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1

Lossy Data Compression ofVibrotactile Material-Like Textures
Shogo Okamoto, Member, IEEE, and Yoji Yamada, Member, IEEE
Abstract—Tactile content will be delivered over the Internet in the near future. Vibrotactile material-like textures that resemble thesurfaces of wood, leather, etc., are representative of such content. We performed lossy compression of texture data for reducing
the data size. We confirmed the effectiveness of two compression strategies: quantization and truncation of data beneath a shifted
perceptual threshold curve. In the quantization strategy, the amplitude spectra of vibrotactile textures could be quantized in 14 steps.
This reduced the data size to approximately one quarter without any noticeable quality deterioration. The method for truncating
frequency components with amplitudes smaller than a shifted perceptual threshold curve was also effective, and it was preferable
to the automatic deletion of sub-threshold amplitudes. We reduced the data size of vibrotactile material textures to 10–20% of their
original size by combining the lossy data compression strategy with Huffman coding, which is a lossless data compression method.
Lossy compression algorithms will enhance the online delivery of vibrotactile material-like textures by decreasing their data size without
significant loss of quality.
Index Terms—vibrotactile texture, quantization, threshold✦

1

I NTRODUCTION

Tactile content will be delivered over the Internet in
the near future via tactile displays installed on computer mice or mobiles. Such devices are already being
developed commercially, for example, iFeel MouseManfrom Logitech, Tangible Mouse from Fuji Xerox, andOrbit 3D by Kensington. Tactile content will be based on
stimulation techniques that have been studied by many
researchers. These techniques include the presentationof textures such as roughness (e.g., [1], [2], [3], [4],[5]), virtual mechanical switches, buttons or slide bars
(e.g., [6], [7], [8], [9]), iconic tactile stimuli [10], [11],contact with objects [12], [13], and affective or social
communication [14], [15]. With the amount of tactile
content increasing, data compression methods are potentially effective for the delivery of such tactile content
through the Internet.
In this study, we address lossy data compression oftactile textures. Textures have a large data size comparedwith virtual mechanical switches or iconic tactile stimuli
because they are spatially distributed on the surfaces ofobjects. We consider material-like textures with irregularsurface patterns, rather than simple textures such as
gratings. An evident contribution of data compressionis the reduction of communication trafﬁc. Moreover, it
can potentially contribute to the understanding of new
aspects of tactile perception. From the history of datacompression for visual and auditory signals, it can beseen that the development of compression algorithms
leads to the investigation of human perceptual mech• The authors are with the Graduate School of Engineering, Nagoya University, Nagoya, Japan.
E-mail: see http://www.asi.mech.nagoya-u.ac.jp/
This work was supported in part by MEXT KAKENHI (23135514).

Digital Object Indentifier 10.1109/ToH.2012.18

anisms from the view point of data compression because compression algorithms exploit such perceptual
characteristics. Conventionally, researchers investigatingtactile perception did not consider compression algorithms; many of them attempted to create guidelines for
haptic interfaces. Hence, data compression techniques
are expected to inspire studies on new aspects of tactile
perception that are related to data compression.
While it is probable that data compression methods
used for sounds or images [16] will be applicable totactile textures, there have been no previous reportson the use of such methods; therefore, the extent towhich textures can be compressed is unknown. Someof the compression methods used for sounds or images
truncate information that is irrelevant for the requisite
qualities; hence, we need to clarify whether truncations
are appropriate for tactile textures. The objectives ofthis study are to test the applicability of lossy datacompression algorithms to vibrotactile material-like texture data and to investigate their suitability in terms ofpotential data reduction ratios. We employ two types offundamental compression algorithms, namely, quantization and truncation of sub-threshold data. These will beelaborated in sec. 4.3.
We consider vibrotactile stimuli that are commonlyused for tactile displays. Although a variety of vibrotactile displays are available, we use a display with a single
vibratory source known as a “contactor” or “tactor.” This
type of display is the most fundamental, and a single
contactor would be preferable in commercial products
because it would reduce costs. For example, vibrotactile
displays with a single contactor were used in [5], [6], [7],[13], [14]. In contrast, vibrotactile displays with multiple
actuators have also been represented by pin matricesin [1], [2], [4], [17], and a shearing stress display in [18].

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The current study is an extension of our previous
study [19], where we tested the use of lossy data compression algorithms for two types of vibrotactile textures.
To preserve the generality of the algorithms in the current study, we use three types of material-like textureswith new experimental participants. Then, we combine
the compression algorithm with Huffman coding, which
is a lossless compression scheme, in order to estimate thepotential compression ratios of vibrotactile material-liketexture data.

2

R ELATED W ORK

Data compression algorithms are divided into lossy or
lossless schemes, and this study considers the formercase. Lossless schemes such as Huffman coding reduce
the size of data by making use of the stochastic properties of signals. Data compressed by using lossless
schemes are decoded into exactly the same form as thatof the original data. In contrast, lossy schemes utilize
human perceptual properties to convert the original data
into a form that is perceptually close or identical to theoriginal data. The current study is concerned with lossy
data compression schemes.
Compression technologies used for multimedia information are useful for compressing tactile texture
data. Here, we introduce sound and image compression
schemes that are of relevance to the methods used inthis study. We also review studies of haptic information
compression.
2.1 Quantization and Elimination of Sub-threshold
Signals
A fundamental strategy in lossy data compression isquantization. Small quantization errors do not inﬂuence
the subjective quality. Quantization has been introducedin various compression algorithms. One such algorithm
is JPEG, which is a compression technique for still
pictures [16]. JPEG technology computes the discretecosine transformation (DCT) of a picture in order toextract the intensities of individual spatial frequencies(DCT coefﬁcients). The extracted DCT coefﬁcients arequantized using step sizes that are speciﬁc for individual
frequency ranges, based on human luminosity characteristics. Lossless schemes such as differential or Huffman
encoding are then applied to the quantized data. In somecases, people cannot distinguish the original images fromthose compressed to one tenth of the data size [20], [21].
One of the methods in this study also employs DCT and
quantization (see secs. 4.3.1 and 4.3.2).
Another fundamental strategy is the truncation of
signals beyond perceptual thresholds. An example ofthis method is MPEG audio encoding [16], where soundcomponents below perceptual thresholds are removed
during encoding. Masking thresholds speciﬁed for individual critical bands are also employed during encoding.
We also adopt a strategy for removing frequency components with amplitudes below certain thresholds (seesec. 4.3.3).

2

2.2 Lossy Data Compression in Haptics
Data compression of force or position information wasstudied in order to reduce data transfer in haptic systems such as a remote master-slave system. Hinterseer et al. [22], [23], and Nitsch et al. [24], [25] transferred
force or position information to the operators of theirhaptic systems only when information or changes in
information exceeded certain thresholds or discrimination limens, respectively. Shahabi et al. [26] proposed
the compression of force and position data using avariable sampling method or adaptive differential pulsecode-modulation. You et al. [27] and Kuschel et al. [28]used predictive coding methods to decrease the datatransfer in a master and slave system. Jensen et al.
attempted to reduce the data sizes of voxels by clipping
the data around an end effector, which was intensively
refreshed [29]. Jensen’s method is similar to a speedup technique used in haptic rendering rather than datacompression methods. Arimoto et al. investigated theeffects of position data quantization on subjective quality
during haptic manipulation of virtual objects [30]. Borst
compared the uniform and non-uniform quantizationof force data using a force display and suggested thesuperiority of the non-uniform scheme [31]. The conceptsof the quantization of stimuli data and the removal of
subliminal data found in these schemes are common to
the compression methods used for tactile textures in thecurrent study.
Data compression of force and position feedback has
already been attempted in haptics; however, the compression of tactile stimuli data has not been conducted
extensively. A similar study on the compression of textile
stimuli was reported by Cholewiak et al. [32], where
square gratings were decomposed into major waves
and harmonics using Fourier expansion. The effects ofharmonics on the perceptual thresholds of gratings werethen investigated, before proposing the thresholds of ﬁne
or mid-coarse square gratings based on the thresholds oftheir major waves. This suggests that the high-frequency
harmonic components of square gratings can be ignored
to some extent during the presentation of vibrotactile
textures. The study also suggested that it was possiblethat humans did not perceive changes in the phases
between two sinusoidal waves when the synthetic wavesof these two waves were presented. This suggests thatthe phase information of vibrotactile texture stimuli canbe partially removed. Phase information is particularly
unnecessary during the synthesis of high-frequency vibrotactile stimuli [33]. However, it is evident that few
studies have reported the use of lossy data compression
for tactile textures. This may be partly because the simultaneous manipulation of a large number of physicalvariables such as the vibrotactile amplitudes in manyfrequency bands is rarely addressed in psychophysics,
which is a highly sophisticated discipline that investigates the perception of physical stimuli. We use a simple
experimental design, which is described later; it allows

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3

us to handle such stimuli that involve changes in many
physical variables.

3

E QUIPMENT

3.1

Vibrotactile Texture Display

We used a vibrotactile display with one vibratory source.
The display should enable the users to move their hands
and actively explore spatially distributed textures. We
used the vibrotactile display shown in Figs. 1a and 1b;
it satisﬁes the points stated above.
The vibrotactile stimulator was a piezo-stack actuator(NEC/TOKIN, AHB800C801FPOLF, Sendai, Japan) thatwas installed on a low-friction linear slider (SS series,
NSK, Tokyo, Japan; average friction measured with atypical load of 200 g was 0.10 N). The slider’s position on
the guide was measured using an optical linear encoder(SR-P1000, Canon, Tokyo, Japan) with the resolution set
at 0.4 μm. When a participant in the experiments placed
his/her ﬁnger on the vibrator and moved his/her handalong the X-axis, the vibrator slid along the guide andproduced displacements along the Y -axis that reproduced the surface proﬁle of the texture. The contactor
was circular with a diameter of 11.6 mm. The refresh
rate for the voltage output to the vibrator was 3.0 kHz.
The output force of the stimulator was approximately
800 N, which was sufﬁciently large compared withthe force applied by the ﬁnger to prevent the latterfrom causing the output displacements to decay. Thus,
feedback control was not required to ensure set displacements. The maximum output displacement of thestimulator was approximately 80 μm with an applied
voltage of 150 V. The displacement changed linearlywith the input voltage when the frequency was ﬁxed.
The frequency response curve was relatively ﬂat andit did not exhibit resonance in the range used in theexperiments (up to 400 Hz). The frequency response
magnitude curve reached -3 dB at 270 Hz. To compensate
for attenuation at high frequencies and ensure that thedesired displacements were output, the voltage inputs tothe stimulator were multiplied by the inverse functionof the frequency response curve. Voltage was applied
to the stimulator through a bipolar ampliﬁer (FRA5014,
NF, Yokohama, Japan, nominal frequency response was
2 MHz).
3.2

Material-like Texture

We used material-like textures with irregular surface
height patterns. We measured the surface roughness
proﬁles of 11 materials, including wood, paper, andcloth. A non-contact surface measurement method (NH3SP, Mitaka Kohki, Mitaka, Japan; nominal resolutionof 1 nm) was used to measure the surface proﬁles. It
measured the surface of a randomly selected portionof each texture for 10 mm with an interval of 0.5 μm.
Different types of textures were used to ensure thegenerality of the effects of the compression algorithms.

Fig. 1. Experimental setup. a) Use of the vibrotactile
display. b) Linear slider type vibrotactile display

We played back the 11 measured material textures using
the above tactile display and we selected three materials
that felt obviously different. These were a board madefrom the wood of a Judas tree, a piece of sandpaper(#1500), and a piece of artiﬁcial leather (DI-NOC Film,
LE-137, 3M). The measured proﬁles of these texturesare shown in Fig. 2. We displayed these proﬁles asheight variations to human ﬁnger pad. Note that thesevariations do not exactly match those experienced while
stroking real materials. Hence, these textures are called
material-like textures.

4

L OSSY DATA C OMPRESSION A LGORITHMS

4.1 Perceptual Characteristics of Vibrotactile Stimuli
Compression methods exploit the discriminability anddetectability characteristics of speciﬁc amplitudes foundin vibrotactile stimuli. The discriminability indicates
how supraliminal stimuli should be treated. A typicalindex for discriminability is the differential threshold,which has a Weber ratio of 10–20% (computed from [34]and [35]) when used for vibratory amplitudes. This
indicates that amplitudes can be somewhat coarsely
quantized. The detectability indicates how to handle subliminal stimuli. Subliminal vibrotactile stimuli need notThis article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.

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Fig. 3. Process flow for the compression of vibrotactile material texturesmaterial length. Each of these processes is described indetail in the following sections.
Samples of the texture’s height yn (n = 0, ..., N − 1),which are measured as described in sec. 3.2, are converted into amplitude spectra Ck (k = 0, 1, ..., N − 1),
where N is the number of samples (N = 20000) and
Ck is the amplitude of the frequency component fk .
The DC component C0 was set to zero because it does
not inﬂuence perception. Components with frequencies
higher than 400 Hz were removed when the texture was
explored at a typical hand velocity v. This velocity was
set to encompass a range where natural explorations
were not disturbed (50 mm/s). In the experiments described below, participants conducted their explorations
according to the rhythm of a metronome, and they useda speciﬁed stroke length to maintain an average velocity(as described in sec. 5.2). Based on v, fk is determinedbyfk =Fig. 2. Surface profiles of material textures

be delivered to users; hence, the compression algorithm
eliminates amplitudes below the detection threshold.
These two properties of vibrotactile stimuli have been
discussed in terms of frequency space, and it is known
that the quality of stimuli can be expressed in frequency
space, such as power spectra [36], [37], [38]. Thus, thecompression of material textures was also performed infrequency space in this study.

v·kSampling frequency
N/D · v·k =·k =Number of samples
ND

where D is the distance over which the texture surface
was measured (10 mm). N/D is equivalent to the numberof sampling events per millimeter.
4.3 Data Compression Algorithms for Vibrotactile
Textures4.3.1 Linear Quantization
Quantization is one of the most popular strategies forlossy data compression. The amplitudes are quantized
between the maximum and minimum Ck . The quantized
amplitude spectrum Lk is determined by
Lk = round(

4.2 Data Compression using Discrete Cosine Transformation
Fig. 3 shows the process of data compression. First, thetexture’s surface proﬁles (Fig. 3a) are converted into
amplitude spectra using a discrete cosine transformation(DCT) (Fig. 3b) and data compression algorithms arethen applied to the spectra (Fig. 3c). Finally, the modiﬁed or compressed spectra are converted into a surface
proﬁle using inverse DCT (Fig. 3d). Although we measured material surfaces for 10 mm, the generated surface
proﬁles repeated this procedure for a virtually inﬁnite

(1)

Ck
)·Δ
Δ

(2)

where Δ is the quantization step. Δ is given as
Δ=max(C1 , ..., CN −1 ) − min(C1 , ..., CN −1 )
L−1

(3)

where L is the number of quantization steps, which
determines the compression level. Fig. 4 shows an example of amplitude spectra and the surface proﬁle ofuncompressed and linearly quantized (L = 4) wood
textures. Given that each amplitude of the uncompressed
texture was written in 2 bytes, the data size of thecompressed texture in the ﬁgure was 12.5% of the size

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5of the uncompressed data. Here, the compression ratio
is deﬁned as
Data size of compressed texture
Compression ratio =.
Original data size
(4)
4.3.2 Log Quantization
There are two types of quantization schemes: uniform
and non-uniform quantization. The step size is constantin uniform quantization schemes, whereas the step size
varies in non-uniform schemes. An example of a nonuniform scheme is log pulse-code-modulation where thestep size varies logarithmically. Low-level signals are
ﬁnely quantized; thus, quantization errors become small.
In contrast, high-level signals are coarsely quantized.
The application of ﬁne quantization steps to low amplitudes and coarse quantization steps for high amplitudes is expected to effectively reduce the data size,
while maintaining data quality by taking into accountWeber’s law. We used a log function to determine
the step sizes. Positive and negative amplitude values
were quantized separately. With a positive Ck , the logquantized amplitude Nk is determined bylog10 Ck − log10 S) · Δ+ + log10 S
Δ+
if Ck > S
max (log10 Ck |Ck > 0) − log10 S+.
Δ =L/2 − 1log10 Nk = round(

(5)

(6)

With a negative Ck , Nk is determined bylog10 (−Ck ) − log10 S) · Δ− + log10 S
Δ−
if Ck < −S
max (log10 −Ck |Ck < 0) − log10 S−.
Δ =L/2 − 1log10 Nk = round((7)

Fig. 5. Log-quantized sandpaper texture: L = 6
The amplitudes are quantized between the maximum
or minimum Ck and S. S is a very small amplitude
that hardly inﬂuences the perceived texture (here, 0.05μm). For Ck with an amplitude lower than S, Nk isdetermined by
Nk = sign(Ck ) · S(8)

if |Ck | ≤ S.

(9)

Clearly, S affects the performance of the compression
algorithm. S needs to be sufﬁciently small, but quantization errors increase if it is too small. An accurate
determination of S will be achieved in future work.
Fig. 5 shows an example of a log-quantized sandpaper
texture and its amplitude spectrum. The amplitudes
were quantized in 6 steps. Larger amplitudes were quantized more coarsely. The data compression ratio of the
texture shown in Fig. 4 was 16.2%.
4.3.3 Truncation of Data beneath Shifted Thresholds
Assuming that stimuli below the detection thresholdlevel can be removed while still maintaining the perceptual quality of textures, a third compression method isused to eliminate vibratory amplitudes that are smaller
than the thresholds. When they are removed, the amplitude spectra are determined byb00
if log10 Ck < log10 b(F ) +
Tk =
(10)
20
Ck otherwise

Fig. 4. Linearly quantized wood texture: L = 4

where b(F ) and b0 are the detection thresholds at frequency F and a variable for shifting the thresholdcurve, respectively. b0 determines the compression levelof the method. For example, amplitudes smaller than thethreshold curve are truncated when b0 = 0 dB. WhenThis article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.

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Fig. 6. Sandpaper texture with truncation of amplitudes
below log10 b(F ) + b0 |b0 =0
b0 = −2 dB, amplitudes smaller than the -2-dB shifted
threshold curve are truncated. With the latter value, thecompression ratio was worse than with b0 = 0 dB. The
function b(F ) was initially acquired using a psychophysical method of adjustment involving six participants,
with the same equipment used in this study. b(F ) was
acquired while the hand remained still.
Fig. 6 shows the sandpaper texture compressed using
this method, when b0 = 0 dB. Fig. 6b shows thatthe compressed texture included no amplitudes lower
than the threshold curve. In this example, 45% of theamplitudes were truncated and assigned as zero. Thisalgorithm alone did not reduce the data size of the
texture. However, the algorithm inﬂuences the efﬁciencyof the lossless data-compression algorithms because it
affects the statistical properties of the amplitudes. Using this algorithm will result in more highly efﬁcientcompression using Huffman coding or other methods
because the number of zero values in the amplitude
signals increases.

5

E XPERIMENT: S UBJECTIVE C OMPARISON
OF C OMPRESSED T EXTURES

5.1 Subjective quality measurement compatible
with ITU-R
For subjective quality assessment of compressed textures, we use a grading scale based on the recommendations of the International Telecommunication Union(ITU). ITU standardized the methods for subjectively assessing the impairment of audio-visual content. Such impairment is caused by lossy data compression, poor de-

6

coding, electromagnetic disturbance, etc. ITU-R BT.50012 (Methodology for the subjective assessment of thequality of television pictures) [39] recommends the usageof grading scales such as the one used in our study, or
continuous quality-rating scales like a numerical scale.
These methods are advantageous in that they allow
assessors to retain both subliminal threshold levels andquality impairment curves. Subliminal thresholds indicate the best compression levels that do not involve
signiﬁcant quality degradation. On the other hand, thequality impairment curves indicate the quality impairment over the thresholds. In general, subliminal threshold levels and quality impairment curves are useful forthe practical implementation of data compression.
Although the ITU-R methods are well accepted inindustry, they are not as rigorous as well-establishedpsychophysical methods (e.g., [40]). For example, the useof adjecitves such as “possibly the same” and “possibly
different” are prone to variable interpretations by participants and can be susceptible to response biases. We
therefore collected additional data with two participants
using a signal detection paradigm to verify the experimental results.
5.2 Tasks and Participants
Overview: The participants scored the subjective dissimilarity between the uncompressed and compressed textures. They rated the dissimilarity using afour point grading scale. Three types of algorithms wereapplied to the wood and sandpaper texture data. Linear
quantization and truncation of sub-threshold stimuli wasapplied to the surface of the artiﬁcial leather texture data,
but not the log quantization algorithm. This was because
log quantization produced similar performance to linear
quantization with the wood and sandpaper textures [19].
Thus, we focused on the two methods other than the log
quantization with the leather texture.
Tasks: In each trial, participants explored and compared the uncompressed and compressed textures using
the vibrotactile texture display described in sec. 3.1. In
each trial, all textures were presented to the participants
for a period of 5 s. To maintain an average hand velocityof 50 mm/s (see sec. 4.2), participants moved theirhands in strokes of 40 mm following the rhythm of a
metronome (1.25 Hz) with a pattern of one stroke perbeat. Marks on the desk indicated the stroke distance(Fig. 1a). During the exploration of two textures ineach trial, participants were required to maintain ﬁnger
contact status with the contactor. Participants recorded
their answers after exploring the two textures. The participants manually recorded the texture similarity as“same,” “possibly the same,” “possibly different,” or“different” on an answer sheet.
Test Stimuli: The texture compression levels wereset at 5–7 grades with each compression method. In
addition to the compressed textures, uncompressed textures were included as test stimuli. Table 1 shows theThis article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.

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TABLE 1
Compression level of textures used for evaluation
TextureWood
Sandp.
LeatherComp. algorithms
Lin. quant. [step]
Log quant. [step]Threshold-cut [dB]
Lin. quant. [step]
Log quant. [step]Threshold-cut [dB]
Lin. quant. [step]Threshold-cut [dB]Compression levels
L = 14, 12, 10, 8, 6, 5, 4
L = 14, 12, 10, 8, 6
b0 = −12, −8, −4, 0, 4, 8
L = 14, 12, 10, 8, 6, 5, 4
L = 14, 12, 10, 8, 6
b0 = −12, −8, −4, 0, 4, 8, 12
L = 14, 12, 10, 8, 6, 5, 4
b0 = −12, −8, −4, 0, 4, 8, 12

compression levels used in the experiments for each typeof texture. Each test stimulus was presented four times intotal. For the wood texture, 76 trials were performed in
total (19 textures × four repetitions) for each participant.
For the sandpaper texture, 80 trials were performed (20textures × four repetitions). For the artiﬁcial leather
texture, 60 trials were performed (15 textures × four
repetitions). The order of test stimuli presentation was
random.
Participants: The participants were 15 university
students who were recruited and paid according tomethods approved by the ethics committee of the Engineering School of Nagoya University. Each participant
sampled two textures of the three; thus, each type of
texture was evaluated by a total of 10 participants. A
speciﬁc participant conducted the experimental tasks
with one type of the texture then, after a short break, theyevaluated another type of the texture. The order of texture presentation was balanced. The participants listened
to pink noise through noise-cancellation headphones toeliminate the sounds generated by the stimulator.
5.3

Results

Wood: Fig. 7 shows the means and standard deviations of the dissimilarity scores between the quantized
and uncompressed wood textures. The standard deviations were calculated among participants. The values
in the ﬁgure were computed by assigning a value of0, 1, 2, or 3 to “same,” “probably the same,” “probably different,” and “different,” respectively. In general,the dissimilarity score increased (similarity decreased)
as the data size of the compressed textures decreased.
The changes in the scores were not monotonic. With
linear and log quantization, the changes showed a slightplateau at L = 12, 10 and 8. The scores increased
exponentially using small quantization step number of
L = 4 or 6 with linear and log quantization, respectively.
A pair-wise t-test was used to test the signiﬁcance ofdifferences between the uncompressed and compressed
texture scores (Table 2). Signiﬁcant increases were observed in the dissimilarity scores with both linear andlog quantization for compression levels of 22.4% (L = 12)
or less, as shown in the left and middle columns of thetable.
Fig. 8 shows the means and standard deviations of
the scores for the threshold-cut wood textures. The dis-Fig. 7. Subjective dissimilarity between quantized and uncompressed wood texture. Filled symbols are significantly
different from the uncompressed texture.

Fig. 8. Subjective dissimilarity between threshold-cut anduncompressed wood texture. Filled symbols are significantly different from the uncompressed texture.

similarity between the threshold-cut and uncompressed
textures increased monotonically as the textures werecompressed further with an increase in b0 , which was
the size of the threshold curve shift. As shown in theright column of Table 2, textures compressed with a levelof -4 dB had dissimilarity scores that were signiﬁcantly
different from the uncompressed texture.
Sandpaper: Fig. 9 shows the dissimilarity scoreswith the quantized sandpaper textures. A similar generaltrend was observed to that found with the wood textures, where the dissimilarity tended to increase as thecompression ratio decreased. With linear quantization,
the scores remained low when L = 14–10. However, thescores increased exponentially with small quantization
steps. Table 3 shows the results of the statistical analysisof the scores for the sandpaper texture scores. With
linear quantization, signiﬁcant differences were observed
between the scores of the uncompressed and compressed
textures when the compression ratios were 22.4% and18.8% or less, as shown in the left columns. With log

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8TABLE 2
Wood: t-test to compare the results with compressed and uncompressed wood textures
Compress.
level
L = 14
L = 12
L = 10
L=8
L=6
L=5
L=4

Linear quantization
Log quantization
Threshold-cut
Compress.
Compress.
Compress.
Compress.
t0 (9)pt0 (9)pt0 (9)
pratio [%]
level
ratio [%]
level (dB)
23.8
0.946
0.369
L = 1423.8
1.923
0.0867b0 = −12
0.394
0.703
22.4
3.900
3.64E-3∗∗
L = 12
22.4
3.541
6.30E-3∗∗
b0 = −8
1.283
0.232
20.8
3.733
4.68E-3∗∗
L = 1020.8
5.612
3.29E-4∗∗
b0 = −4
3.616
5.61E-3∗∗
18.8
3.740
4.62E-3∗∗
L=8
18.8
3.585
5.89E-3∗∗
b0 = 03.387
8.04E-3∗∗
16.2
4.975
7.65E-4∗∗∗
L=6
16.2
23.32
2.33E-9∗∗∗b0 = 47.413
4.05E-5∗∗∗
14.5
9.251
6.81E-6∗∗∗
b0 = 813.838
2.27E-7∗∗∗
12.5
15.93
6.69E-8∗∗∗*, **, and *** indicate the signiﬁcance levels of 0.05, 0.01, and 0.001, respectively.

TABLE 3
Sandpaper: t-test to compare the results with compressed and uncompressed sandpaper
Compress.
level
L = 14
L = 12
L = 10
L=8
L=6
L=5
L=4

Linear quantization
Compress.
t0 (9)
ratio [%]
23.8
1.568
22.4
3.569
20.8
1.093
18.8
3.386
16.2
7.255
14.5
8.152
12.5
25.57

p
0.151
6.04E-3∗∗
0.303
8.05E-3∗∗
4.79E-5∗∗∗
1.90E-5∗∗∗
1.03E-9∗∗∗Compress.
level
L = 14
L = 12
L = 10
L=8
L=6

Log-quantization
Compress.
t0 (9)
ratio [%]
23.8
1.756
22.4
1.940
20.8
5.195
18.8
7.467
16.2
5.228

p
0.113
0.084
5.68E-4∗∗∗
3.82E-5∗∗∗
5.43E-4∗∗∗

Threshold-cut
Compress.
t0 (9)
plevel (dB)b0 = −12
1.152
0.279
b0 = −8
1.378
0.202
b0 = −4
1.006
0.341
b0 = 02.270
0.0493∗b0 = 4
3.840
3.97E-3∗∗
b0 = 8
6.647
9.41E-5∗∗∗b0 = 12
15.26
9.73E-8∗∗∗

TABLE 4
Leather: t-test to compare the results with compressed and uncompressed leather
Compress.
level
L = 14
L = 12
L = 10
L=8
L=6
L=5
L=4

Linear quantization
Compress.
t0 (9)
ratio [%]
23.8
1.954
22.4
0.995
20.8
4.378
18.8
5.947
16.2
10.114
14.5
8.702
12.5
9.078

Threshold-cut
p0.0825
0.346
1.78E-3∗∗
2.16E-4∗∗∗
3.26E-6∗∗∗
1.12E-5∗∗∗
7.96E-6∗∗∗

quantization, signiﬁcant differences in the scores wereobserved when the compression rates were below 20.8%,
as shown in the middle columns.
Fig. 10 shows the dissimilarity scores of the thresholdcut sandpapers. As found with wood textures, the scores
increased almost monotonically as the compression level
increased. Statistical tests showed that compressed textures where b0 = 0 or greater produced signiﬁcantly
higher dissimilarity scores compared with the uncompressed textures as shown in the right columns of Table 3.
Leather: Fig. 11 shows the dissimilarity scores ofthe linearly quantized leather textures. In general, thedissimilarity scores increased with the compression of
the texture. Quantized textures with L = 4–6 were highly
dissimilar to uncompressed textures and the scores were
high. Table 4 shows the results of statistical tests applied
to the scores. The scores for the quantized leather textures were signiﬁcantly higher than the uncompressed
textures when the compression ratios were 20.8% (L =10) or less, as shown in the left columns.
Fig. 12 shows the dissimilarity scores between thethreshold-cut and uncompressed leather textures. The

Compress.
level (dB)b0 = −12b0 = −8b0 = −4b0 = 0b0 = 4b0 = 8b0 = 12t0 (9)

p

0.984
0.267
0.824
0.335
2.79E-15
5.01
6.94

0.351
0.796
0.431
0.745
1.00
7.32E-4∗∗∗
6.76E-5∗∗∗dissimilarity scores of the threshold-cut leather textures
were not signiﬁcantly different from the uncompressed
texture when b0 was -8 to 4 dB. The right columns ofTable 4 show that signiﬁcant differences among scores
were observed with a compression level of b0 = 8 and
12 dB.
5.4 Comparison with sensitivity index (d )To validate the results obtained with grading scales,
we obtained additional data using a discrimination task
based on signal detection theory [40]. We report sensitivity index that is independent of participants’ response
biases.
Task: Two of the participants were invited for
additional experiments. They compared original (uncompressed) and compressed textures and answered
whether or not they were the same. The experimental
procedures were the same as those in sec. 5.2.
Stimuli: The stimuli were the linearly quantizedand threshold-cut textures in Table 1. The uncompressed
textures were also included in the stimuli set. Eachtexture was presented 20 times for the individual participants. As a result, 280 (14 textures × 20 repetitions),

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9

Fig. 9. Subjective dissimilarity between quantized anduncompressed sandpaper.

Fig. 11. Subjective dissimilarity between quantized anduncompressed leather

Fig. 10. Subjective dissimilarity between threshold-cut
and uncompressed sandpaper

Fig. 12. Subjective dissimilarity between threshold-cut
and uncompressed leather

300 (15 textures stimuli × 20 repetitions), and 300 (15 textures × 20 repetitions) trials were conducted for wood,
sandpaper, and leather textures, respectively.
Results: We calculated d values using the participants’ answers. Figs. 13 and 14 show the average dvalues of the two participants for linearly quantizedand threshold-cut textures, respectively. The ﬁlled symbols are the stimuli that were determined signiﬁcantly
different from the uncompressed ones using four point
grading scales in the previous section. The values nearsymbols indicate their d values.
The threshold levels determined using the grading
scales, which were L = 12 for the wood and sandpaper and L = 10 for leather textures, corresponded tod values of 0.67–0.87. For threshold-cut textures, thethresholds levels that were determined using grading
scales, which were b0 = −4, 0, and 8 dB for thewood, sandpaper, and leather textures, respectively, corresponded to d values of 0.60–1.15. Thus, for both thelinear quantization and threshold-cut algorithms, thethreshold levels determined using grading scales were0.6–1.15 in d values.

In most psychophysical studies, d = 1 is typicallyused as the performance criterion for deﬁning a perception threshold. The thresholds obtained with grading
scales were roughly consistent with those that would
have been obtained by setting d = 1 in a discrimination
experiment using signal detection theory.

6

D ISCUSSION

6.1 Compression Ratios of Vibrotactile Material-likeTextures
Table 2 shows that participants reported no perceptualchanges in quantized wood textures, even when thedata size was compressed to 23.8%. Similarly, Tables 3
and 4 show that no perceptual changes were reportedwith compression of 23.8% and 22.4% for sandpaper andleather, respectively. These results indicate that vibrotactile material-like textures can be compressed to approximately 25% of the original data size by quantization, andthey can be quantized using 12–14 steps. We suggest thata variety of textures can be compressed to this extent,

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10TABLE 5Compression ratios achieved by a combination with
Huffman coding

Wood
Sandp.
LeatherFig. 13. d values of linearly quantized textures: Filled
symbols were significantly different from the uncompressed textures in accordance with four point grading
scales.

Compression ratio (compressed/uncompressed) [%]Linear quant. only
Linear quant. + Huffman
23.8% (L = 14)
22.3%
23.8% (L = 14)
17.5%
22.4% (L = 12)
12.1%

zation alone decreased the data sizes to approximately
25% of the original size while maintaining the perceptual
quality of textures. A combination with a lossless scheme
resulted in more efﬁcient compression of textures. The
performances of these methods were conﬁrmed using
single type of vibrotactile display and a limited variety
of texture stimuli. In the future, compression algorithms
will be evaluated against other types of vibrotactile
displays and textures.
6.2 Sub-threshold Data Should NOT be Automatically Removed

Fig. 14. d values of threshold-cut textures: Filled symbols were significantly different from the uncompressed
textures in accordance with four point grading scales.
because similar performances were observed with thethree different types of texture.
The threshold-cut removed amplitudes lower than theshifted threshold curves. Thus, the amplitudes weretruncated below the -8-dB, -4-dB and, 4-dB shiftedcurves for wood, sandpaper, and leather, respectively,
while still maintaining the subjective similarity to theuncompressed textures. As a result, 28.7%, 33.7%, and53.7% of data were assigned a value of zero with eachtype of textures. This is appropriate for lossless datacompression algorithms such as Huffman encodings.
Practical data compression methods are a combination of
lossy and lossless data compression schemes. We applied
the Huffman encoding [16] to the quantized textures,as shown in Table 5. The table indicates that linear
quantization coupled with Huffman encoding reduced
the data size to 22.3%, 17.5%, and 12.1% for the wood,
sandpaper, and leather textures, respectively excluding
the data size of decoding trees or tables.
In summary, the quantization and threshold-cut methods were effective for the lossy data compression ofvibrotactile textures. The application of linear quanti-

We assumed the perception of vibrotactile textures was
not affected by the deletion of frequency components
with amplitudes below the perceptual thresholds. However, the experimental results did not support this assumption. A threshold-cut algorithm with b0 = 0 dB
removed the amplitudes below the perceptual thresholds, but the participants detected differences between
the threshold-cut and original textures of wood andsandpaper textures under these conditions. Perceptualchanges in wood textures were also reported when
the algorithm truncated amplitudes lower than a -4-dB
shifted threshold. Thus, the sub-threshold amplitudes
should not be automatically removed.
A possible major reason for this phenomenon was thatthe threshold curve used by the algorithm was for single
frequency vibratory stimuli. It is known that subliminal
noise could help the perception of vibrotactile stimuli [41], [42]. Hence, the deletion of amplitudes below theperceptual thresholds by information compression may
affect the perception of vibrotactile textures. In contrast,
we should note that the perceptual thresholds could
be raised by some reasons. In such cases, the stimuli
below the threshold levels are less likely to inﬂuence
the perception of textures. For example, noisy vibratory
stimuli increase the perceptual thresholds of receptive
units when the sensitive frequency bands are located in
the noise frequency [35], [43]. Furthermore, hand movements could affect the thresholds. The threshold curveused in this study was acquired when the hand was heldstill, however voluntary hand movements could elevatethe perceptual thresholds of vibratory stimuli applied toﬁngers [44].
The differences between the results for materials canbe attributed to the differences in frequency components
included in each material. Bensmaı̈a et al. attempted to
explain the subjective similarity between two ﬁne tex-This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.

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tures on the basis of the similarity of frequency spectra ofskin vibrations caused by stroking them [36], [37]. They
claimed that the effect of vibratory power on the subjective quality of textures varied with frequency bands.
Some frequency bands signiﬁcantly inﬂuence the quality
whereas the others do not. It is likely that the deletion ofthese minor frequencies does not affect quality change.
Thus, the valid compression levels of threshold-cut are
possibly dependent on the frequency spectra of material
textures; however, it seems that the psychological aspects
for quantitatively discussing this possibility have notbeen sufﬁciently considered thus far.
6.3 Quantization non-monotonically changes thesimilarity
In general the compression made textures dissimilar tothe original ones. Hence, Figs. 7–12 show the downwardslopes. However, as exceptions, some compressed textures resembled the original ones. For example, for the
linear quantization of the wood texture, the dissimilarity
at L = 8 (square in Fig. 7) was unexpectedly small.
Further, L = 10 for sandpaper (diamond in Fig. 9) andL = 12 for leather (Fig. 11) were these exceptions. These
exceptional phenomena were prominent with the quantization algorithms rather than with the threshold-cut
algorithm. We speculate that this was due to the changes
in stimuli energies. In the threshold-cut algorithm, theenergy of the stimuli decreased with the compression
ratio. Hence, when textures were compressed further,
they became more dissimilar to the original ones. In
contrast, quantization could increase the stimuli energy.
This increase might have unexpectedly made the compressed textures similar to the original ones. Bensmaı̈a et
al. reported that the sum of weighted power spectrum ofvibrotactile stimulus possibly determined the quality ofstimuli [36], [37]. Even when the spectra of two stimuli
were different, these stimuli could be perceptually close
if their sums of weighted spectra were close.
6.4

Limitation of current approaches

Although this study conﬁrmed the effectiveness of lossy
data compression of vibrotactile material-like textures,the current algorithms have a problem in assuming
the hand velocity. We computed the frequency spectraof vibrotactile stimuli on the basis of a constant handvelocity of 50 mm/s. However, it originally depends on
individuals. This means that the tactile stimuli presented
to users depend on their exploratory hand speeds. Unlike visual or audio signals, the required sampling rateand compression ratio for texture data also depends on
individual users or their hand velocities. The algorithms
are not necessarily optimal for users who explore virtual
textures at speeds signiﬁcantly different from the supposed average speed. The problem of user dependency
seems to be unique to haptic content; it is necessary toinvestigate and develop compression algorithms independent of hand velocities.

11

7

C ONCLUSION

We studied the applicability and appropriate compression ratios for lossy data compression of vibrotactile
material-like textures. In particular, we focused on theuse of quantization and the truncation of sub-thresholdsignals as compression schemes. We tested these methods using a vibrotactile display and three types of material surface roughness patterns. In a series of psychological experiments, participants compared compressed
and uncompressed textures and rated their differencesor similarities. We used these results to identify thebest compression levels that did not lead to perceptual
quality changes. We found that quantization was significantly effective for this purpose. Spectral amplitudes ofthe vibrotactile textures were linearly quantized using
approximately 14 steps, which reduced the data size toless than the 25% of the original data. We also found thatthe truncation of frequency components below a shifted
perceptual threshold curve was effective. However, it
was shown that sub-threshold amplitudes should not
be automatically removed and a shifted curve should
be applied. The amount of shift depended on the typeof texture, but it was expected to range from -8 to
4 dB. A combination of these two lossy compression
schemes with Huffman coding can potentially enableconsiderable reduction in data size. Further studies on
this topic can contribute to the availability of haptic
content on the Internet.

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Shogo Okamoto (M’ 06) received a B.S. degree
in engineering from Kobe University in 2005, and
M.S. and Ph.D. degrees in information sciencesin 2007 and 2010, respectively, from the Graduate School of Information Sciences, Tohoku
University. Since 2010, he has been an assistantprofessor at the Graduate School of Engineering, Nagoya University. His research interests
include haptic interfaces and human factors.

Yoji Yamada received a Ph.D. degree from theTokyo Institute of Technology, Japan, in 1990.
He had been an Associate Professor at Toyota
Technological Institute. In 2004, he joined the
National Institute of Advanced Industrial andScience Technology (AIST) as a group leaderof Safety Intelligence Research Group.In 2009,
he joined the Department of Mechanical Scienceand Engineering, Graduate School of Engineering, Nagoya University as a Professor.