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An Objective Index that Substitutes for Subjective Quality of
Vibrotactile Material-Like Textures
Shogo Okamoto and Yoji Yamada
Abstract— The presentation of textures is a major applicationof vibrotactile displays. Lossy data compression is an effective
approach for reducing a data size of such textures when
delivering them through the Internet. This study developed
an objective index that well described material-like textures’quality changes caused by data compression processes. We
introduced a linear combination of the power and amplitude
spectra that were weighted by the inverse of a detection threshold curve of vibrotactile stimuli. This combination described thequality deterioration of compressed textures to an accuracyof approximately 80%. These objective indices enhance thedevelopment of the lossy data compression algorithms without
psychological evaluation tests of subjective quality changes inthe textures.

I. I NTRODUCTION
The vibrotactile display is one of the most prevalent tactile
displays. The presentation of virtual textures of materials
such as cloth or paper is a major application of these displays.
Several researchers have attempted to present the textures of
specific materials such as cloth, paper or metal (e.g., [1],[2], [3], [4], [5]). In the near future, the tactile textures will
be delivered on the Internet through vibrotactile displays
installed on computer mice or mobiles in our daily lives.
Such devices have been already commercially attempted by,for example, iFeel MouseMan from Logitech or a tangible
mouse from Fuji Xerox Corp.
In spite of the growing broadband, the data compression ofaudiovisual data is effective for data reduction especially formobiles for which communication bands tend to be limited.
Data reduction methods are also effective for the deliveryof tactile textures. We have proposed lossy data compression algorithms for vibrotactile displays [6]. We developed
three types of the algorithms and showed that the linear
quantization of vibrotactile amplitudes could reduce data
sizes of the textures by approximately 75% while remaining
their subjective qualities. In the field of haptics, the data
reduction for tactile textures has been rarely attempted whilesome force/position feedback systems employed such data
reduction (e.g., [7], [8], [9]).
Psychological experiments are needed for evaluating theperformance of the data compression algorithms. Experimental participants compare uncompressed and compressedvibrotactile textures and rate their quality differences subjectively. At least several participants need to take part inThis work was partly supported by MEXT KAKENHI 22800030 and the
Nitto Foundation.
The authors are with the Department of Mechanical Science and Engineering, Graduate School of Engineering, Nagoya University, Japan. E-mail:see http://www.mech.nagoya-u.ac.jp/asi/en/

978-1-61284-455-8/11/$26.00 ©2011 IEEEthe experiments for such an evaluation. The cost of these
psychological experiments is a large burden on developersof the algorithms. An objective index that accounts for thequality changes in the compressed textures is effective fordiminishing such costs and enhancing the development of
the algorithms.
The objective of the present study is to develop an objective index that accounts for subjective quality in material
textures that are deteriorated by data compressions. The
objective index predicts the perceptual quality changes intextures from their physical characteristics. Such objective
indices for tactile textures have yet to be reported so far.
One engineering benefit is that these indices allow us toevaluate the performance of compression algorithms without
conducting psychological experiments, which accelerates thedevelopment of such algorithms. Further, good indices contribute to understanding of perceptual properties of vibrotactile material-like textures by identifying physical quantities
that influence our perception.
In the present article, we focus on the development of
the objective index that well describes the results of psychological experiments. As to such experimental results, we use
those in our previous report [6]. An experimental setup (Section II), the data compression algorithms (Section III), andprocedures and results (Section IV) are briefly overviewed.
In Sections V and VI, we describe the development of theobjective index and its evaluation, respectively. We apply
the index to two types of material-like textures in this study,
while the goal of this index is the objective rating of various
vibrotactile textures.
II. E QUIPMENT AND M ATERIAL
A. Vibrotactile Texture Display
A vibrotactile display composed of one tactor (Fig. 1) wasused in this study. As a stimulator, a piezo-stack actuator(NEC/TOKIN, AHB800C801FPOLF, Sendai, Japan) was installed on a frictionless linear slider (SS series, NSK, Tokyo,
Japan). The slider’s position on the guide was measured by
an optical linear encoder (SR-P1000, Canon, Tokyo, Japan)
whose resolution was set to 0.4 µ m. When a participant in
the experiments placed his/her finger on the vibrator andmoved his/her hand along the X-axis, the vibrator slid along
the guide and produced displacements along the Z-axis,
reproducing the surface profile of the material’s texture. 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 is large enough compared to the force applied3060

is given by

Fig. 1: Experimental setup and its usage.

by the finger that the latter does not cause the output displacements to decay. The maximum output displacement wasapproximately 80 µ m at an applied voltage of 150 V. The
displacement changed linearly with the input voltage when
the frequency was fixed. The frequency response curve wasrelatively flat and did not exhibit resonance in the range used
for the experiments (up to 400 Hz). The frequency response
reached -3 dB at 270 Hz. To compensate for attenuation
at high frequencies so that the desired displacements are
output, the voltage inputs to the stimulator were multipliedby the inverse function of the frequency response curve.
Voltage was applied to the stimulator through a bipolar
amplifier (FRA5014, NF, Yokohama, Japan). The contactor
was circular with a diameter of 11.6 mm.
B. Material Textures
As material-like textures for the experiments, a board
made from the wood of the Judas tree and sandpaper(#1500) were chosen. A non-contact surface measure (NH3SP, Mitaka Kohki, Mitaka, Japan) was used to measure thesurfaces for 10 mm with an interval of 0.5 µ m. These two
types of textures are perceptually dissimilar and easy for theexperimental participants to discriminate them. In section 5,
the objective measure is adopted to these textures that are
fairly considered to have different characteristics.
III. L OSSY DATA C OMPRESSION OF V IBROTACTILE
T EXTURES

Ck=(2n + 1)kπ
2 N−1
∑ yn cos ( N ) k = 1, ...N ′
N n=0

(1)

Ck

=

0 k = 0, N ′ + 1, ...N − 1(2)where N is the number of samples: N = 20000. This is
type-II DCT with the factor of 2/N that makes the DCT
indices express the amplitudes of each frequency component.
The DC component C0 was not used, since it does not
influence perception. The N ′ th DCT index corresponds to theamplitude of the 400-Hz component. Because the commandrefresh rate of the vibrotactile display was 3.0 kHz, elementswith a frequency higher than 400 Hz were removed inorder to maintain smooth profiles of the texture surface. The
frequency f k for the kth DCT index is determined by
fk =N/L · v
v·k
Sampling frequency
·k =
·k =
Number of samples
N
L

where L and v are the distance over which the texture surface
was measured (10 mm) and the average velocity of participants’ exploratory hand movements, respectively. The average velocity was set in a range in which natural explorations
were not disturbed (50 mm/s). In the experiments described
below, participants conducted their exploration following therhythm of a metronome and used a specified stroke length toachieve this average velocity as far as possible (as describedin Section IV-A).
The data-compression algorithms described in the next
subsection were applied to Ck and converted it into Ck′ . The
converted DCT indices Ck′ were re-converted to texture heightprofiles y′n through an inverse DCT. y ′n was acquired from
y′n =

N′

∑ Ck′ cos (k=1(2n + 1)kπ)
N

The two compression algorithms used in this study wereoriginally introduced in [6]. The compressions were performed in frequency space in order to make use of perceptual
properties of vibrotactile stimuli, such as detection anddeferential thresholds. These thresholds are often discussed
in frequency space.
Discrete cosine transformation (DCT) was used to convert
the texture profile to a frequency spectrum. By computing
the DCT of texture height samples y n (n = 0, ..., N − 1),
amplitude spectra Ck (k = 0, 1, ...N − 1) were acquired. Ck

n = 0, 1, ...N − 1.

(4)

B. Data Compression Algorithms for Vibrotactile Material
Textures
1) Linear Quantization: Quantization is one of the mostpopular strategies for lossy data compression. The quantized
amplitude spectrum L k is determined by
Lk = round(

A. Data Compression using Discrete Cosine Transformation

(3)

Ck
)·∆
∆

(5)

where ∆ is the quantization step. ∆ is expressed as∆=max(C1 , ...,CN ′ ) − min(C1 , ...,CN ′ )
L−1

(6)

where L, the number of quantization steps, determines thecompression level. Figs. 2a and 2b show an example ofthe surface profile and DCT indices, respectively, of theuncompressed and linearly quantized (L = 4) wood textures.
Given that each DCT index of the uncompressed texture waswritten in 2 bytes, the data size of the compressed texture in
the figure was 12.5% of the size of the uncompressed data.

3061

2) Truncation of Data beneath Shifted Thresholds(Threshold-Cut): Assuming that vibrotactile amplitude elements beneath the detection threshold level can be removed
while maintaining subjective quality, we may use the method
described here to eliminate vibratory amplitudes smaller than
the thresholds. When they are removed, the DCT indices are
determined byb00
if log10 |Ck | < log10 b( fk ) +
(7)
Tk =
20
Ck otherwise
where b( f k ) and b0 are the detection thresholds at frequency
fk and a variable for shifting the threshold curve, respectively. b0 determines the compression level of the method.
For example, when b 0 = −2 dB, amplitudes smaller than the-2-dB-shifted threshold curve are truncated.
The function b( f k ) was preliminarily acquired by a psychophysical method of adjustment involving six participants,
using the same equipment as that in this study. For the
12 frequencies, detection thresholds were investigated. The
values of the intermediates of the investigated frequencies
were determined by linear interpolation. The thresholds wereacquired while the hand was still.
Figs. 3a and 3b show the surface profiles and DCT
indices, respectively, of the wood textures compressed by thismethod when b 0 = 0 dB. Fig. 3b shows that the compressed
texture does not include vibratory amplitudes smaller than
the threshold curve. In this example, since 51.2% of theamplitudes are truncated, the compression ratio is regarded
as 48.8%. However, it should be noted that the actual
compression ratio depends on encoding algorithms. Hence,
this value is a brief estimation.

Fig. 2: Linearly quantized wood texture: L = 4

Fig. 3: Wood texture of which amplitudes beneathlog10 b( fk ) + b0 |b0 =0 are truncatedIV. E XPERIMENT: S UBJECTIVE C OMPARISON OFDATA -C OMPRESSED T EXTURES
A. Tasks and Participantsa) General: The participants evaluated the subjective
similarity between the uncompressed and compressed vibrotactile wood textures and sandpaper. These two types oftextures were evaluated by different participants. They rated
the similarity on a four-point grading scale. The compression
levels of the textures were 6 or 7 grades for both thecompression methods.
b) Tasks: In a single trial, the participants explored andcompared the uncompressed and compressed textures. In thetrial, each texture was presented to the participants for 5 s.
To adjust the average hand velocity of the participants to
50 mm/s (see Section III-A), the participants moved theirhands in strokes of 40 mm in accordance with the rhythm ofa metronome (1.25 Hz) in a pattern of one forward stroke forone beat and withdrawal for two beats. Marks on the desk
indicated the stroke distance (Fig. 1). During the explorationof two textures in a single trial, the participant was required
to attempt to retain the contact status between his/her finger
and the stimulator. After exploring the two textures, theparticipants manually recorded the similarity as “same,”“possibly the same,” “possibly different,” or “different.”c) Test Stimuli: The texture compression levels were
fixed to 6 or 7 grades for each compression method. Table I
lists the compression levels used in the experiments. In
addition to the data-compressed textures, the uncompressed
textures were included in the test stimuli. In total, thirteen
and fourteen test stimuli were prepared for wood textures

3062

TABLE I: Compression level of textures used for test stimuli
Wood
Sandp.

Linear quant. [step]Threshold-cut [dB]Linear quant. [step]Threshold-cut [dB]

L = 14,12,10,8,6,4
b0 = −12,−8,−4,0,4,8
L = 14,12,10,8,6,5,4
b0 = −12,−8,−4,0,4,8,12

the figure were computed by assigning values of 0, 1, 2,
or 3 to “same,” “probably the same,” “probably different,”
and “different,” respectively. It should be noted that thevalue for uncompressed texture–the rightmost circle anddiamond in Fig. 4–was not 0. In general, the score increased(similarity decreased) as the data size of the compressed
textures decreased. The changes in the scores were notmonotonic. For linear quantization, the changes showed aslight plateau around L = 8. For small compression rates oflinear quantization, the scores increased exponentially.
f) Sandpaper: Fig. 5 shows the dissimilarity rates between the uncompressed and compressed sandpaper textures.
Just as for the wood textures, the dissimilarity tended toincrease as the compression ratio decreased.
V. D EVELOPMENT OF O BJECTIVE I NDEX THATACCOUNTS FOR S UBJECTIVE Q UALITY C HANGE OFC OMPRESSED T EXTURES

Fig. 4: Subjective dissimilarities between the compressed anduncompressed wood textures

Fig. 5: Subjective dissimilarities between the compressed anduncompressed sandpaperand sandpaper, respectively. Each test stimulus was presented
four times in total. Hence, each participant performed 52 (13textures × 4 repetitions) or 56 (14 textures × 4 repetitions)trials for wood texture and sandpaper, respectively. The orderof presentation of test stimuli was random.
d) Participants: The participants were eight volunteers
in their 20s from the authors’ laboratory, excluding theauthors. Hence, these experiments are preliminary studies.
To shut out the sounds generated by the stimulator, theparticipants listened to pink noise through noise-cancellation
headphones.
B. Results: Changes in Subjective Quality of Compressed
Texturese) Wood texture: Fig. 4 shows the averages and standard deviations of the dissimilarity rates between the uncompressed and compressed vibrotactile wood textures forthe two types of data-compression methods. The values in

A. Related Studies: Pacinian-Filtered Power Spectrum
Bensmaı̈a et al. reported that the power of cutaneous
mechanical vibrations can be used to describe the subjective
intensity of vibrotactile stimuli or fine textures. The difference in perceived roughness of two fine textures correlatedwith the difference in the power of high-frequency vibrations of the finger pad when those textures were exploredby bare fingers [10]. They weighted the frequency power
spectrum of cutaneous vibrations by the square of the inverse quasi-detection threshold curve of Pacinian corpuscles.
These Pacinian-filtered power spectra also correlated withthe subjective intensities of vibrotactile stimuli at high frequencies [11]. They limited their studies to high-frequency
vibrations; however, we need to develop an objective index
taking account of the stimuli of low- or middle-frequency
bands around tens of hertz, so that the index can be applicable to material-like textures that have frequency components
across wide frequency bands.
B. Approach of This Study: Threshold-Filtered Power andAmplitude Spectrum
To develop a new objective index, first, we extend thePacinian filter used by Bensmaı̈a et al. to the entire frequency
band. Second, in order to properly evaluate the perceptual effects of the vibrotactile stimuli at tens of hertz, we introduce
a threshold-filtered amplitude spectrum. These two features
are described in the following two subsections.
1) Extension of Weighting Filter across the Entire Vibrotactile Frequency Band: Weighting the power spectrumby the inverse of the detection threshold curve is equal
to weighting the vibratory power in accordance with thesensation magnitude of each frequency stimulus. This isbecause, especially near the detection threshold level, theprofiles of equal sensation magnitude curves are similar to
those of the detection threshold curves [12]. Following thisidea, we extend the Pacinian filter to the entire frequency
band. To this end, we use the detection threshold curve forthe vibrotactile stimuli of the entire frequency band as a

3063

the amplitude spectrum weighted by the inverse of detection
threshold curve is determined by
N′

|Ck |
A= ∑
k=1 b( f k )

and

A′i =

N′

|C′ |

∑ b( fkik ) .

(9)

k=1

A and A′i denote the uncompressed and compressed textures,
respectively. The objective index is defined by a linear
connection of the relative error of the sum of weighted
spectra. The index isFig. 6: Profiles of the psychophysical weighting filters forvibrotactile stimuli
weighting filter of frequency spectra so that the objective
index can be available to the vibrations of tens of hertz.
2) Introduction of Amplitude and Power Spectra: Theconcept of the Pacinian filter was originally introduced by
Makous et al. [13]. They attempted to explain the masking
effects of noisy vibration stimuli that shift the detection
threshold of vibrotactile stimuli as an analogy to the phenomena of auditory critical bands. The Pacinian filters usedby Makous and Bensmaı̈a et al. were the square of theinverse detection threshold curve of Pacinian corpuscles.
However, because the detection threshold level of Pacinian
corpuscles is much smaller than that of Meissner corpuscles(roughly smaller than one-tenth), weighting by the squareof the inverse threshold curve underestimates the effects ofthe vibratory stimuli of tens of hertz for which Meissnercorpuscles are most sensitive. In addition, such weighting by
the square function is not valid except by analogy to auditory
perception.
In this study, we introduce the amplitude spectrum thatis weighted by the inverse of the detection threshold curvein addition to the power spectrum that is weighted by thesquare of the inverse threshold curve used by Makous andBensmaı̈a et al. The threshold-filtered amplitude spectrum is
expected to evaluate the perceptual effects of the stimuli oftens of hertz, whereas the threshold-filtered power spectrum
tends to underestimate the effects of these stimuli. Fig. 6
shows the weighting values of threshold filters. The squared
inverse filter almost neglects the effects of the vibrations oftens of hertz, whereas the inverse filter does not completely
diminish them.
C. Equations of the Objective Index
The sum of the power spectrum that is weighted by thesquare of the inverse detection threshold curve is given by
N′

Ck2
P= ∑
2
k=1 b( f k )

and

Pi′ =

N′

C′2

∑ b( fkik )2 .

(8)

k=1

P and Pi′ are the sums of threshold-filtered power spectra for
the uncompressed and compressed textures, respectively. The
suffix i denotes the type of compressed texture. The sum of|A − A′i||P − Pi′ |+b
Iob j·i = a 1
1′′
2 (P + Pi )2 (A + Ai )(10)

where a and b are the contribution ratios of the power
and amplitude spectra to the subjective quality indices,
respectively.
For comparison of the proposed objective index mentioned
above, we prepare two types of indices, I p and Ia . Each iscomposed of either the power spectrum or the amplitude
spectrum. I p is defined by the relative error of the sum of
the weighted power spectrum and is given by|P − Pi′ |.
I p·i = 1′
2 (P + Pi )(11)

Ia is defined by the relative error of the sum of the weighted
amplitude spectrum and is given by|A − A′i |Ia·i = 1.
′
2 (A + Ai )(12)

The constant variables in the indices, a and b were
determined by multiple regression analyses that involved theexperimental results of Section IV. The analysis minimized
the sum of square residuals between the subjective andobjective indices, which is given by||S − O||

(13)

where S and O are the vectors of subjective and objective
indices, respectively. They are
S = (Isb j·1 , ..., Isb j·i , ..., Isb j·M )T ,

(14)

T

(15)

O = (Iob j·1 , ..., Iob j·i , ..., Iob j·M )where M is the number of compressed/uncompressed textures involved in the analysis. I sb j·i is the subjective dissimilarity between the uncompressed and compressed textures
specified by i. These subjective dissimilarities are the averages of all participants’ answers acquired in Section IV. We
did not use the result of the linearly quantized sandpaperwith L = 4 for the regression analysis. This is because
all the participants answered the dissimilarity between thiscompressed and uncompressed texture as “different” in theexperiment. In such case, 4-grading scales were invalid toestimate the subjective dissimilarity.

3064

Fig. 7: I p for wood textures

Fig. 8: Ia for wood textures

VI. C OMPARISON OF O BJECTIVE AND S UBJECTIVEQ UALITY I NDICES
A. Wood texture
Figs. 7 and 8 show I p and Ia for the compressed wood
textures, respectively. First, we qualitatively compare I p(Fig. 7) and the corresponding subjective dissimilarities inFig. 4. In general, I p increased as the data size of thecompressed textures decreased, which is consistent with thegeneral trend of subjective indices. The change in I p showeda plateau around the quantized texture of L = 8 (diamonds
in Fig. 7), which is similar to the trend observed for the
subjective indices. On the other hand, I p values of thresholdcut textures (circles in Fig. 7) were relatively smaller thanthese of quantized textures (diamonds in the same figure).
This feature does not match that of subjective indices. This isbecause the algorithm of threshold-cut mainly removed lowfrequency stimuli in the case of wood texture (see Fig. 3). I p
underestimated the effects of the changes in low-frequency
stimuli.
Second, we look at Ia (Fig. 8). As well as I p , Ia also tended
to increase as the data size of the textures became smaller.
The Ia for the threshold-cut textures (circles in Fig. 8) werelarger than those of quantized textures (diamonds in Fig. 8),
which shows a trend similar to that of the subjective indices.
On the other hand, I a did not clearly show a plateau aroundL = 8.
Fig. 9 shows Iob j and subjective dissimilarities for thewood textures. The subjective dissimilarities are the sameas those in Fig. 4. The free variables for I ob j were (a, b) =(0.67, 0.44). R 2 between Iob j and the subjective dissimilarities was 0.851. This value was higher than that between I p(R2 = 0.680) or Ia (R2 = 0.456) and subjective dissimilarities.
Iob j described the subjective dissimilarities of compressedwood textures better than I p and Ia did. These R2 values areshown at the leftmost part in Fig. 10.
B. Sandpaper
Fig. 11 shows I p for the sandpaper. In general, I p increased
as the data sizes of the textures decreased except for the
one quantized with L = 5. This is due to the nonlinear

Fig. 9: Subjective dissimilarity and I ob j for wood textures

Fig. 10: R2 between the subjective and objective indices.

changes in the power caused by the quantization. Comparing
the I p values with the trends of subjective dissimilarities
in Fig. 5, I p for threshold-cut textures (circles in Fig. 11)
were relatively smaller than those for the quantized textures(diamonds in the same figure). As well as the case of wood
textures, this is because I p is insensitive to the low-frequency
vibrations that the threshold-cut algorithm removed from thesandpaper.
Fig. 12 shows Ia for the sandpaper. I a for threshold-3065

Fig. 12: Ia for sandpaper

Fig. 11: I p for sandpaper

Fig. 13: Subjective dissimilarity and I ob j for sandpaper

cut textures (circles) were much larger than those for thequantized textures (diamonds). These differences between
the textures compressed by two types of algorithms werelarger than those for the subjective dissimilarities of them inFig. 5.
Fig. 13 shows Iob j and the subjective dissimilarities forsandpaper. The subjective dissimilarities are the same as
those in Fig. 5. The free variables for I ob j were (a, b) =(0.52, 0.58). R 2 between Iob j and the subjective dissimilarities was 0.883. This is higher than R 2 between I p or Ia andthe subjective dissimilarities, which were 0.612 and 0.667,
respectively (center of Fig. 10). For sandpaper, as well as
the wood textures, the developed objective index I ob j welldescribed subjective dissimilarities of compressed sandpaper
textures.
C. Gross Analysis: Wood and Sandpaper
Fig. 14 shows Iob j vs. the subjective dissimilarities for bothwood textures and sandpaper. I ob j was computed using theexperimental results of both textures. The free variables were(a, b) = (0.581, 0.464) and R 2 = 0.790. This value is higher
than those of I p and Ia indices as shown at the rightmost partin Fig. 10. The figure shows that in all cases, I ob j has higher
R2 values between the subjective indices than I p and Ia .

Fig. 14: Subjective dissimilarity vs. Iob j for wood texturesand sandpaper. Solid line describes the match of subjective
and objective indices.

VII. D ISCUSSION : T HRESHOLD -W EIGHTED A MPLITUDE
AND P OWER S PECTRA C AN BE G OOD O BJECTIVE
I NDICES
This study developed an objective index that substitutes
for the subjective quality index for vibrotactile materiallike textures. The objective index is a linear combination of
the power and amplitude spectra of vibratory stimuli. These
spectra were weighted by the inverse of the detection threshold curve. The weighted power spectrum described the variations of subjective quality indices to an accuracy of approximately 60%, while the linear combination of the weighted
power and amplitude spectra did so by approximately 80%.
Bensmaı̈a et al. [10], [11] found that the Pacinian-filtered
power spectrum of vibrotactile stimuli or cutaneous mechanical vibrations correlated with the perceptual intensities
of high-frequency vibrations or perceived roughness of finetextures. On the other hand, the experimental results of thepresent study suggest that for vibrotactile material texturesthat are composed of low or intermediate frequencies ofaround tens of hertz, the combination of threshold-filtered3066

power and amplitude spectra well describes the subjective
differences in the textures, although its application is currently limited to two types of textures. We speculate thatthe developed index well described the material textures
because the combination of threshold-filtered amplitude andpower spectra properly evaluated the perceptual effects ofthe stimuli at tens of hertz in which Meissner corpuscles are
sensitive and the stimuli at high frequency around hundredsof hertz in which Pacinian corpuscles are sensitive. In otherwords, I p functions for high-frequency range and I a functions
for both high and low frequency ranges, however, it isinadequate for describing the quality changes alone. I p andIa work for vibrotactile material-like textures in a mutuallycomplementary manner.
VIII. C ONCLUSIONSThis study developed an objective index that substitutes
for subjective quality indices for vibrotactile material-liketextures. We found that a linear combination of power
and amplitude spectra of vibrotactile stimuli weighted by adetection threshold curve well describes the quality changes
in textures. We applied this objective index to two types ofvibrotactile material-like textures that come from the surfacesof wood and sandpaper, respectively. The subjective qualitiesof these textures were manipulated by two types of lossy datacompression algorithms. The index described the changes
in the subjective quality of data-compressed textures to an
accuracy of approximately 80%. The index was shown to bea good predictor of quality changes in vibrotactile material
textures. The developed objective index should be applied to
the various type of textures, not just to two types in this study
for its validation. Good objective indices are expected tolower the costs of psychological experiments needed for theenhancement of data-compression algorithms and contributeto understanding human perceptual properties by clarifying
the effective physical quantities.

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