The Fishbone Tactile Illusion
Masashi Nakatani∗

Robert D. Howe†

Susumu Tachi‡

The University of Tokyo

Harvard University

The University of Tokyo

A BSTRACTThis paper describes a novel tactile illusion in which a convex andconcave shape cannot be distinguished through stroking by the ﬁnger tip. The shape consists of a set of parallel ﬂat ridges a few mm
wide, separated by a few mm, a fraction of a mm high, and oriented perpendicular to the direction of ﬁnger tip motion. A similarcentral ridge underneath the ﬁnger tip is either at the same heightas the space between the perpendicular ridges (concave), or raisedat the same height as the tops of the perpendicular ridges (convex).
We investigated the relationship between (1) the width of the central
ridge and (2) the spatial frequency of the ridges. Our results showedthat the smaller the size of the central ridge, the easier for subjects
to feel an illusory concave shape. Also, the higher the spatial frequency, the more easily subjects could feel a concave shape. Thisillusion may provide a means for rendering geometric information
without creating physical shapes, in both virtual environments andin the real world.
Keywords: tactile illusion, geometric perception, tactile rendering, brightness contrast
1

Figure 1: An example of the pattern for inducing an illusionary concave shape. The shape shown on the left is a milled aluminum plate,
and the right is a CAD model of this pattern.

patterns that evoke similar illusory perceptions. We then discusspossible explanations for the illusion, in terms of associations between distributed skin stimulus and inferred surface geometry. Finally, we propose potential applications of this illusion in design ofobject surfaces and tactile displays.

I NTRODUCTION

When we touch an object, we can easily tell the difference between
convex and concave surface geometry. This ability comes quite
naturally, and tactile sensation usually provides reliable perception.
We have found, however, a novel tactile illusion in which a concave
shape is perceived even though it is actually a ﬂat surface or a convex shape. The illusion occurs when stroking the ﬁnger tip along
the smooth central strip between the set of raised ridges shown in
Figure 1. It also occurs for ﬂat textures (surface height variation<< 1 mm) with a smooth central strip.
Perceptual illusions have been the subject of considerable interest in a variety of sensory modalities, with visual illusions receiving
the most attention. Perhaps the oldest report of a tactile illusion isfrom Aristotle [1]. Recently, several examples of haptic illusions
have been presented in the research literature [7] [10] [12], including some that are analogous to visual illusions [9] or that involvethe interaction between visual and tactile sensation [3] [4]. Illusion research can contribute to fundamental understanding of themechanisms by which humans reconstructs the outside world fromsensory stimulus. In addition, illusion mechanisms may prove useful in the design of displays or sensors, for example, in designing
information compression approaches that minimize perceptual effects.
In this paper we present examples of our illusionary phenomenon, and show the results of sensory experiments for evaluating this illusion quantitatively. In particular, we examine the rangeof stimulus parameters that successfully evoke the illusion, including ridge height and central strip width. We also describe texture∗ e-mail: nakatani@star.t.u-tokyo.ac.jp† e-mail: howe@deas.harvard.edu‡ e-mail: tachi@star.t.u-tokyo.ac.jp

2

AN OVERVIEW OF THE ILLUSION

The designation “Fishbone Tactile Illusion” (FTI) derives from theshape of the prototypical stimulus which is most effective in evoking the illusory perception (Figure 1). If a ﬁnger tip is freely
stroked back and forth along the centerline of the pattern (the ﬁsh’s“spine”), the adjacent ridges generate strong stimulus to the sidesof the ﬁnger pad skin. This generates a perception that the center ofthe pattern is concave, i.e. the central strip is lower than the ridge
height, whether this central strip is in fact higher, lower, or the sameheight as the ridges. This illusion occurs regardless of the scanning
direction of the ﬁnger; for example, the pattern may be rotated 90
degrees and the ﬁnger stroked laterally. In addition, this illusion
can be perceived both in passive touch and active touch. For theraised ridge stimulus, the concave perception occurs with both adry surface or with lubrication.
The illusion also occurs if a smooth central strip is placed between a variety of surfaces that provide cutaneous stimulus. In particular, the lateral surfaces can be rough pattern with small surface
height variation, such as ﬁne sandpaper. However, if the central
smooth area is too wide, it becomes difﬁcult to feel the illusory
indented shape. This suggests that the difference between surface
characteristics within the same ﬁnger tip contact area is essential
for this illusion. In the following section, we present simple psychophysics experiments that examine the dependence of the concave perception on the stimulus parameters.

3

SENSORY EVALUATION EXPERIMETNS

3.1

Experiment 1: Central strip width vs. perceived depth

Methods. A set of aluminum stimulus plates was created using a 3D
milling machine (MDX-20, Roland Inc.); one example is shown in
Figure 2. The black areas are raised with respect to the white areas
by 0.1 mm. Each plate contained two adjacent patterns, one with acentral strip the same height as the ridges (shown as black in Figure2a), and one with a central strip the same height as the inter-ridge
spaces (white in Figure 2b). Ridge widths and inter-ridge spacing
were 1.3 mm. There were six values for the width of the central
smooth area (w=1.3, 2.0, 3.0, 5.0, 8.0, 10.0 mm) for each of thetwo shapes (a and b) shown in Figure 2.
To assess concave perception as a function of central ridge width,
subjects held the test plate in both hands, then actively stroked thecentral ridges of each pattern with the adjacent thumb. Subjects
were asked to select which pattern was concave in a two-alternative
forced-choice procedure with unlimited time. Only a single trial
was conducted for each pattern to minimize learning effects. Subjects could not see the test plate.
In a subsequent trial, subjects evaluated the depth of the illusory concave perception, using a “reference stimulus plate” shownin Figure 3. This plate had a series of 5 mm wide concave strips
machined to a depth of 0.1 mm to 1.5 mm in 0.1mm intervals. Subjects compared the illusory depth of the central strip stimulus platein Figure 2a to this reference plate by freely stroking both test andreference plates with their right index ﬁnger. In both trials, there
were seven subjects (ﬁve male, two female, ages 22 to 30), all righthanded.
Result. Results are shown in Figure 4. At the smallest central strip
width (1.3 mm), all subjects chose the illusion as concave in preference to the actual concave pattern. The strength of the illusion
decreased as the central strip width increased, with approximately
equal responses at 3.0 mm width. Above 5.0 mm width, subjects
almost universally chose the actual concave pattern over the illusion. In the depth evaluation trial, where subjects compared the test
stimulus to the reference plate, the mean perceived depth was approximately 0.25 mm for widths of 5 mm and less, then decreased
to less than 0.1 mm perceived depth for central strip widths of 10mm. No subject reported a depth greater than 0.4 mm. Following
the experiment, we used an ink transfer test to conﬁrm that subjects
were able to touch the bottom of each reference groove up to at least
0.5 mm.
0.1mm

(a)

(b)

1.3mm
1.3mm

0.6 - 1.0 mm

0.1 - 0.5 mm

Figure 3: Reference stimulus metal plate and CAD model. The depth
increased by 0.1mm in successive grooves. Width of the grooves is
5mm. Subjects compared this reference stimulus and test stimulus
sets to evaluate the subjective depth perception.

3.2 Experiment 2: Ridge spatial frequency vs.
depth

perceived

Method. To investigate how the spatial frequency of the ridges affects the concave illusion, a stimulus consisting of thin cardboard
paper, 0.25 mm thick, was incised with a series of cuts (Figure 5).
The slits were made with a computer-controlled cutting machine(Design Cutter Stika SX-12, Roland Inc.) to ensure precise positioning. This stimulus was replaced every trial, to eliminate surface
wear. Line intervals were 1, 2, 3, 4, 6, 8, 10 mm. The smooth central strip width was 3 mm and the lateral slits were 10 mm wide oneach side.
Subjects evaluated the subjective depth of the central smooth
strip through comparison with the reference stimulus plate used in
the ﬁrst experiment. To help standardize the velocity of subjects’
ﬁnger movement, subjects were instructed to synchronize their ﬁnger movement with the audio signal from a metronome, so that theentire length of the stimulus pattern was covered between successive metronome beats (tempo 90 beats/min, stimulus length about
40 mm, ﬁnger velocity about 60 mm/s). Subjects were allowed tosee the pattern to ensure that the ﬁngers remained in the central
strip. Five subjects participated (three male, two female, ages 22 to30).
Results. The result showed that subjective depth amplitude decreased as the distance between stimulus slits increased (Figure 6)
for the range of the tested values. The mean subjective depth wasaround 0.2-0.1mm for line intervals of 1 to 4 mm. For spacing
above about 6 mm, stimulus depth was zero for 4 of the 5 subjects
and 0.1 mm for the ﬁfth subject. This suggests that at these low
spatial frequencies, the stimulus in the lateral areas is not sufﬁcient
to create the illusion.
3.3 Other informal tests
In addition to the experiments reported above, we conducted a series of informal tests to further explore the dependence of the illusion on stimulus conditions.
3.3.1 Effect of the height of the smooth surface
We created ﬁshbone pattern test plates with a smooth central strip
raised above the ridge heights. The height difference between background and the top of the smooth area was up to 0.3 mm. Subjects
still perceived concave geometry with these highly convex surfaces.

Figure 2: Machined aluminum stimulus plates containing two complementary stimuli and corresponding CAD models. (a) Illusionary
concave shape (actual convex shape) (b) Concave shape, reversing
the height distribution of (a). Black areas are raised 0.1 mm above
white areas.

3.3.2 Material Difference including temperature difference
To verify that it is possible to create this illusion by simply usingmaterials of different surface properties, we created the examples
shown in Figure 7. A 3 mm wide acrylic plate was sandwichedPercentage for answering (a)as a concave shape [%]

100

60
40
20

0

scanning
direction

1.3 2 3
5
8
10
The width of the smooth area [mm]averagesubject 1
subject 2
subject 3
subject 4
subject 5
subject 6
subject 7

0.1
0
-0.1
-0.2

interval

-0.3
-0.4
0

10mm 10mm
3mm

1.3 2 3
5
8
10
The width of the smooth area [mm]Figure 4: Results of experiment 1. Top: Fraction of subjects choosing the illusionary concave shape in preference to the actual concave
shape. Bottom: Subjective depth of the test plate selected by comparison with the reference stimulus plate in Figure 3.

with different kinds of materials (a) synthetic wood (main component is polyurethane); (b) foamed aluminum; and (c) natural wood.
The surface of each face was cut ﬂat by using a milling machine.
These three materials exhibit three very different ranges in friction
when cut, from very low (a) to very high (b). In informal experiments, most subjects felt an indentation in the acrylic plate area
when stroking (b) and (c), but no subject reported that (a) felt concave. This correlates with the higher surface roughness of the surrounding material in (b) and (c) compared with (a). In addition,in object (c), the roughness of the surface was slightly different inregions (1) and (2) (see Figure 7), and some subjects reported a perception of an inclined concave shape at the boundary between (1)and (2).
On the other hand, thermal conductivity difference does not appear to generate the illusion. We created the same type of composite object by gluing an acrylic plate between a pair of aluminum
bars, which were then machined smooth. No illusion of depth resulted. These materials had very low and approximately equal surface roughness, and it was very difﬁcult to judge by touch whether
it was made of one material or two.
3.3.3

smooth area

80

0

Subjective depth for the centerline [mm]lateral rough areas

Vertical stimulus isolation using a pin matrix

To help to separate the relative contributions of vertical and horizontal skin stimuli in the illusion, we used a passive high density pin
matrix [11]. This passive device is composed of steel pins 0.8 mm
in diameter with 1.0 mm center-to-center spacing. The pins’ movement is constrained by close-tolerance holes in ﬁberglass boards toallow free movement in the vertical direction and essentially prohibit motion in the vertical direction. Users place the index ﬁnger
over the top of the pin array and grasp the boards between thumband middle ﬁnger, then stroke the array over the test surface (Fig-

Figure 5: Stimulus pattern in experiment 2. Black lines represent
slits in the cardboard substrate (Readers can readily create a concave
illusion stimulus from this ﬁgure. Please see Appendix).

ure 8). Each pin samples the height information from the surface
pattern and relays it to the ﬁnger tip. Under these conditions theconcave shape illusion is also produced. As the pin array removes
most, if not all, of the lateral stretch from stroking the test pattern
directly with the ﬁnger tip skin, this suggests that the illusion canbe produced through vertical displacement alone. This is further reinforced by the observation that lubrication of the test surface does
not eliminate the illusion.
4

GENERAL DISCUSSION

The results above show that the ﬁshbone tactile illusion is a robust
sensory phenomena across a speciﬁc range of stimulus parameters.
The key requirements appears to be a smooth central region up to afew mm wide with a signiﬁcant tactile stimulus on either side. The
spatial frequency, materials and pin matrix tests suggest that a rangeof tactile stimuli in the lateral regions are effective in inducing theillusion, as long as the spatial period of stimulation is less than a
few mm. Thermal conductivity differences, however, do not appear
to produce the illusion.
4.1 Causes of the Fishbone Tactile Illusion
Figure 9 represents the information ﬂow of the sensory signal fromthe patterned surface to mechanical skin stimulus to neural signal processing to conscious perception. We advance two plausible
mechanisms to explain the concave illusion. First, the mechanicaldeformation of the ﬁnger tip may be same for both the concave andconvex patterns. This might occur, for example, if the dominantstimulus for the ridged patterns in Figure 2 is from the edges thatare perpendicular to the direction of ﬁnger tip motion; in this case,both the concave and convex patterns produce the same stimulus.
The second mechanism is an association between roughness perception and shape perception, so that the absence of surface rough-Subjective depth for the centerline [mm]averagesubject 1
subject 2
subject 3
subject 4
subject 5

0.1

0

-0.1

-0.2

-0.3

Fishbone texture
0 1 2 3 4
6
8
10
The interval of the line in the rough area [mm]Figure 6: Results of Experiment 2. The smaller the interval between
slits (i.e., the higher the spatial frequency), the deeper the illusory
perception.

High density pin matrix

Figure 8: Rubbing ﬁshbone tactile pattern with a high density pin
matrix. Stroking the test pattern with a pin matrix, which delivers
only vertical height information to ﬁngertip.

Fishbone tactile texture

(a)

(b)

(c)
Finger surface deformation(1)

Mechanicaldeformation

Finger inner tissue deformation(2)

Neural encoding
Tactile signal
processing

Neural signal processing
Geometric perception

Figure 7: Examples for evaluation of depth illusion surface diﬀerences. An acrylic plate (width 3 mm) is sandwiched between (a)synthetic wood; (b) foamed aluminum; and (c) natural wood.

ness is interpreted as the absence of a surface. While the initial
experiments presented here cannot deﬁnitively establish the basisof the illusion, in the following sections we discuss the evidence
for the causal mechanism.
4.1.1

Mechanical deformation

If the mechanical stress patterns within the ﬁnger tip skin are identical between the concave and convex ﬁshbone patterns, then they
will be perceptually indistinguishable. For the raised ﬁshbone pattern in Figure 2, this is plausible because the leading and trailingedges of the ridges encountered by the ﬁnger tip are likely to induce the largest integrated stresses in the skin. The stresses induced by the ends of the ridges adjacent to the smooth central strip
are presumably much smaller in magnitude, and are approximately
equal for the concave and convex patterns [8]. To help understandthe difference between patterns, we conducted preliminary experimental measurements of the ﬁnger skin deformation behavior. A
microscope and high speed camera (120 frames/s) imaged then ﬁnger print deformation as the ﬁnger was stroked over concave andconvex ﬁshbone patterns machined on a transparent acrylic plate.
Analysis of the ﬁnger print deformation revealed little difference
between the patterns.
There are, however, two problems with mechanical deformation
alone as an explanation for the illusion. First, if the perpendicularedges on the surface pattern are the only information used for geometric perception, the result should be the same for various widthsof the smooth area in experiment 1 above. In contrast, the exper-

Figure 9: Diagram of information ﬂow for tactile signal. The surface
information is transformed into a tactile signal through mechanicalinteraction with the skin, then the signal is processed in the central
nervous system.

imental results showed a strong variation of perceived depth withcentral strip width. Second, even if the patterns produce indistinguishable mechanical stimulus, there is no apparent reason why the
concave interpretation would dominate the convex perception andnot vice versa. This difﬁculty is further illustrated by the spatial
frequency (slit cardboard) and materials experiments above, whichshowed that distributed surface roughness a fraction of a mm inheight was quite effective in producing the illusion. In this case,there was no “true concave” surface as a comparative stimulus, so
the universal perception of a concave surface requires another explanation.
4.1.2 Tactile signal processing
The second potential mechanism is based on the processing of thetactile signal in the central nervous system. In particular, tactile
stimulus may be interpreted as both conﬁrming the presence of asurface texture and the presence of the surface itself. In other words,
the absence of tactile sensations in the smooth central strip and thepresence of tactile sensations in the adjacent regions may be interpreted as the absence of a surface in the center, i.e., a concave shape.
This association between surface texture and surface shape is presumably based on the observation that ﬂat surfaces typically havethe same texture across the entire surface. Therefore the absenceof sensation in the central region implies the absence of a surface.
This is an interesting argument because it implies that the surface

Roughness
difference
by printing

APPENDIX
Concave
Illusion

The illusionary concave shape can be readily perceived by making
a cut paper stimulus as shown in Figure 5. In fact, the ﬁgure itself
may be printed (preferably on relatively thick paper) and used as atemplate for cutting the slits with a razor blade or graphics knife.
We have also found that some laser printers deposit sufﬁcient toner
to allow the illusion by simply stroking the ﬁnger along the central
strip of the printed pattern.

Figure 10: An example of a potential application of the illusion.

geometry may be reconstructed by not only from the stimulus of
the local contact area itself but by information from other regionsof the contact area as well.
This mechanism is supported by the spatial frequency experiment, where decreasing the slit interval and thus the tactile stimulus
decreased the illusion. It also consistent with the dominance of theconcave illusion over a potential convex illusion, because both concave and convex ﬁshbone test patterns have smooth central regionsthat provides little tactile stimulus, and the absence of stimulus canonly denote lack of a surface and thus a concave shape. This mechanism requires that the central stimulus is below some threshold.
This threshold value may be effected by the relative stimulus magnitudes of the central and lateral regions, so that, for example, theconcave illusion persists even for signiﬁcant central roughness if
the lateral region roughness is also high. This scaling of perceived
magnitude is observed in other sensory systems, e.g. “brightness(lightness) contrast” in vision [1] [2].
An additional constraint on the illusion is that the difference inthe mechanical skin stimulus between the concave and convex patterns cannot be too large, or the central nervous system would presumably detect the difference based on prior experience, and theillusion would fail.
This suggestion that the ﬁshbone tactile illusion is based on alearned association between surface texture and surface shape has
analogies in other sensory modalities. One example is the sizeweight illusion, where people assume that the size of an object covaries with its weight. Studies have shown that such visual sizeweight cues are not only consciously perceived but are directly usedin programming motor commands in manipulation [6]. Anotherexample is proximity-luminance covariance in vision, based on thefact that in many settings, objects appear dimmer and lower contrast
as their distance from the viewer increases [5].

4.2

Potential applications

The illusion reported in this paper can produce a virtual concave
perception by simply creating a roughness distribution, without creating actual shapes. Therefore, it may be possible to extend the illusion to create useful surface patterns. For example, such a surface
might assist in achieving a desired grasp of an object, as illustrated
in Figure 10. The users might be induced to conﬁgure the ﬁnger
tips or operate a control in speciﬁc ways without verbal or visual
instructions. This method may also prove useful for tracking a speciﬁc trail on a map, or it may be applied to a surface which must
be dragged in a wheel interface. Because of the simplicity of producing the illusion through surface printing with rough inks, it may
be possible to add new tactile features to a variety of commercial
products.

ACKNOWLEDGEMENT
We are grateful to Susan Lederman for helpful discussions on analyzing the tactile illusion, Naoki Kawakami, Hiroyuki Kajimoto,Christopher Wagner and Douglas Perrin for experimental advice,
and Yasuo Sakurai for developing materials and apparatus for thisstudy. This research is supported by Japan Society for the Promotion of Science for Young Scientists (17-11884).

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