Three-Dimensional Localization of a Finger in
Water Using Human Body Antenna Signals
Tzu-Hsuan Hsia

Shogo Okamoto

Nagoya UniversityNagoya, JapanTokyo Metropolitan University
Hino, Japan

Abstract—HumTouch is a touch sensing method that leverages the electric currents of the human body generated by
AC hum-noise present in the surrounding environment. Thissensing principle facilitates the detection of human touch on
semiconductive materials. In this study, we demonstrated thelocalization of a ﬁnger in a plastic tank ﬁlled with puriﬁed water.
The currents emitted by the human ﬁnger were measured usingeight electrodes installed in the tank to estimate the ﬁnger’s
position employing a kernel regression method. The average
estimation errors among the three participants were 3.52, 0.55,
and 0.72 cm in the depth and the other two orthogonal directions,respectively. The localization errors were negligible in the twodimensional plane perpendicular to the depth direction; however,they were substantial in the depth direction within the water.
Index Terms—HumTouch, ﬁnger sensing, water sensor

I. I NTRODUCTION
Touch sensing technologies paly an essential part in ourdaily lives. Recently, sensing methods capable of turning
non-specialized surfaces into touch-sensitive surfaces havegarnered the attention in consumer electronics [1]–[5]. One
example is an ultrasonic touch sensing system that leverages
a strain of ultrasonic waves transferring through a rigid object
such as a wall to detect a touch on it [1].
Our research groups have been developing a sensing methodreferred to as HumTouch [2], [6]–[8] that localizes a humantouch on semi-conductive material surfaces by measuring thecurrent leak from a human body reacting to AC hum-noise inbuildings. The conductive materials in human bodies, such asminerals, react with these electromagnetic waves and generatecurrents in our bodies. When a human contact is made with aconductive or semi-conductive object, current leaks from thebody into the area in the vicinity of the contacted area. This
current can be measured by attaching electrodes to the object
and subsequently connecting with data acquisition devices
as shown in Fig. 1. Thus far, HumTouch has proven to beavailable for granite stone [9], paper and wood painted withsemi-conductive ink [2], [10].
In this study, we investigated the localization performanceof HumTouch when applied to underwater settings. Earlier
studies on human monitoring and detection in aquatic environments have relied on camera [11], global navigation satellite
systems, and inertial measurement units [12]. By contrast,
HumTouch offers an occlusion-free and privacy-preserving
This work was supported by KAKENHI #20H04263 and #23H04360.

979-8-3503-4017-4/23/$31.00 ©2023 IEEE

Fig. 1. Principle of HumTouch. The human body reacts with the electromagnetic waves generated from AC power lines. The current leaks into the waterand is measured using electrodes in the water. This is used for localization.

method for such purposes compared to previous approaches.
In addition, it is particularly suited for use in small-sized watertanks.
In our previous study, we localized a human ﬁnger ina plastic tank ﬁlled with puriﬁed water in one dimension
using two electrodes [13]. In this study, we investigated thelocalization of a human ﬁnger under puriﬁed water in threedimensions using eight electrodes in the tank.
II. A PPARATUS AND EXPERIMENTAL SETTING
We ﬁlled a plastic tank with puriﬁed water (Puriﬁed water,TRUSCO, Tokyo, Japan) as shown in Fig. 2. The volume of thewater was 37.5×25.0×17.5 cm3 . It was conﬁrmed that similar
results could be acquired using tap water from the western partof Tokyo, Japan. Six locations were marked at three different
heights (total 18 locations) at intervals of 7.5 and 9.0 cm along
the x and y axes, respectively, as shown in Fig. 2 (b). For theheight of the tested locations (z-axis), we selected three levels
as follows: 1 cm below the surface level such that only theﬁngertip was in the water, 11 cm above the bottom such thatthe entire index ﬁnger was in the water, and the bottom ofthe tank. Eight electrodes were attached at the corners of thetank and connected to two synchronized oscilloscopes (HS6DIFF, TiePie Engineering, Netherlands; sampling frequency:
500 kHz) to record the signals.
Three participants volunteered for the experiment. The
participants removed their shoes and remained still during
the experiment to ensure proper connection to the ground.
They inserted their index ﬁnger into the water and held theirﬁngertip at the designated location for approximately 1 s.
Consequently, 18 locations were recorded in one experimental
set and ﬁve such sets were recorded for each participant.

967

(P1)
Mean error: 1.98 cm
y location (cm)3020
100102030x location (cm)
(P2)

(P3)
Mean error: 1.41 cm

Mean error: 1.80 cm

Fig. 2. Experimental setup. (a) Tank ﬁlled with puriﬁed water and eight
electrodes. (b) Top and (c) front view of the tank. Crosses indicate the target
points.

III. K ERNEL REGRESSION MODEL TO LOCALIZE THE
FINGER POSITION

We applied the kernel regression method to estimate thelocation of the ﬁnger in three-dimension. Similar methods
were used for the localization on a plane [2], [6]. Whenthe ﬁnger is inserted into the water, the recorded maximum
voltages are denoted as ve , where e is the eth electrode. Vector
vs = (v1 , v2 , ..., v8 )T incorporates the maximum voltages
detected by the eight electrodes for sample s. When a voltage
set is provided by vs , the corresponding ﬁnger position (x̂, ŷ,ẑ)T is estimated as follows⎡ ⎤ ⎡ n⎤2x̂
s=1 αx,s exp(−|vs − v | )⎢ ⎥ ⎢⎥⎢ ⎥ ⎢ n⎥
2 ⎥⎢ŷ ⎥ = ⎢(1)⎢ ⎥ ⎢ s=1 αy,s exp(−|vs − v | )⎥ ,⎣ ⎦ ⎣⎦n2ẑ
s=1 αz,s exp(−|vs − v | )where n is the number of the samples in the learning set and|.| is the L2 norm. The coefﬁcients αx,s , αy,s , and αz,s are
the sth element of the vectors of coefﬁcients αx , αy , andαz , respectively. The vectors of coefﬁcients are computed asfollows⎡ ⎤⎡ ⎤αxx⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢αy ⎥ = (K + λI)−1 ⎢y ⎥ .
(2)⎢ ⎥⎢ ⎥⎣ ⎦⎣ ⎦zαz
where the vectors x = (x1 , ..., xn )T ,y = (y1 , ..., yn )T , andz = (z1 , ..., zn )T are the coordinates of the touched locations
for the learning samples. The regularization value λ was 0.001
and I was a n × n unit matrix. Matrix K was computed asfollows⎤⎡
exp(−|v1 − v1 |2 ) . . . exp(−|v1 − vn |2 )
⎥⎢
..
..
..
K=⎣
⎦ . (3).
.
.
exp(−|vn − v1 |2 )...

Fig. 3. Results of localization for participants P1, P2, and P3. The ﬁgure at
the top right presents a top view of the results for P1. The black lines indicate
the boundary of the water. The points and error bars indicate the means andstandard deviations of the estimates, respectively.

ﬁve sample sets were used to construct the regression model,and the model was tested using the remaining sample set. This
procedure was iterated ﬁve times for each participant. Fig. 3
shows the mean estimated locations among the ﬁve trials forthe three participants. The average estimation errors for P1,P2, and P3 were 1.98, 1.41, and 1.80 cm, respectively. For
P1, the mean estimation errors along the x, y, and z directions
were 1.21, 0.60, and 4.12 cm, respectively. Further, for P2,
they were 0.66, 0.91, and 2.65 cm, respectively. Finally, for
P3, they were 0.99, 0.64, and 3.79 cm, respectively.
V. C ONCLUSION
In this study, we presented a method for localizing a humanﬁnger while submerged underwater at 18 distinct locations.
The results indicate that the mean estimation errors were lessthan 1.0 cm in both the x and y directions, implying that ﬁnger
localization can be achieved with an error margin smaller
than the size of a ﬁngertip. However, in the longitudinal or
depth direction of the ﬁnger, the mean localization error wasdetermined to be 3.52 cm. This ﬁnding implies that localizing
the tip of elongated human body segments such as ﬁngers
using the methodology employed in this study may present achallenging task.

exp(−|vn − vn |2 )IV. R ESULTS
To evaluate the localization performance, we applied theleave-one-out cross validation. For each participant, four out of968

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