JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015

1

Relationship between spatial variations in static skindeformation and perceived roughness of macroscopic surfaces
Shogo Okamoto, Member, IEEE, Ariei Oishi

Abstract—The perceived roughness of macroscopic surface features
is related to ﬁnger skin deformation. For example, skin indentation
into surface grooves and the spatial variation in slowly adapting type
1 (SAI) mechanoreceptor activities are linked to the magnitude ofsubjective roughness. However, the perception of macroscopic roughness
has not been directly linked to the spatial variations in skin deformation;
therefore, this study investigated the relationship between the subjective
roughness magnitude and the spatial spectrum of skin deformation
through contact with roughened macroscopic surfaces. Experiments were
performed to measure deformation of a ﬁnger pad when it staticallytouched different shaped grating scales. Then, the spatial spectra of skindeformation were computed by applying the Gabor ﬁlter with varying
spatial selectivity. Some spectral components, particularly those for the
spatial period ranging from 2.45–4.00 mm, exhibited a good correlation
with the perceived roughness magnitude. When the optimal spatial
periods were determined for individual subjects, the spectral components
and perceived roughness exhibited a strong linear relationship with anaverage correlation coefﬁcient of 0.94. Therefore, the amount of spatial
variation in ﬁnger skin deformation can be linked to the subjective
roughness intensities of macroscopic surface features.

I. I NTRODUCTION
The relationship between subjective roughness perception and surface features has been widely studied for surfaces with geometricallymacroscopic features larger than approximately 1 mm. Previous
research has successfully formulated surface feature functions, suchas the groove width and spatial frequency of surfaces, to predict
subjective roughness intensities (e.g. [1]–[7]). These studies agree
that the groove width of gratings or the inter-element spacing of
surface dots are the key factors that affect roughness perception, inthat roughness intensities increase with the values of these factors.
This phenomenon is attributed to skin deformation [8], i.e., the skinon a ﬁnger pad penetrates a wider groove to a larger depth. However,when groove width is larger than 3–4 mm, roughness intensities may
not monotonically increase with groove width [5], [9]–[11] because
the skin in the central part of a groove exhibits less deformation.
Furthermore, if a groove is sufﬁciently shallow to enable an indented
ﬁnger pad to reach the bottom (i.e., grove height is small), the skindoes not penetrate the groove, which diminishes subjective roughness
intensity [11].
According to neurophysiological studies, spatially macroscopic
information is recorded by slowly adapting type 1 (SAI) units(e.g., [2], [12]–[15]), and spiking activities have previously been
explained by the stress or strain of the skin tissue surrounding Merkel
nerve endings [16]–[18]. The subjective roughness of specimens
or material surfaces have been expressed by the spatial variationin SAI activities [3], [9], [19]–[21]. Spatial variation refers to thedifference in activities between SAI units, in which receptive ﬁelds
are closely located. Subjective roughness increases with the differencein activities.
Therefore, previous research has indicated that a relationship exists
between the spatial variation or magnitude of skin deformation
S. Okamoto and A. Oishi are with the Department of Mechanical Engineering Systems, Nagoya University, Japan. E-mail: okamoto-shogo@nagoya-u.jp
This study was in part supported by MEXT Kakenhi (#17H04697). The
experimental protocols of this study were approved by the institutional review
board of the School of Engineering, Nagoya University (#19-9).

and roughness perception. For example, Taylor and Lederman [8]investigated how the cross-sectional area or depth of skin penetration
into grooves can represent roughness perception. However, there isa lack of research that directly links the spatial variation in skindeformation and the perceived roughness of macroscopic surfaces.
Therefore, this study is designed to bridge the gap in the existing
psychophysical and neurophysiological studies from the viewpoint ofskin deformation. To achieve this goal, we performed experiments
where human subjects pressed their ﬁnger pads on gratings withdifferent shapes and widths larger than 1 mm. They appraised thegrating scales without sliding motion following the framework of
the magnitude estimation method. Then, spatial ﬁlters with speciﬁcfrequency selectivities were applied to observed skin deformation
images to compute spatial spectra, which were used to derive thespatial variation in skin deformation. The same ﬁltering operation
was performed on the spatial event plots of SAI units in earlier
neurophysiological studies [3], [9], [19], [21], and spatial spectra
were compared with subjective roughness intensities. The aim of
this study is to determine how effectively skin deformation canstatistically explain the subjective response to macroscopic surface
roughness using a few types of grating scales.
We focus on static skin deformation because ﬁnger movement
exhibits a relatively small effect on the judgment of macroscopic
surface features [22]. In contrast, in terms of ﬁne textures, the temporal aspects of skin deformation, i.e., skin vibration and subjective
roughness, are closely linked (e.g., [21]–[23]).
A potential application of the outcome of this study is a roughness
index based on skin deformation, even though the establishment ofsuch an index is not the major objective of the present study. For
numerous material developers and surface designers, it is expensive
to repeat sensory appraisal and impractical to measure neural activity
to evaluate roughness1 . In contrast, it is simple to observe skindeformation. Therefore, this study provides an accessible method forevaluating roughness perception for macroscopic surfaces.
II. M ETHODS
A. Stimuli
As shown in Fig. 1, 3D-printed (Form2, Formlabs, MA, stereolithography, minimal layer pitch: 25 µm) rectangular, triangular, andcircular gratings were used as roughness samples. Rectangular andtriangular gratings were frequently used in earlier studies (e.g., [2],[3], [5], [7]), whereas circular gratings were rarely used. We selected
these three types of gratings to investigate if the spatial variation inskin is related to the subjective roughness of not only common grating
scales but also other types of grating scales. We used Tough v5 resin
as a material. The rectangular gratings were deﬁned by ridge andgroove widths, whereas the triangular gratings were deﬁned only bygroove widths. The vertex angles of the triangles were 30◦ , 45◦ , or60◦ . The circular gratings were deﬁned by circular diameters and theinterval of adjacent circles, where the latter was used only for gratings
with small diameters. For all types of gratings, the depth of a groove
1 In future, fully or partially computerized simulations of unit activities arelikely to be used widely [24], [25].

JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015

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C. Experiment: Subjective roughness magnitude

Inter-cylindergap (0 or 0.5 mm)

20 mm

50 mm

DiameterGroovewidth

2.8—3.5
mm

3 mm

Ridge
width

GroovewidthFig. 1. Schematic diagrams and photographs of the gratings used as roughness
samples. From top to bottom: circular, rectangular, and triangular gratings. The
bottom three-dimensional drawing is a circular grating.
TABLE IS PECIFICATIONS OF THE 16 GRATING TYPES USED IN THE EXPERIMENTS .
VALUES IN PARENTHESES ARE USED FOR THE REGRESSION ANALYSIS .
Type
Rectangular

Triangular

CircularRidgewidth (mm)
0.75
0.75
1.0
1.0
1.5
- (0)
- (0)
- (0)
- (0)
- (0)
- (0)
- (0)
- (0)
- (0)
- (0)
- (0)

Groovewidth (mm)
1.0
1.75
1.0
2.25
1.5
1.5
1.75
2.5
2.75
3.5
4.0
0.5 (1.5)
0.5 (1.75)
0 (2.5)0 (3.0)0 (4.0)Vertex
angle
30◦
30◦
45◦
45◦
60◦
60◦
-

Circular diameter (mm)
1.0
2.25
2.5
3.0
4.0

1) Procedure: The participants appraised the roughness magnitudeof each sample according to a reference modulus stimulus. For
example, if the roughness of a sample was perceived to be 1.5
times that of the modulus, then a value 1.5 times the modulus was
assigned to the sample. The modulus was a triangular grating witha groove width of 1.0 mm (vertex angle of 30o ), which was notincluded as an experimental grating. This grating was presented tothe participants after consecutively presenting four test stimuli. For
subjective inspection, each participant laid their thumb on a roughness
sample, which was placed on an electric weight scale, and a loadof ∼300 gf was maintained for a few seconds before reporting theintensity of the sample. Furthermore, the subjects were instructed not
to slide their thumbs. These conditions were also employed to image
skin deformation, as described in Sec. II-E. We used the thumb tophotograph the large stable contact region. The roughness samples
were presented to each subject in a randomized order, and eachsample was tested three times per participant. The entire procedurerequired approximately 45 min for individuals, including the initial
5 min for practice.
2) Data analysis: For individuals, to prevent the effects of outlierson experimental results, the median values of the roughness magnitude were calculated from the three responses for each roughness
sample. These median values were normalized such that their geometric mean was 1 among all types of gratings. We did not perform
logarithmic transformation on these normalized values because, as
discussed later, they exhibited a strong linear relationship with thegroove width of the roughness samples and the spatial spectrum ofskin deformation.
D. Regression analysis of perceived roughness via macroscopic surface features
The subjective roughness values were estimated using regression
analysis by utilizing ridge width, groove width (GW ), and the squareof groove width as potential explanatory variables2 . In terms ofgroove width, the values provided in parentheses in Table I wereused, where the ridge widths for the circular and triangular gratings
were zero. The net distance between circular peaks was used as thegroove width of the circular gratings. For this analysis, the stepwiseﬁtfunction of Matlab (Matlab2019a, MathWorks Inc., MA) was usedwith a statistical signiﬁcance level of p < 0.05 for variable selection.
The subjective roughness values averaged among the participants
were utilized for this operation.
E. Image acquisition and processing

B. Participants

After magnitude estimation experiments, the participants again laid
their right thumbs on each roughness sample, and a cross-sectional
picture was obtained from the distal direction, i.e., from the tip,using a digital camera (RX-10II, Sony, Japan, 20.2 million pixels,
macro-photography mode). Lighting conditions were adjusted so thatthe interface between the two materials was clear. Each participant
maintained a ﬁnger load of 300 gf on the electric weight scale forthe duration of image acquisition.
The images were processed using Gimp 2.10.12, as follows:
Optically zoomed images were shrunk to achieve a uniﬁed resolution of 700 pixels per 10 mm, i.e., 0.014 mm/pix (Fig. 2a). The

Seven male university students in their 20s (age: 23 ± 1.5 years
old) were recruited for this study. The students provided written
informed consent. All subjects were right handed and declared notactual disabilities. The subjects were unaware of the study objectivesprior to the experiments.

2 GW , GW 2 , ridge width, and spatial wave length (GW + ridge width) are
the potential predictors of subjective roughness [3], [5], [7], [26]. However, in
our setup, for the triangular and most circular gratings, ridge width was zeroand wave length and GW were equal. For such cases, either wave length or
GW should be used to prevent the problem of collinearity, and we selected
GW .

was designed to be sufﬁciently large such that the ﬁnger skin did
not reach the bottom of the groove. Originally, 30 types of gratings
were manufactured. From these, the gratings that allowed for theacquisition of clear images of skin deformation through the processdescribed in Sec. II-E were selected. Gratings were also selected toensure variable subjective roughness values. The speciﬁcations of the
ﬁnal 16 types of gratings are given in Table I. The dimensions of theroughness samples were 50 × 20 × 10 mm.

JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015

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Determining the optimal value of σ was outside the scope of thisstudy. However, the range of values of σ tested in this study (σ= 0.9–1.4 mm), which was close to that used in [19], [21] (σ =1.12 mm), did not substantially inﬂuence the computational results.
Therefore, we adopted σ = 1.1 mm. In contrast, the optimal valuesof λ depended on individual subjects. The values of λ ranged from
λ = 1.0–5.0 mm, which included the value (λ = 2.8 mm) usedin [19], [21], where λ was determined to best explain subjectively
reported roughness. In our study, within this range, the value of λ foreach participant was determined to achieve the maximum correlation
coefﬁcient between subjective roughness values and spatial spectral
components (also see the second paragraph in Sec. IV).
Fig. 4 shows a few examples of the computation with λ =2.66 mm, which is the optimal value found in Sec. III-B. Larger
skin deformation leads to larger ﬁlter outputs. Further, ﬁlter outputs
increase as the spatial periods of the skin deformation become closer
to λ.
III. R ESULTS
Fig. 2. Image processing procedure to determine the deformed skin surface
line. (a) Cross-sectional image of thumb before image processing. (b) After
applying edge detection to the image. (c) Selection of the skin surface using
an automatic selector. (d) Black and white image of the skin surface region.
(e) Central curve determined along the x-direction. Red dots represent theskin surface region acquired in (d). The image processing shown in (c)–(d)was conducted using Gimp 2.10.12.

brightness level was adjusted to clarify the boundary between theskin and grating, and the optical boundary was computed using thephotocopy function (Fig. 2b). The skin boundary was extracted using
the intelligent scissors tool, which automatically separates different
objects in an image. The separated region was visually inspected
and manually rectiﬁed if necessary (Fig. 2c). Then, the images weretransformed into black and white binary images (e.g. Fig. 2d). The
images were loaded into Matlab (Matlab 2019a, Mathworks, MA)
to calculate the curve that passed through the center of the skinsurface region in the x-direction, i.e., the red dots in Fig. 2e. Finally,quadratic and linear trends were removed from the curve and the skinboundary was acquired as a black curve (Fig. 2e). Skin boundary
curves were acquired for each combination of participant and grating
type, resulting in 112 curves.
F. Computation of the spatial spectra of static skin deformation
The one-dimensional Gabor ﬁlter was applied to the skin deformation curve. The two-dimensional version of this ﬁlter was used
for the spatial event plots of SAI units in earlier studies [19]–[21].
Further, a similar operation was used in [3], [9].
The one-dimensional Gabor ﬁlter is a harmonic function withan attenuating amplitude, which functions as a ﬁlter with a peaksensitivity at the spatial period, λ mm, to compute the spectra ofskin deformation. The proﬁle of the ﬁlter is deﬁned by−x22πxg(x) = exp( 2 ) cos(
)
2σ
λ

(1)

where σ determines the attenuation of the amplitude (Fig. 3a). Thisﬁlter and the skin deformation curve, y(x) (Fig. 3b), were convoluted
along the x-axis:
s(x) = (g ∗ y)(x).

(2)

As shown in Fig. 3c, the maximum absolute output value,max(|s(x)|), was used as a spectral component for λ in the lattercomputation.

A. Relationship between surface features of roughness samples andsubjective roughness
For the rectangular and triangular gratings, the stepwiseﬁt function
found that only groove width signiﬁcantly affected subjective roughness (t(7) = 15.95, p < 0.001), and the regression equation wasdetermined as follows:
R = 0.54GW(3)

where R and GW are the subjective roughness value and groove
width, respectively. The contributions of RW (t(7) = −1.77, p =0.11) and GW 2 (t(7) = −0.50, p = 0.63) were not observed.
Whereas the above analysis was conducted by involving the geometric means of all the participants, we also computed the gradient of
the regression line for each combination of the individual participants
and types of grating scale. The gradients were statistically signiﬁcantfor 17 of the 21 cases (7 participants × 3 types of grating) withp < 0.05, and the other four cases had a p < 0.10, which meansthat the subjective roughness covaried with the groove width for mostparticipants and types of grating scales.
Fig. 5a shows the relationship between the geometric mean ofsubjective roughness for all participants and the groove width ofgratings. The subjective roughness of the rectangular and triangulargratings was closely correlated with GW , with a correlation coefﬁcient of r = 0.98. This value was close to those obtained in previous
studies where subjective roughness was estimated using the geometricparameters of macroscopic surface roughness, i.e., 0.99 in [3], 0.96
in [7], 0.99 in [5], and > 0.99 in [26]. When regression analysis was
conducted for individuals, the mean and standard deviation of theircorrelation coefﬁcients was r = 0.96 ± 0.027.
Including the circular, rectangular, and triangular gratings, theregression equation was
R = 0.41GW + 0.23

(4)

with a correlation coefﬁcient of r = 0.87. GW (t(12) = 6.71,
p < 0.001) signiﬁcantly affected subjective roughness, whereas RW(t(12) = −1.59, p = 0.14) and GW 2 (t(12) = −0.67, p = 0.51)
did not. Fig. 5a shows that roughness intensities were overestimatedfor the circular gratings. This suggests that GW should only be used
to estimate the subjective roughness of rectangular and triangulargratings but not circular gratings. It is noted that circular gratings
were rarely used in previous studies.
Fig. 5b shows the individual variation in the relationships between
groove width and subjective roughness for three participants andJOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015a) One-dimensional
Gabor filter: g(x)4b) Skin surface deformation: y(x) (mm)

1

0.1
0

0

-0.1
-2

0

2

0

10

x (mm)

ൌ

Filter output(a.u.)c) Filter output: s(x)Maximum
absolute value

100Absolute
value

-10
0

10

x (mm)

Fig. 3. Application of Gabor ﬁlter to the measured skin deformation. a) Gaborﬁlter with spatial sensitivity designated by λ. b) Skin surface deformation. c)
Output of the convolution on a) g(x) and b) y(x). The maximum absolutevalue was used as the spatial spectral component for λ.
Rectangular (GW = 0.75 mm, RW = 1.75 mm)
20
10

0.4
0.2

0

0

-10

-0.2
0

2

4

6

8

10

0

2

4

6

8

10

0

2

4

6

8

10

0

2

4

6

8

10

Rectangular (GW = 1.0 mm, RW = 2.25 mm)
20
10

0.4
0.2

0

0

-10
0

2

4

6

8

10

Circular (GW = 3.0 mm)
0.4
0.2
0
-0.2
0

2

4

6

8

10

Filter output (a.u.)

Skin deformation (mm)

-0.2

20
10
0
-10

Triangle (GW = 1.75 mm)
0.4

B. Relationship between subjective roughness and the spatial spectral component of skin deformation
Fig. 6a shows the relationships between spatial spectral components and subjective roughness for three example participants,
where different colors correspond to different participants. A linear
relationship was observed for all participants; however, the gradientsof the linear ﬁts and the distribution of roughness and spectral
component values differed among the participants. These differences
may indicate that spatial spectral components largely depend on thephysical properties of individual ﬁnger pads, i.e., the softer the skin,
the larger the skin deformation. The mean correlation coefﬁcient
between spectral components and subjective roughness among theseven participants was 0.85 ± 0.07, with maximum and minimum
values of 0.93 and 0.72, respectively. This value was comparable
to that between groove width and subjective roughness, i.e., 0.82 ±0.07. Fig. 6b shows the mean values of subjective roughness andspatial spectral components for individual roughness samples. The
means of these two values were closely correlated with a correlation
coefﬁcient of r = 0.94.
Roughness intensities were estimated using their linear relationships with the spatial spectral components of skin for each participant.
Fig. 6c shows the relationship between estimated and reported roughness intensities. Even though the intensities of the circular gratings
were overestimated when using groove width, as shown in Fig. 5a,the same trend was not observed when spatial spectral components
were used. Instead, the roughness intensities of the triangular gratings
tended to be underestimated, i.e., the majority were located above the
1:1 line.
As mentioned previously, the optimal values of λ for individual
participants were used in the analysis. Fig. 7 shows the correlation
coefﬁcients between the spatial spectral components and subjective
roughness for different values of λ for each individual (upper panel)and the means and standard deviations (lower panel). The value of
λ that exhibited the peak correlation coefﬁcient differed among theparticipants. The optimal values of λ ranged from 1.15–3.50 mm,
and the mean was 2.66 mm.

20
10

0.2

IV. D ISCUSSION

0

0

-10

-0.2
0

2

4

6

8

10

0

2

4

6

8

10

0

2

4

6

8

10

Triangle (GW = 2.75 mm)
0.4

20
10

0.2

0

0

-10

-0.2
0

2

4

6

x (mm)

8

10x (mm)

Fig. 4. Examples of skin deformation (left) and corresponding ﬁlter outputs(right) for four types of roughness samples. Red dotted curves are the absolutevalues. λ = 2.66 mm.

their regression lines. They include the highest and smallest gradientsamong those for all participants.
Even though the mean subjective roughness values for all participants were used in the above analyses, Fig. 5c shows the individual
subjective intensities estimated by GW using all types of roughness
samples, where the regression equation was established for each individual. The correlation coefﬁcient ranged from 0.67–0.88 for all sevenparticipants, with a mean and standard deviation of r = 0.82 ± 0.07.

Subjective roughness intensities were accurately estimated using
the groove widths and spatial spectral components of skin deformation (Figs. 5 and 6, respectively). The results could suggest that theroughness estimation based on skin deformation is comparable to thatbased on groove width. Macroscopic surface features characterized
by groove width can typically predict subjective roughness withcorrelation coefﬁcients of almost 1 (r = .96–.99) [3], [5], [7], [26].
Estimates based on skin deformation are not expected to exhibit
correlation coefﬁcients higher than these values. Earlier studies successfully estimated roughness intensities using the spatial variation in
the activity of SAI units or their spatial spectral components [3], [19]–[21]. This study computed the spatial spectra of skin deformation
and revealed that skin spectral components are closely correlated tosubjective roughness. This result is intuitive considering that Merkel
discs exist immediately beneath the superﬁcial layer of the skin;however, this relationship has not been demonstrated previously.
Therefore, assuming that the observed skin deformation is applicable
to a variety of surface textures, which requires further experimental
veriﬁcation, this relationship has important industrial applications formaterial and surface design.
In this study, we used the optimal value of λ for each individual
participant. It is natural that λ depends on individuals owing todifferences in the biomechanical properties of ﬁngers. Any differencein the mechanical properties of skin will lead to a difference in its

JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015b) Groove width vs. reported perceived
roughness for 3 representative participants0

r = 0.88

r = 0.70

12

1

r = 0.82  0.07
422Perceived roughness

Regression line
for three types ofscales (r = 0.87)
0Rectangular
Triangle
Circularr = 0.81

Regression line
for rectangularand triangles(r = 0.98)

1c) Estimates vs. observation of individual
perceived roughness for 7 participants
3

Rectangular
Triangle
Circular

Perceived roughness

Perceived roughnessa) Groove width vs. reported perceived
roughness (mean) for 7 participants

2

5

0

0

4

2

Groove width (GW)

0
0

1

2

3

Estimated perceived roughness

Groove width (GW)

Fig. 5. Subjective roughness vs. grating width. a) Mean subjective roughness from 7 participants vs. groove width. The dotted line is a regression line for therectangular and triangular gratings, for which 77 samples were used. The solid line is a regression line for the three types of grating scales, for which 112
samples were used. b) Subjective roughness vs. groove width for three individuals and their regression lines. Each regression is based on 16 samples. They
include the lines of highest and lowest gradients. Different colors correspond to different participants. The same participants appear in Fig. 6a. c) Reported
and estimated roughness values for 112 samples. The solid line indicates the match between the estimated and reported perceived roughness.

2

3

3

  .82,
 3.20 mm

  .84,
 3.00 mm

1c) Roughness estimated by spatial spectral
component for 7 participants

Rectangular
Triangle

Circular

Perceived roughness  .93,
 2.50b) Spatial spectral component vs. perceived
roughness (mean and s.d.) for 7 participants

Perceived roughness

Perceived roughnessa) Spatial spectral component vs. perceived
roughness for 3 representative participants

2

1

Rectangular
Triangle
Circular2

1

r = 0.85

  0.94
0

0

0

50

Spatial spectral component value (a.u.)

030

Spatial spectral component value (a.u.)

0
0

1

2

0.07
3

Estimates by spatial spectral component

Fig. 6. Subjective roughness estimated by the spatial spectral component of skin. a) Reported subjective roughness vs. spectral component for three participants
including those with the highest and lowest gradients deﬁned by linear regression. Only three participants are shown for visual clarity and 16 samples wereused for each regression. The same participants appear in Fig. 5b. b) Means and standard errors of subjective roughness and spectral components computedfrom 112 samples of 7 participants. c) Estimated and reported roughness values for 112 samples of 7 participants. The line represents an exact correlation
between reported and estimated roughness intensities.

spatial ﬁlter effect [27]. Finger size particularly affects the sensitivityof spatial pattern recognition [28]. It will be interesting to investigate
the determinants of λ in future. Finger size and softness may
potentially inﬂuence λ.

Correlation coefficient between subjective
roughness and spatial spectral component

1

Individuals

0
1

Mean

0
1

2
2.66 3
4
Wavelength (ߣ) of Gabor filter (mm)5Fig. 7. Top) Correlation coefﬁcients between subjective roughness andspatial spectral components computed using the Gabor ﬁlter of λ. Each color
corresponds to a different participant. Bottom) Mean and standard deviationsof the correlation coefﬁcients of all study participants. The mean correlation
is maximum at λ = 2.66 mm.

In our experiments, spatial components and subjective roughness
exhibited a close correlation (r ≥ 0.82, lower panel of Fig. 7) inthe range of λ = 2.45–4.00 mm,. If a speciﬁc value of λ is strongly
preferred over other values, subjective roughness should exhibit aclear peak intensity for gratings with the spatial period of that valueof λ. However, previous studies do not exhibit such phenomena. A
few studies have reported roughness intensity as an inverted U-shaped
function of groove width with a peak value [3], [5], [10]; however,these peaks were only moderate plateaus. In contrast, Gescheider et
al. [29] reported a clear peak of subjective roughness intensity fora dot spacing value of 2.42 mm. In the work of Connor et al. [19],where Gabor ﬁlters were applied to the spatial distributions of SAI
activities, the correlation coefﬁcient between gross mean subjective
roughness and spatial components was larger than 0.90 for λ = 2.0–
4.0 mm. In the study of Blake et al. [20], the optimal λ was within
the range of 2.0–3.0 mm (2.6 mm), with which spatial components

JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015

accurately estimated subjective roughness. These ﬁndings are notinconsistent with other studies where the mean activities of SAI
units were used to accurately predict subjective roughness [2], [3],[11], [30]. In brief, the majority of previous research agrees with theﬁndings of this study, i.e., the preferred spatial period ranges from
λ = 2.0–3.0 mm or 2.0–4.0 mm and that this spatial preference is
not particularly selective in this wide range.
This study did not include the results for gratings with a groove
width of less than 1.0 mm. For these gratings, the peak-to-peakdisplacement of the pictured skin deformation was limited to several
times the spatial resolution (0.014 mm/pixel) of our imaging method.
Therefore, future research should improve imaging conditions. Another challenge is the use of nonperiodic roughness scales; the present
study employed periodic grating scales. One evident problem of
nonperiodic scales is that surface roughness is not homogeneous ina ﬁnger–scale contact area, and it is not clear how subjects capture
the surface features of such scales. Further, for the extension of thepresent approach to dynamic touch, we need a totally new approach.
V. C ONCLUSIONSPrevious studies have highlighted the relationship between perceived macroscopic surface roughness and the spatial variations in
the activities of SAI units and the relationship between perceived
roughness and macroscopic surface features such as groove width.
However, this study is the ﬁrst to report the relationship between
the spatial variations in skin deformation and roughness perception
for macroscopic surfaces. This was achieved by computing the spatial
spectra of skin deformation using the cross-sectional images of ﬁnger
pads on different shaped gratings. The spatial spectral componentsof speciﬁc spatial periods were closely correlated with subjective
roughness intensities, with a mean correlation coefﬁcient of 0.94. Furthermore, the optimal spatial periods differed among the participants,
with a mean of 2.66 mm and a range of 2.45–4.00 mm. Therefore,
the strong correlation between roughness perception and spectral
components suggests that the peak spatial frequency preferably lies
around this point but with a broad range.
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