A Data Adjustment Method of Low-priced Data-glove
based on Hand Motion Pattern

Kenji Funahashi
Department of Computer Science
Nagoya Institute of Technology
Nagoya 466–8555 Japan
Email: kenji@nitech.ac.jp

Yutaro Mori1

Hiromasa Takahashi2

Yuji Iwahori

Nagoya Institute of Technology
Department of Computer Science(1 present: NEC Solution Innovators, Ltd.)
Chubu University(2 present: Chubu Electric Power Co.,Inc.)
Kasugai, Aichi 487-8501 Japan
1
Email: moriyu@center.nitech.ac.jp Email: iwahori@cs.chubu.ac.jp
2
Email: hiromasa@center.nitech.ac.jp

Abstract—A data glove is one of the major interfaces used in thefield of virtual reality. In order to get detailed data about thefinger joint angles, we must use a data glove with many sensors.
However, a data glove with many sensors is expensive and alow-priced data glove does not have enough sensors to capture
all the hand data correctly. In our previous work, we propose amethod to obtain all finger joint angles by estimating the patternof hand motion from the low-priced data glove sensor values. In
our experiment system, we assumed some representative handmotion patterns as grasping behavior. We also assumed that
other hand motions can be represented by synthetic motion of
the representative patterns. In our previous work, we used thedata glove with sensors covering two joints of each finger. In thispaper, we estimate the finger joint angles when using the data
glove whose sensors cover only the middle angle of each finger.

Figure 1. 5DT Data Glove 5 Ultra

Keywords–Data-glove; Hand motion estimation; Finger joint
angles estimation.

I. I NTRODUCTION
Virtual Reality (VR) is a rapidly growing research fieldin recent years. VR technologies give us various advantages.
There are simulators to practice an operation and to fly a plane
as examples of VR technologies. These simulators enable us to
avoid the risk and to save on cost. VR researches that targets
to households also have been attracted. A data glove is oneof the major interfaces which are used in the field of VR. It
measures curvatures of fingers using bend sensors. In order toobtain accurate hand motions, it is necessary to use a data glove
which has many sensors, but it is expensive. It is preferable
that an interface is small scale and low cost. Various types ofresearches about data glove have been conducted [1][2][3]. On
the other hand, there is a low cost data glove which measures
an angle for each finger through one sensor. But it cannot get
detailed data directly. For example, the 5DT Data Glove 5
Ultra and DG5 VHand have a single sensor on each finger,
so they have five sensors in the whole hand (see Figures 1
and 2). However, there are three finger joints for each finger, asingle sensor can not measure all of these three angles directly.
In our laboratory, we have proposed a method to get plausibleuser hand motion pattern from the low-cost glove. This method
estimates the kind of hand motion patterns using each relation
among angles of fingers during operation. Then, it estimates
all finger joint angles by estimating the types of hand motion
patterns from the correlation between each finger angle in the

Figure 2. DG5 VHand

hand motion pattern [4]. We assume some representative handmotion patterns, and consider that other hand motions can be
represented as a synthetic motion of the representative handmotion patterns. In addition, we calculate the ratio of each
representative motion pattern. Moreover, estimating each finger
angle using the result, we express any hand motion patterns
other than the representative hand motions. In our previous
work, we have used 5DT Data Glove (see Figure 1) whose
sensors cover two joints of each finger. Here, we estimate
finger joint angles when using the data glove DG5 VHand(see Figure 2) whose sensors cover only the middle angle ofeach finger.
The rest of the paper is structured as follows. In Section II,
we describe how to estimate finger joint angels. In Section III,
we apply this method to the data-glove that sensor positons
are limited. In Section IV, the experimental results are shown.
Finally, we conclude in Section V.

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Epij, Fpij,
Gpij, Hpij

Figure 3. Overview of method-.#/-0#(&1(2/3#(-'04#!

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Figure 4. Detail of method

II. E STIMATION OF F INGER J OINT A NGLESIn section II, we describe an estimation method of finger
joint angles using 5DT data glove which has been developedin our laboratory (see Figure 3).
A. Representative Hand Motion Patterns
To estimate finger joint angles, this method limits user’s
hand motion to grasping motion. First of all, we chose four
representative hand motion patterns (see Figure 5)[4] fromhuman’s grasping motion (Figure 6)[5].
Furthermore, we assume that a human’s grasping motion
can be represented as a synthetic motion of representative
hand motion patterns. To derive three finger joint angles froma single sensor value, we use the following method (seeFigure 4). We sample many sets of the sensor values with the
low-priced data glove when some subjects open their hand first
and then close it to each representative hand motion patterns.
Also, we sample the sets of the true angles of finger joints
for the same representative patterns, provided that we use true
angles obtained from a data glove which has a lot of sensors.
We use Immersion CyberGlove as data glove with a lot of
sensors. Then, the sensor values and the true angles of finger
joints at the same time are associated. We show an example
of correspondence in Figure 7.
We derive the following numerical formulas using thiscorrespondence.
θpi1
θpi2
θpi3

2
θpi2
3
= Epi2 Si3 + Fpi2 Si2 + Gpi2 Si + Hpi2
= Epi3 Si3 + Fpi3 Si2 + Gpi3 Si + Hpi3

=

(1)
(2)
(3)

where pattern p is one of representative hand motion patterns.
Angles θpi1 , θpi2 and θpi3 express the DIP, PIP, and MP joint
angle of the finger i for the pattern p. The DIP, PIP, andMP joint mean the first, second and third joint of a finger
respectively. The Si is sensor value of finger i. And Epij , Fpij ,Gpij and Hpij are constant parameters for the pattern p, finger
i and joint j. These parameters, Epij to Hpij , are calculated
by pre-experiment. Besides, DIP joint angle is obtained byproportional connection with PIP joint angle (eq. 1)[6]. Joint
angles of finger i of pattern p are obtained by these numericalformulas.
B. Hand Motion Estimation and Angles Estimation
To represent user’s hand motion as synthetic motion ofrepresentative hand motion patterns, we need to know how
similar the user’s hand motion is and to which representative
hand motion patterns. Then, we set the following formulabased on the probability density function of the multivariate
normal distribution for n points in the five dimensional feature
amount space.
1
Lpn = exp{− (S − µpn )T Σ −1
pn (S − µpn )}2(4)where S is the sensor value vector. And µpn and Σ pn
represent mean vector of sensor sample values, and variancecovariance matrix of sample point n (an integer satisfying
1≤n≤a number of samples) in representative hand motion pattern p. Besides, µpn and Σ pn are obtained by pre-experiment
for an average user. If the sensor values are obtained actuallyfrom the glove, we select the maximum value according to thefollowing formula.
Lp = max{Lpn (S : µpn , Σ pn )}n(5)Thus, we get the likelihood on representative hand motion
pattern p in current sensor values. After that, we decide theratio rp of hand motion pattern p according to the following
formula.
rp =LpPΣp=1 Lp(6)

Figure 7. Example of correspondence

where P is the total number of representative hand motions,which takes the value of four. As stated above, we can obtainθpij and rp . At last, each angle θij of current hand posture isderived by the following formula.
θij =

P
∑

rp ·θpij(7)

p=1

III. DATA - GLOVE THAT S ENSOR P OSITIONS ARE L IMITEDIn section III, we describe an estimation method of finger
joint angles using DG5 data glove whose sensor positions arelimited only to PIP joints.

Figure 5. Representative hand motion patterns!"#$%#&%

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A. MP Angle for Representative Hand Motion Pattern
Although we mentioned above representative hand motion
patterns are selected, the pattern Parallel Ext. is almost the
motion related only to MP joints. When doing the Parallel
Ext. pattern, the sensor values hardly change. We tentatively
use three other patterns as representative hand motion patterns
for now.
For the 5DT data glove whose sensors cover PIP and MP
joints, the DIP angle is related to PIP directly, as mentioned in
the previous section. It means the sensor values contain all of
their information. However, using DG5 whose sensors are only
on PIP, the motion of MP does not change the sensor value.
Of course, we assume that the hand motion is a grasping one,so the MP angle of a finger is related to the PIP angle of thesame finger. Then we can assume that the MP of a finger isrelated to the PIPs of all fingers.
We consider a new estimation model to obtain angles forrepresentative hand motion patterns using multiple regression
analysis. First, we make a estimation equation with explanatory
variable is a set of sensor values, and response variable is each
MP joint angle, as follows.
θpi3 =

5∑

Cpif 3 Sf + Ipi3

(8)

f =1

Figure 6. Candidates of representative motions

where θpi3 is MP joint angle of finger i of representative
pattern p, Sf is sensor value of finger f , and Cpif 3 and Ipi3
are constant.

Now, a subject opens his hand first and then closes it
to each representative pattern with DG5 data glove, the setof sensor value Sf (time) of finger f at time is sampled.
Then, the subject moves his hand as each same pattern with
CyberGlove which has many sensors, the set of angle value
θpi3 (time) is sampled as true one.
Here, we should get the constant Cpif 3 and Ipi3 . The
residual sum of squares Q is represented as in (9).


2
5

∑
∑
Q=
θpi3 (time) − 
Cpif 3 Sf (time) + Ipi3  (9)


time

The constant Cpif 3 and Ipi3 to be obtained make Q represented
as the minimum of the equation from (9). And the Cpif 3 andIpi3 that make Q minimum satisfy following equation.
∂Q
∂Q
=
=0
∂Cpif 3
∂Ipi3

(14)

Solving this, coefficient Cpif 3 and constant Ipi3 are obtained
to estimate MP joint angle for representative pattern with (8).
The angles of PIP are obtained directly from the sensor value
with (2), and the angles of DIP are also obtained only from
PIP with (1).

f =1Focusing on coefficient Cpi13 where f = 1;

∑ (
)2
Q=
S1 (time)Cpi13

time


5
∑
+ 2S1 (time)Cpi13 Cpif 3 Sf (time) + Ipi3 
f =2− 2θpi3 (time)S1 (time)Cpi13
2
5∑
Cpif 3 Sf (time) + Ipi3 
+
f =2



− 2θpi3 (time) 

5
∑

(10)

Σpn = Apn B pn



f =2


(
)2 
+ θpi3 (time)(11)

Using the partial differentiations also with Cpif 3 and Ipi3 ;

5
∑
∑
∂Q
=2
Sf (time)
Cpif 0 3 Sf 0 (time)
 0∂Cpif 3
time
f =1

(12)

+Ipi3 − θpi3 (time)


5

∑
∑
∂Q
=2
Ipi3 +
Cpif 3 Sf (time)

∂Ipi3
time
f =1


−θpi3 (time)(15)

Here the Moore-Penrose pseudo-inverse matrix Σ+
pn for Σpn
is described as:
(
)−1
T
T
T
Σ+
=
B
A
Σ
B
ATpn
pn
pn
pn
pn
pn
(16)
)−1
(
)−1 (
ATpn
= B Tpn B pn B Tpn
ATpn Apn

Cpif 3 Sf (time) + Ipi3 Using the partial differentiations with Cpi13 ;

5
∑
∑
∂Q
=2
S1 (time)
Cpif 3 Sf (time)∂Cpi13
time
f =1


+Ipi3 − θpi3 (time)B. Hand Motion Estimation with Pseudo-Inverse Matrix
When the variance of sensor values is zero at the sample
point n of representative hand motion pattern, the variancecovariance matrix will be abnormal at the sample point n.
It means the inverse matrix of variance-covariance matrix of
sensor values Σ−1
pn can not be obtained, and the likelihood forthe sample data of representative pattern p can not be obtainedwith (4).
So we use Moore-Penrose pseudo-inverse matrix to solve
it. The variance-covariance 5 × 5 matrix of sensor values Σ−1pnwhich is abnormal at the sample point n is represented as next
equation with 5 × r matrix Apn and r × 5 matrix B pn where
rank (Σpn ) = r;

(13)

Using this Moore-Penrose pseudo-inverse matrix Σ+
pn for (4)instead of the inverse matrix of variance-covariance matrix of
sensor values Σ−1
pn at the sample point n where inverse matrix
can not be defined, the likelihood is obtained and the ratioof each hand motion pattern is determined with (5) and (6),respectively. Now, we can use a low-priced data glove whose
sensors cover only the middle angle of each finger to estimate
all finger joint angles of current hand posture with (7).
IV. E XPERIMENT AND R ESULTWe performed an experiment to confirm the effectivenessof the method described above. The experiment system wasconstructed using the DG5 Data Glove whose sensor positions
are limited only on middle joints. Other hand motions thatwere different from representative patterns were tested. The
minimum of Activities of Daily Living (ADL) needs thefollowing hand motions (see Figure 8) [7].
1)
2)
3)
4)
5)
6)
7)

Power grasps (used in 35% ADLs)
Precision grasps (30% ADLs)
Lateral grasps (20% ADLs)
Extension grasps (10% ADLs),
Tripod grasps,
Index pointing, andBasic gestures.

We tested five motions; 1)–5).

(1) Power grasp(2) Precision grasp(3) Lateral grasp

Figure 9. Result CG for Power grasp(4) Extension grasp(5) Tripod grasp

Figure 10. Result CG for Precision grasp(6) Index pointing(7) Basic gestures

Figure 8. Hand motions needed for ADL

TABLE I. ERROR OF FINGER JOINT ANGLES [DEGREE]

thumb

index

middlering

littleaveragePower G.

7.3

12.0

10.5

12.5

10.0

10.5

Precision G.

8.1

9.2

7.2

7.0

6.8

7.7

Lateral G.

9.4

6.0

8.8

7.5

10.5

8.4

Extension G.

9.8

8.1

11.0

11.3

9.0

9.9

Tripod G.

8.5

8.5

7.2

11.6

10.9

9.3

average

8.6

8.7

8.9

10.0

9.4

9.2

The subjects opened their hands and then closed them toeach test pattern 1)–5) with DG5 data glove. The average of
estimated joint angles were compared with the true angles
obtained from CyberGlove which had many bend sensors.
Table I shows the average error of finger joint angles. Eacherror is around 10 degrees. The result using the 5DT data glove
whose sensors cover two joints of each finger also had about
10 degrees error [4]. This means that the lower-priced data
glove can obtain joint angles accurately enough.
Actual hand posture images and the CG images generated
from estimated joint angles are shown in Figures 9 and 10.
The MP joints that were not covered with bend sensors are
estimated from the sensors on PIP joints.
V. C ONCLUSION
In this paper, we described a useful method using a lowpriced data-glove based on hand motion patterns. It estimates
all finger joint angles using the data glove whose sensors
cover only the middle angle of each finger. The method has
been expanded from our previous method using a data-glove
whose sensors cover two joints of each finger. A data glove
is one of the major interfaces which are used in the fieldof VR. It measures curvatures of fingers using bend sensor.
However, in order to obtain accurate hand motions, it isnecessary to use an expensive data glove which has many
sensors. On the other hand, there is a low cost data glove
which measures an angle for each finger through one sensor.

It cannot get detailed data directly. Our method estimatesplausible user hand motion patterns using each relation among
angles of fingers during the operation of the low-cost glove
first. Then, it estimates all finger joint angles by estimating thetypes of hand motion patterns from the correlation between
each finger angle in the hand motion pattern. We assumed
some representative hand motion patterns, and considered that
other hand motions could be represented as synthetic motionof these. The ratio of each representative motion pattern iscalculated using Moore-Penrose pseudo-inverse matrix, and all
finger angles are estimated using multiple regression analysis.
With the low priced data-glove being useful, it is expected thatVR systems that target households will become more popular.
In the future, we should reconsider the representative handmotion patterns because we removed Parallel Ext. from ourprevious research based on medical knowledge. We should
also expand the target hand motion patterns to various ones
that are not only grasping patterns.
ACKNOWLEDGMENT
The authors would like to thank our colleagues in ourlaboratory for useful discussions.
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