-

gents (I

) and then evaluate the tangents (T

) to

the vectors going from R

to InB

(see Figure 4).

4.3 Blending Mesh

The points derived through the two blending pro-

cesses constitute the scattered 3D data which will

be triangulated. In this work, we use the Tight Co-

cone (Dey and Goswami, 2003) algorithm to con-

struct water-tight surfaces. Since we need only two

parts of the generated spheroid to ﬁll the holes, we

must eliminate a number of unnecessary facets to de-

rive optimal lighting results. The evaluation of the

patch point normal vectors is achieved by averaging

the normals of the output surface facets and the nor-

mals of the pre-existant component facets that share

the point.

i,initial

InB

B’

FBPC

RBPC

Figure 4: Introducing additional points and blending curves.

5 COMPLEXITY AND

PERFORMANCE EVALUATION

The input to our framework is a segmented poly-

hedron model and its associated skeleton hierar-

chy information. At the following experiments we

decompose characters into components using the

Blender (http://www.blender.org/) software. A sum-

mary of the characteristing studied models (courtesy

of (efrontier, 2006; AIM@SHAPE, 2008)) is given in

Table 1.

We evaluate our proposed algorithms with respect

to two criteria: quality and performance. All tests

were performed on an 2.4 GHz Intel Core Quad with

2GB of RAM.

Figure 5: Comparison on a human model between our re-

ﬁned skeleton and a default hand-made skeleton.

Table 1 provides computation times for extracting

skeletons from the above models. Most of the time

is due to the principal directions and kernels centroid

computation which is performed in

∑

i=0

O(n

logn

)

and

∑

i=0

O(n

logn

) + O(r

logr

) time respectively,

for a character with k components where the ith com-

ponent has n

vertices and r

kernel points. The local

and hierarchical reﬁnement methods times are negli-

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306

Figure 6: Avoidance of the typical LBS “candy-wrapper” artifact. (Left) is a reference pose, (middle) upper arm is rotated

about its axis, and on (right) upper arm is rotated 180

about its axis.

gible compared to the overall performance. However,

we observe from measures of Table 1 that skeleton ex-

traction complexity appear to be nearly linear on the

number of triangles.

Figure 7: Reﬁned oriented bounding boxes and skeletons of

the components of a horse model.

It’s difﬁcult to compare our method with other re-

cent methods, since the input model should be seg-

mented. Figure 3 illustrates the qualitative superior-

ity of our reﬁned skeletons and aligned OBBs over

the original principal axis algorithm. In general, our

method generates reﬁned skeletons in less than half a

minute for dense models (Figures 3, 5, 7). Thus, if our

method is used in conjunction with a fast decomposi-

tion method, it will be a very efﬁcient overall process.

Figure 5 illustrates the similarity between the default

skeleton generated by Poser software and a skeleton

extracted by our method.

Table 1: Experimental models and performance of their

skeletonization steps (time measured in seconds).

Model Vertices Kernel Centroid Principal Axis Total

Cow 3825 1.982 0.868 2.995

Horse 8964 2.086 0.924 3.178

Dilo 26214 4.701 2.022 7.150

Human 74014 10.244 4.649 14.893

We create animations by re-targeting hand-made mo-

tion data to the skeletons extracted from the original

meshes. Figures 6 and 8 show animated poses us-

ing our rigid skinning technique. We also provide

snapshots depicting a closer view of a human knee

mesh to demonstrate the robustness of the skinning

process (Figure 1). These visual results conﬁrm that

our method is indeed free of artifacts exhibited by pre-

vious LBS methods working only on a single mesh.

Figure 8: Cow multiple part animation. Patched parts are

highlighted in yellow.

However, the overall processing time of our skin-

ning method is very high for a real-time animation

due to the computation of new points which takes

O(n

· n

) time to complete ( n

and n

are the

numbers of Replaced points of moving and its parent

components and n

is the cardinality of In-between

set) and the triangulation algorithm O(n

) complex-

ity, where n is the number of the constructed points.

For instance, Table 2 shows the time performance of

our rigid skinning animating ﬁgure’s 1 human’s knee

from initial pose to extreme angles where moving and

its parent components consist of 891 and 1000 ver-

tices, respectively.

6 CONCLUSIONS AND FUTURE

WORK

We have proposed a robust skeleton-based animation

framework for 3D characters. Approximate reﬁne-

ment algorithms have been presented to improve ex-

SKELETON-BASED RIGID SKINNING FOR CHARACTER ANIMATION

307

Table 2: Rigid skinning performance of human’s knee ani-

mation (time measured in seconds).

Frame n

n Time

1 26 28 24 64 0.390

2 27 28 23 93 0.421

3 26 31 22 116 0.456

4 27 32 23 150 0.510

5 28 34 24 188 0.572

6 35 37 24 214 0.654

Mean 28 32 23 137 0.501

tracted skeleton’s orientation. We have developed a

novel rigid skinning method that eliminates the po-

tential shortcomings from self-intersections, provid-

ing plausible mesh deformations.

Considering completeness there is need for fur-

ther investigating in a more quantitative manner the

grouping functions. Further, one could try replac-

ing the angle-weighted algorithm with an optimiza-

tion method which will compute the principal axis

orientation more accurately.

Finally, to achieve real-time animation an alterna-

tive triangulation method should be employed and its

GPU realization should be investigated.

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