Statistical Analysis of Joint Determination for Skeleton Driven
Animation of Human Hands
E. Chaudhry
1
, L. H. You
1
, X. Jin
2
and Jian J. Zhang
1
1
National Centre for Computer Animation, Bournemouth University, U.K.
2
State Key Lab of CAD & CG, Zhejiang University, China
Keywords: Virtual Characters, Skeleton Driven Animation, Joint Determination, Statistical Analysis, Skin Deformation.
Abstract: Skeleton driven character animation is the most popular animation technique. It has been widely applied in
the current computer animation industry. Correct determination of joint positions plays a very important role
in creating realistic skin deformation of character animation. Current various approaches of skeleton driven
character animation have not addressed this issue. In this paper, we propose a statistical method to
determine the correct joint position using the statistical data analysis of different X-ray joint images. First,
we measure different joint positions from sample X-ray images. Then, we statistically analyse the data, and
obtain relative mean and maximum and minimum positions together with the relative range of joints which
are used to determine correct joint positions.
1 INTRODUCTION
Skeleton driven character animation is most
frequently applied in computer animation since
various commercial animation packages use the
technique of skeleton driven character animation.
Skeleton driven skin deformation is essential for
realistic character animation as the realism of an
animated character depends on the appearance and
motion of the character. Skeleton driven character
animation involves the following steps. First, a skin
surface for the virtual character is created. Then this
surface is mapped onto the skeleton. The animator
spends a lot of time and effort to deform the skin
surface realistically in relation to the motion of the
skeleton. The realism of an animated character
depends on the correctness of this relationship
between skin and skeleton movement. Most
character animation is driven by skeleton. The
quality of skeleton driven character animation
depends on correct joint positions. Currently, joint
determination is a manual process where animators
place joints on to a 3D model without any reference
data. Hence this manual process may not produce
correct joint positions leading to an unrealistic skin
deformation.
The concept of joint-related skin deformation
was first explored by Thalmann et al. (1998). The
basic concept of skeleton subspace deformation was,
later on, explained by Lander (1998, 1999). The
problem of shrinkage around a joint during bending
or twisting was discovered by Weber et al. (2000).
Wang and Philips (2002) proposed a multi-weight
envelop technique to overcome this problem. Mohr
and Gleicher (2003) proposed to add additional
joints. Kavan and Zara (2005) introduced spherical
blend skinning. Yang et al. (2006) suggested curve
skeleton skinning approach. The research work
carried out by Yang et al. (2006) used influence
joints and blend weights as a solution to this
problem. Vertices are transformed by using a
number of weights for smooth transformation of
bones around the joints of character’s skeleton. This
method is quite interactive and uses minimum
animation data.
In order to address this issue, in this paper, we
will develop a method which presents the relative
mean, maximum and minimum positions together
with the relative range of joints from the statistical
analysis of available X-ray images. These data can
be used to determine the positions of joints correctly.
2 STATISTICAL ANALYSIS OF
JOINT DETERMINATION
The basic idea of our proposed method is to find out
the statistical data from the X-ray images of joints
123
Chaudhry E., You L., Jin X. and Zhang J..
Statistical Analysis of Joint Determination for Skeleton Driven Animation of Human Hands.
DOI: 10.5220/0004303201230126
In Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information
Visualization Theory and Applications (GRAPP-2013), pages 123-126
ISBN: 978-989-8565-46-4
Copyright
c
2013 SCITEPRESS (Science and Technology Publications, Lda.)
available from internet and hospitals and use these
statistical data to guide the placement of joints of
character models. Figure 1 shows the five X-ray
images of a human right hand.
a b
c d
e
Figure1: X-ray images of the fingers of a human right
hand from five different persons.
The lengths between the joints are calculated by
using Image Processing tool in Mat lab. For each of
grooming, middle, ring and little fingers, the length
between the first joint and the second joint from the
root of fingers is marked as
1
J , that between the
second and third joints was marked as
2
J , and the
length beyond the third joint was marked as
3
J . For
the thumb, the length between the first joint and the
second joint from the root of the thumb is marked as
1
J , and that beyond the second joint was marked as
2
J . The obtained values of
1
J ,
2
J and
3
J for all
the fingers shown in Figure 1 were given in Table 1.
In the table, the numbers indicate the length between
two adjacent joints of a same finger. For example,
the numbers 339.96, 188.83 and 169.97 for the
grooming finger of Figure 1a indicate
96.339
1
=J ,
83.188
2
=J
, and
97.169
3
=J
.
The total length
J
of each of the fingers is the
sum of
1
J
,
2
J
and
3
J
, i. e.,
∑
=
=
I
i
i
JJ
1
(1)
where
2I
=
for the thumb, and
3I =
for all other
fingers.
Then we determined the relative value of each of
1
J and
2
J . Since the position of the first joint will be
determined by its relative position to the wrist joint,
we only consider the second and third joints which
are determined by
1
J and
2
J . The relative values
1
~
J
and
2
~
J
of
1
J and
2
J are:
J
J
J
J
J
J
2
2
1
1
~
~
=
=
(2)
Taking the grooming finger in Figure 1a as an
example, the total length of the finger is:
76.69897.16983.18896.339
321
=++=
++= JJJJ
(3)
and the relative values
1
~
J
and
2
~
J
of
1
J
and
2
J
of
the grooming finger are:
2702.0
76.698
83.188
~
4865.0
76.698
96.339
~
2
2
1
1
===
===
J
J
J
J
J
J
(4)
One of the advantages using the relative values
1
~
J
and
2
~
J
of
1
J and
2
J is the obtained results can
be easily extended to other models. For example,
one built grooming finger model has a total length of
1000. According to the relative values
1
~
J
and
2
~
J
of
1
J
and
2
J
given in Eq. (4), we can find
1
J
and
2
J
of the built grooming finger model to be
0.4865 1000 486.5
×
=
and
0.2702 1000 270.2×=
.
With the same method, the obtained total length
J
, and relative values
1
~
J
and
2
~
J
of
1
J and
2
J of
the grooming finger are 724.41, 0.4728, and 0.2695
for Figure 1b, 739.78, 0.4862, and 0.2792 for Figure
1c, 826.53, 0.5047, and 0.2731 for Figure 1d, and
793.68, 0.4728, and 0.2708 for Figure 1e.
If there are
M
X-ray grooming finger images,
the relative mean values
1
J
and
2
J
can be
determined from the relative values
1
~
J
and
2
~
J
of the
M
X-ray grooming finger images through the
following equation:
GRAPP2013-InternationalConferenceonComputerGraphicsTheoryandApplications
124
∑
∑
=
=
=
=
M
m
m
M
m
m
J
M
J
J
M
J
1
22
1
11
~
1
~
1
(5)
where
m
J
1
~
and
m
J
2
~
are
1
~
J
and
2
~
J
of the
th
m
X-ray
grooming finger image.
According to Eq. (5) and the five X-ray
grooming finger images given in Figure 1,
5
=
M
and
the relative mean values
1
J
and
2
J
of the grooming
finger are:
2726.0
~
5
1
0.49460.4728)0.5047
4862.04728.04865.0(
5
1
~
5
1
5
1
22
5
1
11
==
=++
++==
∑
∑
=
=
m
m
m
m
JJ
JJ
(6)
We also give the maximum and minimum
relative values among all the values of
k
J
~
of the
M
X-ray images through the following equation:
{
}
{}
kMkkkk
kMkkkk
JJJJJ
JJJJJ
~~~~
min
~
~
~
~
~
max
~
321min
321max
L
L
=
=
(7)
where
1=k
is for the thumb, and
1=k
and
2
=
k
are
for all other fingers.
According to Eq. (7) and the five grooming
finger images given in Figure 1, the maximum and
minimum relative values
max1
~
J
and
min1
~
J
for the five
X-ray grooming finger images are:
{
}
{}
{}
{}
4728.0
4728.05047.04862.04728.04865.0min
~~~~
min
~
5047.0
4728.05047.04862.04728.04865.0max
~
~
~
~
max
~
15131211min1
15131211max1
=
=
=
=
=
=
JJJJJ
JJJJJ
L
L
(8)
The relative range can be easily found by
considering the difference between the maximum
and minimum relative values, i.e.,
minmax
~
~
kkk
JJR −=
(9)
According to Eq. (9), the relative range for
1
J of
the five X-ray grooming finger images is:
0.03190.4728-0.5047
~
~
min1max11
==
−= JJR
(10)
With above method, we calculated the relative
mean values and maximum and minimum relative
values together with the relative range of
1
J and
2
J
of grooming, middle, ring and little fingers and those
for
1
J
of the thumb from the five images in Figure 1,
and listed the obtained statistical data.
Once a finger model is built and its total length
J
is known, we can use the statistical data determine
the mean, maximum, minimum and range.
Taking
1
J
of a built grooming finger model as
example, if the total length of the model is
1000=J
,
the mean value of
1
J is
6.49410004946.01000
1
=×=×J
, the maximum value
of
1
J is
7.50410005047.01000
~
max1max1
=×=×= JJ
,
the minimum value of
1
J is
8.42710004728.0.01000
~
min1min1
=×=×= JJ
, and the
range of
1
J is
31.910000.03191000
1
=×
=
×
R
which is
the same as
9.318.4727.504
~~
min1max1
=−=− JJ
.
3 APPLICATION EXAMPLE
It can be seen clearly from Figure 2c and 3c that
different skin deformations were generated by
different joint positions. The skin deformation
caused by the joints determined with the statistical
method given in this paper creates a more realistic
appearance than that caused by the manually
specified joints.
Figure 2a: Human rigged
model.
Figure 3a: Human rigged
with correct joint
positions.
Figure 2b: Human finger
animated.
Figure 3b: Human fingers
animated by our method.
Figure 2c: Problem of
limbs crossover which
gives un-realistic skin
deformation.
Figure 3c: Correct joint
positions gives realistic
skin deformation.
StatisticalAnalysisofJointDeterminationforSkeletonDrivenAnimationofHumanHands
125
4 CONCLUSIONS AND FUTURE
WORK
In this paper, we have presented a statistical method
to determine the positions of joints based on
available X-ray images and statistics. We have also
obtained the statistical data of the joint positions of
human fingers.
For our future work, we will use more X-ray
images of human fingers to obtain the statistical data
and extend our proposed method to a whole human
model. We will also investigate the statistical data of
people with different age and sex groups and
provide more useful statistical data for correct
determination of joints of skeleton driven character
models.
ACKNOWLEDGEMENTS
This research is supported by the grant of UK Royal
Society International Joint Projects / NSFC 2010. The
woman rig hand model used in this paper is from the
(http://animationjobs3d.blogspot.in/2012/03/female-maya-
model.html).
REFERENCES
Thalmann, N.M., Laperrière, R., Thalmann, D., Joint-
dependent local deformations for hand animation and
object grasping, In Proceedings of Graphics interface,
1988, pp. 26-33.
Lander, J., Skin them bones: Game programming forth
web generation, Game Developer Magazine (May,
1998) 11-16.
Lander, J., Over my dead, polygonal body, Game
Developer Magazine (October 1999) 11-16.
Weber, J., Run-time skin deformation, In Proceedings of
Game Developers Conference, 2000.
Wang, X.C., Phillips, C., Multi-weight enveloping: least-
squares approximation techniques for skin animation,
In Proceedings of 2002 ACM
SIGGRAPH/Eurographics symposium on Computer
animation, ACM Press, 2002, pp. 129- 138.
Mohr, A., Gleicher, M., Building efficient, accurate
character skins from examples, ACM Transactions on
Graphics 22, 3 (2003) 562-568.
Kavan, L., Žára, J., Spherical blend skinning: A real-time
deformation of articulated models, In Proceedings of
the 2005 Symposium on Interactive 3D Graphics and
Games, 2005, pp. 9-15.
Yang, X.S., Somasekharan, A., Zhang, J.J., Curve skeleton
skinning for human and creature characters. Computer
Animation and Virtual Worlds 17, 281-292 (2006).
Table 1: Data from X-ray images.
Grooming Middle Ring
Figure 1a
1
J
2
J
3
J
339.96 188.83 169.67
1
J
2
J
3
J
375.28 255.60 184.37
1
J
2
J
3
J
358.40 226.47 191.09
Figure 1b
342.47 195.24 186.70
389.42 239.15 197.31 372.98 226.72 212.12
Figure 1c
359.67 206.58 173.53
394.47 260.98 195.31 366.78 247.01 200.40
Figure 1d
417.16 225.70 183.67
446.49 261.72 209.62 442.49 267.65 227.06
Figure 1e
375.25 214.96 203.47
419.47 271.77 223.35 382.13 247.86 219.75
Little Thumb
Figure 1a
1
J
2
J
3
J
284.66 174.72 169.11
1
J
2
J
270.83 230.95
Figure 1b
291.24 166.72 170.56
259.53 251.34
Figure 1c
289.73 172.52 180.18
264.05 231.33
Figure 1d
334.51 180.32 196.25
301.67 264.72
Figure 1e
294.10 168.67 195.09
285.76 239.81
GRAPP2013-InternationalConferenceonComputerGraphicsTheoryandApplications
126
