522024 IEEE Haptics Symposium (HAPTICS)
IEEE Trans. on Haptics Short Papers
Copyright held by IEEE

IEEE TRANSACTIONS ON HAPTICS, VOL. 17, NO. 1, JANUARY-MARCH 2024

Short Papers
Bumps and Dents are Not Perceptually Opposite When Exploring With Lateral
Force Cues
Mirai Azechi and Shogo Okamoto , Member, IEEE
Abstract—Virtual tactile bumps and dents are presented by controlling
frictional forces on a surface tactile display, a flat touch screen with tactile
feedback functions. This technology enables users to touch and feel threedimensional objects. The resistive force against a sliding finger is increased
and then decreased compared to a base level to present a bump. The orderof increase and decrease is inverted for a dent. Thus, the difference between
bump and dent presentations lies in the change order of the resistive force.
However, bumps and dents are not simply opposite when investigating
psychophysical functions with only lateral force cues available, withoutheight and depth information. The results demonstrate that bumps are moreeasily detected with high surface gradients or resultant force changes andsmall widths. In contrast, these parameters do not influence the detection ofdents among different participants. These findings contribute to a deeper
understanding of tactile perception of surface shapes.
Index Terms—Shape, convex, concave, surface tactile display, force
shading.

I. INTRODUCTION
Surface bump shapes can be discerned solely through lateral resistive
forces without any vertical surface displacement by gliding a finger
across the shape [1], [2], [3], as different surface shapes produce distinct
lateral force patterns [4]. This discovery represents a groundbreaking
advancement in surface tactile displays, creating virtual bumps anddents on flat touch panels equipped with variable friction display
devices [5], [6], [7], [8], [9], [10] and facilitating more engaging andassistive haptic content development. However, surface shapes, whether
bumps or dents, may not be correctly distinguished when the change infriction force is limited [11]. Hence, elucidating the specific resistive
force patterns that promote accurate recognition of surface shapes isessential. However, what parameters of bumps and dents should becontrolled to make them more identifiable using only lateral force cues?
Some researchers have investigated the perceptual aspects of bumpstimuli in surface texture displays. Kim et al. compared preferences forthree distinct friction patterns associated with bumps [5]. Their findings
revealed that friction force could be better controlled by referencing
Manuscript received 25 September 2023; revised 1 December 2023; accepted
11 January 2024. Date of publication 24 January 2024; date of current version
21 March 2024. This work was supported by the MEXT Kakenhi under Grants
23H04360 and 20H04263. This paper was recommended for publication by
Associate Editor V. Levesque and Editor D. Prattichizzo upon evaluation of thereviewers’ comments. (Corresponding author: Shogo Okamoto.)
This work involved human subjects or animals in its research. Approval of all
ethical and experimental procedures and protocols was granted by Institutional
Review Board, Hino Campus, Tokyo Metropolitan University under Application
No. H22-31.
The authors are with the Department of Computer Science, Tokyo Metropolitan University, Hachioji 192-0397, Japan (e-mail: azechi-mirai@ed.tmu.ac.jp;
okamotos@tmu.ac.jp).
This article has supplementary downloadable material available athttps://doi.org/10.1109/TOH.2024.3357806, provided by the authors.
Digital Object Identifier 10.1109/TOH.2024.3357806

Fig. 1. Lateral resistive force when a finger slides over a bump or dent. Surface
displacement and resistive force for (a, b) bump and (c, d) dent.

the gradient of a virtual bump. This conclusion was also validated bya surface tactile display featuring force feedback capabilities [9], [12].
Haghighi Osgouei et al. demonstrated the effectiveness of increasing thebase friction level in presenting bumps using an electrostatic frictionvariable display, which only elevates surface friction [6]. Azechi andOkamoto compared the recognition of three types of electrostatic friction stimuli, each corresponding to the gradient functions of Gaussianfunctions with varying width and gradient parameters [11]. Smith et al.
compared conditions involving the presentation of the bump’s displacement and conditions involving the force field resulting from the surface
gradient [3]. They also examined bump and dent classification in active
and passive touch conditions. These studies aimed to identify effective
friction patterns for presenting bumps in surface texture displays andinvestigate the perceptual mechanisms associated with surface shapes.
However, their primary focus did not involve determining the specificparameters of force or shape profiles that influence bump and dent
recognition.
Another area of research interest involves comparing bumps anddents. Previous studies [1], [3], [6], [13] have suggested that the key
distinction between bumps and dents lies in the order of the rising anddeclining slopes, as depicted in Fig. 1. When a fingertip glides over a
bump, it initially encounters the rising slope, increasing the resistive
force required to overcome it. Subsequently, on the declining slope, theresistive force decreases due to the elastic properties of the skin. Hence,
to simulate a bump, the friction force applied to the finger on a touch
panel is first increased and then decreased. Conversely, for a dent, thisorder is inverted. However, our prior study [14] observed divergent discrimination behaviors among participants regarding bumps and dents.
When designing their haptic content, tactile display developers must beaware of differences in the effective force profiles for bumps and dents.

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53

Fig. 3. Design parameters (maximum gradient and σ) of the two-dimensional
Gaussian bump and dent.
TABLE IPARAMETERS OF BUMP AND DENT SPECIMENS

Fig. 2. Apparatus used to decouple the vertical displacement and lateral force.
The specimen, a flat bar with a bump or dent at the center, was explored by aspherical end at the leaf spring tip.

This study addresses the scenario in which humans categorize surface shapes as either bumps or dents based on the variation in lateralresistive forces as a finger encounters a bump or dent. Specifically, we
examine the effects of maximum gradient and width of Gaussian-shaped
bumps and dents on their recognition. In the experiment, a finger isplaced on a linear slider, through which a lateral resistive force is applied
to the finger without its vertical displacement. A similar experiment was
conducted in our previous study [14]; however, the gradient and widthof the surface shape were not independently controlled, and a discussionof individual contributions to shape recognition was not undertaken.

II. METHODS
A. Apparatus
We employed a force-displacement decoupling system in which abump or dent was slid over with a plastic sphere measuring 2 mm
in diameter. The resulting lateral force was transmitted to a fingertip
through a leaf spring, as illustrated in Fig. 2. One end of the leaf
spring was affixed to a linear slider, restricting its movement along
the x-axis. Consequently, the fingertip on the slider did not experienceany displacement in the y-direction (direction normal to the fingerpad). A specimen bar featuring a bump or dent shape on its surface,as described in Section II-B, was positioned parallel to the linear guide.
The apparatus is similar to that used in our previous experiment [14].
To measure the force profiles generated when exploring these shapes,
we integrated two load cells (Micro load cell, Phidgets Inc., Canada)
into fixtures designed to support the specimen. The specimen was
secured by positioning the load cells with a preload on either side.
The signals obtained from the load cells were processed using dynamic
strain amplifiers (DPM-911 A, Kyowa Electronic Instruments Co.
Ltd., Japan). The position of the linear slider along the x-axis wasmeasured by an encoder (RE30E-500, Nidec Copal Electronics Corp.,
Japan, 500 pulses/revolution) with a string wound around a pulley(diameter of 10 mm) aligned with the encoder’s axis of rotation. The
force and position data were recorded using a data acquisition system(USB-6216, National Instruments Corp., TX) at a sampling frequencyof 1 kHz. These data were not collected during the main experimental
session involving the invited participants because participants would
be distracted by a few tens of seconds required to reset the amplifiers.

B. Stimuli: Bump and Dent
As shown in Fig. 3, we employed Gaussian functions as the profiles for bumps and dents, with their maximum gradient and widthFig. 4.

Balance of contact force and gradient on a slope.

controlled across three levels, as outlined in Table I; these levels were
established as geometric progressions with factors of 1.32 and 1.68,
respectively. Thus, nine specimens were utilized for each bump anddent, corresponding to the three gradient levels multiplied by the threewidth levels. For selecting the parameter values, the authors and one of
their colleagues tested 30 prototype specimens covering parameters in
Table I. The parameters with which the mean proportions of accurate
categorization were between 60% and 90% were then employed. These
people were excluded from the main experiment.
The shapes of the bump and dent were determined using a Gaussianfunction as follows:
y(x) = ±h exp

−x2
,
σ2

(1)

where h and σ denote the height and width of the shape, respectively.
The height or depth at x = σ is 37% of that at x = 0. Gaussian functions
were preferred by previous researchers [1], [3], [6] to benefit from its
continuous derivative function.
When a bare finger interacts with these shapes, their height andwidth can be independently varied. The height and depth were notconveyed as normal displacement cues in our experimental setup. When
only lateral forces were transmitted to a finger exploring the shape,
the maximum and minimum lateral forces exerted a more significant
perceptual influence than the height and depth. As discussed below,
the gradient directly determines the maximum and minimum forces.
Hence, we designated the maximum gradient as a design parameter forthe stimuli.
As shown in Fig. 4, under the point contact and small-friction
condition, the static contact force is balanced by
dy
fx
,
=
fy
dx

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(2)

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IEEE TRANSACTIONS ON HAPTICS, VOL. 17, NO. 1, JANUARY-MARCH 2024

TABLE IIMEAN PROPORTIONS AND STANDARD ERRORS OF CORRECT ANSWERS FOR
BUMPS

Fig. 5.

Example of specimens made of middle-density fiber.

where the lateral and normal components of the contact force aredenoted as fx and fy , respectively. This equation does not hold perfectly
for the contact between a fingertip and bump [4],√ [13].
The maximum gradient occurs at x = ±σ/ 2, where the ratio of
lateral to normal force reaches its peak. The maximum and minimum
gradients are as follows:
√


1
2h
exp −
.
(3)
±
σ
2
The maximum gradient depends on h and σ of the shape; hence, toindependently control the maximum gradient and σ of the shape, we
varied the value of h to determine the maximum gradient. For example,
for a bump with a maximum gradient of 0.0833 and σ = 5.0 mm,
h = 0.49 mm. Similarly, for a bump with a maximum gradient of 0.144
and σ = 14.1 mm, h = 2.37 mm.
As depicted in Fig. 5, the shape specimens were precision-cut frommedium-density fiberboard using a laser cutter (Hajime, Oh Laser Co.
Ltd., Japan). The cut surfaces were refined using fine abrasive papers
after the cutting process. The highest and lowest parts of each specimen
were measured by a caliper (Digimatic caliper, Mitsutoyo Corp., Japan;
nominal resolution: 0.02 mm). The disparities in these values between
the designed shapes and fabricated specimens were minimal, with errorsof less than 5%.
Fig. 6 presents the lateral force profile when exploring the bumps
and dents from left (negative direction of the x-axis) to right (positive
direction of the x-axis). These profiles represent the mean profiles of ten
measurements, during which the slider maintained a consistent speedof approximately 20–30 mm/s. The profiles for the bump and dent withthe same σ and gradient values are symmetric.

C. Ethical Statement
This study was approved by the Institutional Review Board at the
Hino Campus of Tokyo Metropolitan University (Approval ID: H2231).

D. Participants
Ten university students, including two women, participated in the
study and received compensation for their involvement after providing
written informed consent. The study objectives were not disclosed tothe participants prior to the experiment.

E. Procedures
In the training session, participants, while wearing earmuffs, placed
their second finger of the writing hand on the linear slider and moved it
along the x-direction. They explored bumps and dents not used in thesubsequent main session to understand the lateral forces generated bythese shapes’ rising and declining slopes. Participants had the opportunity to visually inspect the specimen shape placed on the apparatus
during this session. This training session lasted approximately 5 min,during which participants familiarized themselves with the resistive
forces produced by these specimens. They were encouraged to determine an appropriate hand speed at which the shapes could be discerned
and were instructed to use this speed in the subsequent main session.
It was empirically shown that realizing an irregularity on a flat surface
at extremely high speeds is easy, but classifying it into a bump or dent
is difficult. In contrast, it is difficult to notice shapes at extremely slow
speeds.
In the main session, participants were blindfolded, and 180 trials
were conducted for each individual (comprising 18 types of specimens multiplied by 10 blocks). The specimens were presented in arandomized order within each block, comprising 18 trials. In each trial,
participants were permitted to explore the shape twice. They moved theslider from left to right across the shape and then reversed from right toleft before responding to whether the shape was a bump or a dent in aforced-choice manner. After every 36 trials, participants took a 3–5 min
break.

F. Analysis
As shown in Fig. 7, for individual participants, the proportions ofcorrect answers for either bumps or dents were approximated using alogistic curve, used to model a probability distribution function, withthe maximum gradient and width of bumps or dents as the explanatory
variables. The regression equation is as follows:p=1
1+ 0.5,
2 1 + exp (−(a1 x1 + a2 x2 + c))(4)

where p, x1 , and x2 denote the proportion of correct answers, maximum
gradient, and width, respectively. The maximum gradient and width coefficients are denoted as a1 and a2 , respectively, and the constant value
in the exponential function is represented by c. For the approximation,
the maximum-likelihood method was employed. In the exponentialfunction, we employed the linear summation of the first-order terms.
This is because, for most participants, the multiplicative term coefficients, including x21 , x1 x2 , and x22 , did not significantly differ fromzero in the preliminary analysis when determining the model function
using the least-squares method.
The χ2 statistic was used to gauge the deviance level between themodel equation and observed proportions. To test the goodness of fit of
the model, the Hosmer-Lemeshow test, based on χ2 , was used, with acritical value for the rejection region set at χ2 (7) = 14.1 at p = 0.05.
If the data of a particular participant were determined not to fit the
regression model, their data would not be used for subsequent analyses.
However, all individuals’ data were retained based on the HosmerLemeshow test results.

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55

Fig. 6. Profiles of resistive forces when sliding a finger across a bump (a)–(c) and dent (d)–(f) from left to right. Each profile is the mean of ten measurements.
Negative values indicate assistive force.

for the gradient is significantly greater than zero (t(9) = 3.36, p =0.0084, two-tailed t-test). Similarly, the mean coefficient for the widthis significantly smaller than zero (t(9) = −7.37, p = 4.22 × 10−5 ,two-tailed t-test). These coefficients indicate that bumps with a steeper
gradient and narrower width are more easily recognized. Appendix
shows the logistic curve for bumps based on the average results among
the participants. It also compares the influences of the maximum gradient and width on the accuracy of shape classification. In contrast, fordents, the mean coefficient for the gradient and width ((t(9) = −0.27,
p = 0.79, two-tailed t-test) and (t(9) = −0.85, p = 0.42, two-tailed
t-test), respectively), are significantly different from zero. Thus, theaccuracy of recognizing dents is not influenced by the gradient or width.

IV. DISCUSSION
Fig. 7. Example of logistic regression analysis of the correct answer proportions against bumps. Data of Participant 9 (P9).

TABLE III
MEAN PROPORTIONS AND STANDARD ERRORS OF CORRECT ANSWERS FOR
DENTSIII. RESULTS
Tables II and III display the mean correct answer proportions forbumps and dents, respectively. The mean correct proportions for bumps
and dents were 0.78 and 0.75, respectively. A Wilcoxon signed-rank
test revealed no significant difference between these proportions (T =1541, p = 0.12).
Table IV provides the partial regression coefficients obtained fromthe logistic regression analysis. Regarding bumps, the mean coefficient

The finding that bumps with greater gradients were more easily
recognized is consistent with the idea that the lateral force magnitude isa key for recognizing surface shapes. A smaller width rapidly changes
the lateral force, enhancing the detection of shape cues. The forcechange rate is more perceptually influential than the force magnitude,
a concept supported by others [15], [16], [17]. However, making thewidth too small may not necessarily lead to easier shape categorization.
If the force changes rapidly over a short time, of the order of tens of
milliseconds, the order of force changes may not be correctly judged
due to temporal masking effects [18], [19], [20]. While earlier studies
on temporal masking effects have not specifically examined a situation
similar to the problem in this study, excessive rapid lateral force changes
could be prone to misjudgment. Exploring the effects of σ values
smaller than those used in this study might reveal that the correct answer
proportion for bumps could reach a local maximum at a certain σ value.
However, bumps with even smaller σ values might not be accurately
categorized due to the rapid changes in the produced force.
While the effects of gradients and widths of bumps on recognition
were discernible, we identified no common perceptual influences ofshape features when recognizing dents. One possible explanation isthat participants might have chosen the “dent” option when uncertain
whether they were encountering a bump. If such a negative bias were
present, we would expect the correct answer proportion for dents

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TABLE IV
REGRESSION COEFFICIENTS OF LOGISTIC REGRESSION ANALYSIS

to be higher than that for bumps. However, the proportions of correct answers for bumps and dents were close, suggesting that dents
were not consistently selected as the default response with increasing
uncertainty.
Based on the introspective reports provided by participants after theexperiment, most participants concurred on a common strategy for
categorizing shapes. They categorized the shape as a bump if they
perceived an increase in lateral force or a slight sticking sensation
followed by a subsequent decrease in force. Conversely, when the orderof these sensations was reversed, they categorized the shape as a dent.
Furthermore, participants acknowledged that detecting the increase inforce was relatively easy but had difficulty recognizing the decrease inforce when exploring the surface.
This observation leads to the speculation that the accurate categorization of bumps and dents depends on how distinctly the drop in lateralforce is perceived. If this speculation were accurate, one might expect
recognizing bumps to be easier than that of dents because bumps cause
a substantial drop in lateral force after reaching their peak, as shown in
Fig. 6. However, the proportions of correct answers were nearly equal
for bumps and dents, casting doubt on this speculation.
The distinction in recognizing bumps and dents might be influenced
by the Weber fraction associated with lateral or friction forces [14],[21]. According to the concept of the Weber fraction, a slight change inforce Δf is more perceptible when it follows an immediate decrease in
the base force level F . Let F0 and F1 represent two base force levels,with F0 > F1 . In such a scenario, the inequality of Weber fractions
holds:
Δf
Δf
<
.
F0
F1

(5)

However, in our problem, applying Weber fraction may not be straightforward. This is because the sign of the lateral force experienced by
the participant changes when exploring the shape. When the tip of theslider traverses a rising slope, the lateral force is resistive (positivein Fig. 6); in contrast, when it descends a declining slope, the lateralforce becomes assistive (negative in Fig. 6). Weber fractions have notbeen extensively discussed for situations involving such sign changes
in lateral force.
Temporal masking effects [18], [19], [20] may also pertain to thedifference between the bump and dent recognition. When encountering
a bump, the succeeding decrease in the lateral force due to the declining
slope may be perceptually obscure, provided an increase in the lateralresistive force is prominent. In contrast, for a dent, a rising slope maymask the immediately preceding decline in a backward manner. The
temporal masking effects for the lateral force will be studied in the
future.

The experimental results suggest that the factors influencing therecognition of bumps and dents differ, but the specific reasons remain
unclear. Additional studies are needed to investigate this further. One
promising approach is to expand the parameter space used in theexperiment. In this study, the mean correct answer proportions forthe nine types of bumps and dents ranged from 0.64 to 0.91 and 0.67
to 0.82, respectively. Therefore, it may be necessary to magnify theparameter space such that the correct answer ratios for dents vary
more substantially to identify the feature parameters influencing therecognition of dents. Additionally, it is worth considering whether
the exploratory motions employed for bumps and dents differ. In thisstudy, participants were allowed to explore each shape twice, potentially
adapting their second exploration based on their experiences from thefirst. Therefore, limiting the number of explorations to one could beconsidered. However, the experimenters observed no apparent differences in exploratory motion between bumps and dents.
Furthermore, differences in hand speed among the participants canbe a key to elucidating the individual differences in the parameter
coefficients in Table IV. Especially, the coefficients for dents than thosefor bumps varied among the participants. Such differences may be
explained by analyzing participants’ hand motions, although we did
not record them in the main experiment. Therefore, we invited eight of
the ten participants on different days and conducted tasks similar to themain experiment but including a small number of trials, i.e., 20 trials,
while measuring the hand speeds. The mean hand speeds of individuals
ranged from 25–44 mm/s with moderate variations. Further, the means
and standard errors of the speed for the first (37.2 ± 8.1 mm/s) andsecond exploration (33.0 ± 7.3 mm/s) exhibit no substantial difference(t(7) = 0.58, p = 0.62, t-test for repeated measures).

V. CONCLUSION
For a considerable time, it has been established that macroscopic
surface shapes can be conveyed using two-dimensional haptic or tactile
displays without invoking normal displacements and forces [1], [2].
Nevertheless, the factors determining the discriminability between
bumps and dents when presented via lateral forces remained unexplored. Our experiment revealed that bumps with greater gradientsand narrower widths were recognized more accurately. However, theseparameters did not exert a significant influence on dent recognition.
Moreover, it was believed that the primary difference between bumps
and dents lay solely in the order of the increase and decrease in lateralforce. However, this study has unveiled the distinction in the perceptual
criteria used to differentiate between them. These findings are specific
to Gaussian-shaped bumps and dents, and further research is needed
to explore their applicability to different shapes and scenarios in the
future.

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