Erratum
Journal of Robotics, Networking and Artificial Life, Vol. 1, No. 1 (June 2014), 60-67

Errata on “Kansei Impression and Automated Color Image Arrangement Methods”(i) Page 62, Line 24 (left)
Error
From Eq.(3), we obtain Eq.(4) and (5) because
y0=f(x0) and y0 + dx = φ(x0 + dx).

(iii) Page 63, Fig. 2
Error

y

Corrected
From Eq.(3), we obtain Eq.(4) and Eq.(5) because
y0=φ(x0) and y0 + dx = φ(x0 + dx).

g(y)(ii) Page 62, Line 2 (right)
Error
Since φ’(x) = Lφ(x), according to Eq. (5), we
derive following Eq. (7).

y =φ ( x )φ ( L)

φ(x0 +dx)y
φ ( x0 )

0

1/ L

x
x0

L

x

x0 +dxCorrected
Since φ’(x) = Lf(x), according to Eq.(5), we derive
the following Eq. (7).

f(x)
Fig. 2. Conceptual image of the transform from uniform
distribution (PDF) to the desired one.7

Correctedyy = φ ( x)φ ( L)

φ(x0 +dx)y
φ ( x0 )

1/ L

0

x
x0

L

x

x0 +dxg(x)Fig. 2. Conceptual image of the transform from uniform
distribution (PDF) to the desired one.7

Journal of Robotics, Networking and Artificial Life, Vol. 1, No. 1 (June 2014), 60-67

Kansei Impression and Automated Color Image Arrangement Methods
Yusuke Kawakami, Tetsuo Hattori, Yoshiro Imai, Haruna Matsushita

Graduate School of Kagawa University, 2217-20, Hayashi
Takamatsu, Kagawa 761-0396, Japan
E-mail: s11d621@stmail.eng.kagawa-u.ac.jp, {hattori, imai, haruna}@eng.kagawa-u.ac.jp
Hiromichi Kawano

NTT Advanced Technology Corporation, 19-18, Nakamachi
Musashino, Tokyo 180-0006, Japan
E-mail: Hiromichi.kawano@ntt-at.co.jp
R.P.C. Janaka Rajapakse

Tainan National University of the Arts, 66, Daci,
Guantian, Tainan, 72045, Taiwan

Abstract
This paper proposes a new color image arrangement method using an elastic transform on some kinds of axes. In
this paper, we present the principle of our method using HMGD (Histogram Matching based on GaussianDistribution). And we describe that the automated method applies the HMGD to input color image only when theimage has single-peakedness in its histogram on the focused axis. And we describe about HPA-HMGD (Histogram
Peakedness Adaptive HMGD) as improvement HMGD. We also show that the method gives a good Kansei effectin the case of applying the HMGD onto Brightness axis. Moreover, we compare processing results of the HPAHMGD and HMGD, we show that HPA-HMGD is better.
Keywords: Automated color arrangement, elastic transform, histogram matching, HMGD, Curvature, HPA-HMGD

1. Introduction
Automated image processing for enhancement and/or
arrangement of color images has been more familiar tous according to the spreading of Digital Camera, Smart
Phone, DVD, etc.1-3 However, we consider that the
research on the automated arrangement method thatbrings about good sensibility effect (or Kansei effect) is
still on the way to practical use.
In this paper, we propose a novel color image
arrangement method using an elastic transform based on
histogram on some kinds of axes.4-6 As for the axes,

there are Brightness axis and principal component one
that can be obtained by Principal Component Analysis(PCA) in the RGB three-dimensional vector space thatis an attribute space of color image. Especially, we
explain the main principle of the proposed method in
the case of using HMGD (Histogram Matching based on
Gaussian Distribution).7 And we show that a curvaturecomputation for the cumulative histogram of original
image will be effective, in order to automatically detect
whether the original image has single peak histogram ornot. Then, we illustrate that the method using the
HMGD works very well for input image that has single
peak histogram on the Brightness axis.

Published by Atlantis Press
Copyright: the authors
60

Yusuke Kawakami, Tetsuo Hattori, Yoshiro Imai, Haruna Matsushita, Hiromichi Kawano, R.P.C. Janaka Rajapakse

Also, we illustrate that the results of improved HMGD
which applies peak detection works better than present
HMGD, which is HPA-HMGD (Histogram Peakedness
Adaptive HMGD).
2. Elastic Transform
Matching

based

on

Histogram ( x)  L  f ( x)dx

(6)0

Since ’(x) = L(x), according to Eq. (5), we derivefollowing Eq. (7).

f ( x)  g ( y ) Lf ( x)2.1. Principle
We describe the principle of histogram based elastictransform in the following. Let f(x) and f(y) be two
probabilistic density functions on real variables x and y,
respectively. The probabilistic density function (PDF) iscorresponding to histogram of gray level image.
However, the histogram is defined on discrete variable.
In addition, let y=(x) be a continuous and monotonous
increase function between variables x and y as shown in
Fig.1.7
In addition, let value of x be the range from 0 to L.
Accordingly, variable y ranges from 0 to (L). Let P
mean the probability. From the above definitions andFig.1, we have Eq. (1) ~ (3).
xL

P(0  x  L)   f ( x)dx  1

x(7)

Therefore, we understand that if we take the transformfunction as Eq. (6), g(y) becomes uniform distribution.
It corresponds to the HE processing, which means thatfunction defined by cumulative histogram transforms
the original histogram into the uniform one.
Inversely, if we define the transform function (x) as anintegral of desired PDF f(x) for example, Gaussian
distribution, we can obtain the desired PDF using the(x) and the uniform distribution such as Fig.2.7
The abovementioned theory means that, if we combine
the both transform, we can obtain the transformationfrom an original distribution (PDF) to a desired one.
This means that an image with original histogram canbe transformed into another image with desired
histogram. We consider that it is the principle of theHistogram Matching (HM).4

(1)

x 0

P(0  y   ( L)) yy  ( L ) g ( y)dy  1(2)

y   (x)

 (L)

y 0

f ( x)dxg ( y)

 P( x0  x  x0  dx)y(3)

 P( ( x0 )  y   ( x0  dx)) ( x0 ) P( y0  y  y0  dy )  g ( y )dy0

From Eq. (3), we obtain Eq. (4) and (5) because y0=f(x0)and y0 + dx = (x0 + dx).

f ( x)dx  g ( y )dy  g ( y ) ' ( x)dx
f ( x)  g ( y ) ' ( x)

(x0 dx)

x

(4)

L

x

x0 dx

x0

f(x)

(5)

Thus, if we know the y=(x) and g(y), then we have thef(x). Using the above equations, we derive the principleof HE. Let (x) be defined by Eq. (6).

Fig. 1. Continuous and monotonous increase function y=(x)and probabilistic density functions f(x) and g(y).7

Published by Atlantis Press
Copyright: the authors
61

Kansei Impression and Automatedyy   (x)

 ( L)g(y)(x0 dx)(a) Originaly ( x0 )1/ L(b) Brightness Axis(c) PC axis

Fig. 4. Examples of HE on Brightness and PC axis.7

0

x
x0

L

x

x0 dxf(x)(a) Original

Fig. 2. Conceptual image of the transform from uniform
distribution (PDF) to the desired one.7(b) HE(c) HMGD

Fig. 5. Examples of the results by HE and HMGD.7

2.3. Detection of Histogram Peakedness by using
Curvature Computation

2.2. Elastic Transform on Axis
We can choose the abovementioned transform such as
HE (Histogram Equalization) and HM (Histogram
Matching) on arbitrary axis (for example, principal
component axis) in the color attribute (RGB) space asshown in Fig.3.7 For example, in the case where the HE
processing on the Brightness axis is applied, the HE
brings about image enhancement by contrast stretching.
In addition, in the case of HE on a principal component
axis in RGB space, we guess that the contrast stretching
will be done along to a certain tone of color.
Fig.4 shows examples of the HE on Brightness axis and
PC (Principal Component) axis.7 Fig.5 shows resultant
examples of the HE and HMGD (Histogram Matchingbased on Gaussian Distribution) on Brightness axis.7
The HMGD processing shows a more moderate effectthan HE. In this paper, we show that the HMGD isuseful for the automated color image arrangement.

In this section, we describe how we detect the histogram
peakedness by using curvature. Let y be a function withrespect to x, the definition of the curvature R is given by
Eq. (8).

 
d2y

R

dx 2

1    
dy 2
dx

(8)

3
2

Let g(x) be a Gauss density function with variance 2
and average a. And also let g(x) be representing ahistogram of input image whose pixel values from 0 to
L. That is,( xa )2

K2g ( x) 
・e 2
 2

(9)

In Eq. (9), K means a coefficient that satisfies following
Eq. (10).
(u a )2L 
K2e 2 du  1

0
 2

(10)

Let y=f(x) be a function representing the cumulative
histogram. Then f(x) can be represented Eq. (11).
Fig. 3. Conceptual image of histogram based elastic transformon arbitrary axis in RGB space.7-9(u a )2x K2f ( x)   g (u )du 
e 2 du (11)

0
0
 2

Published by Atlantis Press
Copyright: the authors
62xYusuke Kawakami, Tetsuo Hattori, Yoshiro Imai, Haruna Matsushita, Hiromichi Kawano, R.P.C. Janaka Rajapakse

Since y  f  x  

 g u du , g(x) can be described asx0

Eq. (12).
( xa )2

dyK2
 g ( x) 
・e 2
dx
 2

(12)

By the same way,

2.4. Improvement of HMGD

d 2 y dg ( x)
K
・e


dx 2
dx
 2

( xa )2

2 2

 1 
・  2 2( x  a ) 2 

( x a )  K2 x  a   a  x  ・e 2 ・ )  g ( x・22
  2



  


2

(13)

Hence, we obtain the following Eq. (14) and we canapproximate to Eq. (8).

RThe real curvature computation is performed on thediscrete values. We can find that there are largely
changing points in the curvature from plus value tominus value at more than one point. So, we easily
understand that the histogram of the original image is
not a single peak type.

a  x  g ( x)21  g ( x) 

3
2 2



a  x  g x 

(14)

2

The curvature R varies the sign according to the value ofx; (x < a) R > 0, (x = a) R = 0, (x > a) R < 0. So we
consider that a histogram with single peak shows thesame characteristic regarding the curvature R of the
cumulative histogram.
Fig.6 shows an example of the curvature computation.7

In the previous section, we described how we detect
histogram peakedness by using curvature computation.
Therefore, we consider that the HMGD will work better
if the peakedness of the original image histogram is fit
the peakedness of HMGD-reference histogram.
The definition of the approximation of curvature R isgiven by Eq. (14) as shown in the previous section.
From Eq. (14), we can find the peakedness brightness
values of the original image.
Let Pb be a peakedness brightness value of the image
which have single peak histogram. From Eq. (9) and(10), we can derive the reference Gaussian distributionfunction gr(x) that the average a correspond to Pb, asshown in Eq. (15).
( x P )2bK2g r ( x) 
・e 2
 2

(15)

In above equation, K means a coefficient that satisfies
Eq. (16).
(u  P )2

b
L 
K
2 2
e
du  1 2 0(16)

Fig.7 shows an example of the HPA-HMGD (Histogram
Peakedness Adaptive Histogram Matching based on
Gaussian Distribution). The HPA-HMGD processing
shows a better result than HMGD.

400

1000

200
Curvature

600

1200

800
600

0
-200
-400

400
-600

200

-800

Pixel Value(b) Histogram of image

-1000
1
17
33
49
65
81
97
113
129
145
161
177
193
209
225
241

0
1
17
33
49
65
81
97
113
129
145
161
177
193
209
225
241

Cumulative Frequency(a) Original image
1400

Pixel Value(c) Curvature of image

Fig. 6. Example of the curvature computation.7, 10(a) Original(b) HMGD(c) HPA-HMGD

Fig. 7. Examples of HMGD and HPA-HMGD

Published by Atlantis Press
Copyright: the authors
63

Kansei Impression and AutomatedFig.8 (a), (b) shows an example of results by HMGD
processing on Brightness axis, where original image has
almost single peak histogram. The set of histogram andcumulative histogram (original image and HMGD
image) are shown in Fig.9(a), (b). And the curvature of
cumulative histogram of input image is shown as well in
Fig.9(c).7 From Fig.9 (b), we understand that the
cumulative histogram of HMGD image clearly
approaches to Gaussian distribution.

1000

65536

900

57344

800

Cumulative Frequency

3.1. HMGD

Similarly, Fig.10 (a), (b) shows another example ofresults by HMGD processing, where original image has
almost single peak histogram.7, 9, 10 For these cases
where the histogram of input image has almost single
peak, the HMGD works very well for resulting a goodfeeling impression (or Kansei effect).

700

Frequency

3. Experimentation

600
500
400
300
200

49152
40960
32768
24576
16384

0
1
25
49
73
97
121
145
169
193
217
241

8192

0

1
23
45
67
89
111
133
155
177
199
221
243

100

Lightness

Lightness(a) Histogram (left) and cumulative histogram (right) oforiginal image (Fig. 8(a))

1000

65536

900

57344
Cumulative Frequency

800

Frequency

700
600
500
400
300
200

40960
32768
24576
16384
8192

100

(a) Original image

49152

0

1
23
45
67
89
111
133
155
177
199
221
243

1
25
49
73
97
121
145
169
193
217
241

0
Lightness

Lightness(b) Histogram (left) and cumulative histogram (right) of
HMGD image (Fig. 8(b))

250
200

Curvature

150
100
50
0
‐50
‐100
1
10
19
28
37
46
55
64
73
82
91
100
109
118
127
136
145
154
163
172
181
190
199
208
217
226
235
244
253

‐150
Lightness(c) Curvature of cumulative histogram oforiginal image (Fig. 8(a)(b) HMGD image
Fig. 8. Example of the result by HMGD.7

Fig. 9. Histogram, cumulative histogram, and curvature of
Fig. 8.7

Published by Atlantis Press
Copyright: the authors
64

Yusuke Kawakami, Tetsuo Hattori, Yoshiro Imai, Haruna Matsushita, Hiromichi Kawano, R.P.C. Janaka Rajapakse

3.2. Comparison of HMGD and HPA-HMGD

Fig.11 (a) ~ (c) shows example of results of HMGD and
HPA-HMGD processing which the original image havemultiple peakedness histogram. The set of histogramand cumulative histogram (original image, HMGD
image and HPA-HMGD image) are shown in Fig.12 (a)~ (c). And the curvature of cumulative histogram of
input image is shown as well in Fig.12 (d).
From Fig.11, we consider that the result of HPAHMGD processing image (Fig.11 (c)) is better than the
result of HMGD processing image (Fig.11 (b)).
Especially, tone of color of Fig.11 (c) is the most natural.

(a) Original image(a) Original image(b) HMGD image(b) HMGD image(c) HPA-HMGD image
7, 9, 10

Fig. 10. Example of the result by HMGD.

Fig. 11. Example of the results by HMGD and HPA-HMGD.

Published by Atlantis Press
Copyright: the authors
65

Kansei Impression and Automated

65536

3500

57344
Cumulative Frequency

4000

Frequency

3000
2500
2000
1500
1000

49152
40960
32768
24576
16384

0
1
25
49
73
97
121
145
169
193
217
241

8192

0
1
23
45
67
89
111
133
155
177
199
221
243

500

Lightness

Lightness(a) Histogram (left) and cumulative histogram (right) oforiginal image (Fig. 11(a))
65536

3500

57344
Cumulative Frequency

4000

Frequency

3000
2500
2000
1500
1000

49152

(a) Original image8-10

40960
32768
24576
16384

0
1
25
49
73
97
121
145
169
193
217
241

8192

0
1
23
45
67
89
111
133
155
177
199
221
243

500

Lightness

Lightness(b) Histogram (left) and cumulative histogram (right) of
HMGD image (Fig. 11(b))
65536

3500

57344
Cumulative Frequency

4000

Frequency

3000
2500
2000
1500
1000

49152
40960
32768
24576
16384

0
1
25
49
73
97
121
145
169
193
217
241

8192

0
1
23
45
67
89
111
133
155
177
199
221
243

500

Lightness

Lightness(b) HMGD image8-10(c) Histogram (left) and cumulative histogram (right) of
HPA-HMGD image (Fig. 11(c))
1500

Curvature

1000
500
0
-500
-1000

1
10
19
28
37
46
55
64
73
82
91
100
109
118
127
136
145
154
163
172
181
190
199
208
217
226
235
244
253

-1500

Lightness(d) Curvature of cumulative histogram of original image (Fig.
11 (a))
Fig. 12. Histogram, cumulative histogram, and curvature of
Fig. 11.

(c) HPA-HMGD image
Fig. 13. Example of the results by HMGD and HPA-HMGD.

Published by Atlantis Press
Copyright: the authors
66

Yusuke Kawakami, Tetsuo Hattori, Yoshiro Imai, Haruna Matsushita, Hiromichi Kawano, R.P.C. Janaka Rajapakse

Fig.13 (a) ~ (c) shows example of results of HMGD and
HPA-HMGD processing which the original image has
single peakedness histogram.
From Fig.13, we understand that the result of HMGD
processing image (Fig.13 (b)) is brighter than HPAHMGD processing image (Fig.13 (c)). And, we have totake into account that the tone of HPA-HMGD image(Fig.13 (c)) is close to original image.
In these cases HPA-HMGD have a good feeling
impression (or Kansei effect) than HMGD. And we
found that HPA-HMGD is corrected image into natural
tones than HMGD.
4. Conclusion

Aiming at automated affective color image arrangement,
we have proposed a concept of Elastic Transform (ET)method based on histogram and/or histogram matching,which can be applied to some kinds of axis such as
Brightness axis. And we have suggested that HMGD(Histogram Matching based on Gaussian Distribution) is
regarded as one of the ET method.
As for the concrete method for automated color image
arrangement, we have proposed a method that applies
HMGD processing to input image after detecting
whether the input image has single peak histogram ornot. In this paper, we have also provided the curvaturecomputation for the peak detection in histogram. And
also we have shown some experimental results.
Furthermore, we suggested the HPA-HMGD as the
improvement of HMGD. Through some experimental,
we understand that the tone of HPA-HMGD image ismore natural than the tone of HMGD image. We
consider that HPA-HMGD processing method will be
useful and promising than HMGD.

References
1. C. R. Gonzalez and E. R. Woods, Digital Image
Processing (Addison-Wesley Publishing Company,
1993).
2. B. Jahne, Digital Image Processing --Concepts,
Algorithms, and Scientific Applications--, 4th edn.
(Springer, 1995).
3. E. S. Umbaugh, Computer Vision and Image Processing:
A Practical Approach Using CVIPtools (Prentice Hall
PTR, 1998).
4. W. Burger and J. M. Burge, Principles of Digital Image
Processing: Fundamental Techniques (Springer, 2009).
5. T. Izumi, T. Hattori, S. Sugimono and T. Takashima,
Color Image Arrangement Using Elastic Transform on
Principal Component Axis (in Japanese), Journal ofJapan Society of Kansei Engineering, 8(3) (2009) 667674.
6. T. Izumi, T. Hattori, E. Fujita, S. Sugimono and H.
Kawano,Feeling
Impression
andQuantities
Accompanying Calculation of Fluctuation in Color Image(in Japanese), Journal of Japan Society of Kansei
Engineering, 9(2) (2010) 243-250.
7. Y. Kawakami, T. Hattori, Y. Imai, H. Matsushita, H.
Kawano, R. P. C. J. Rajapakse, Automated Color Image
Arrangement Method andKansei Impression, inProceedings of International Conference on Artificial
Life and Robotics 2014 (Oita, 2014), ISBN978-49902880-8-2, pp. 260-263.
8. Y. Kawakami, T. Hattori, D. Kutsuna, H. Matsushita, Y.
Imai, H. Kawano and R. P. C. J. Rajapakse, An
Automated Color Image Arrangement Method Based on
Histogram Matching, in Proceedings of 2013
International Conference on Biometrics and Kansei
Engineering (CD) (Akihabara, Tokyo, 2013), ISBN9780-7695-5019-0, pp. 31-34.
9. Y. Kawakami, T. Hattori, D. Kutsuna, H. Matsushita, Y.
Imai, H. Kawano, R. P. C. J. Rajapakse, Arrangement
Effect of Histogram Matching for Image and Sound
Signal, in Proceedings of International Conference on
Humanized Systems 2013 (CD) (Takamatsu, Kagawa,2013), ISBN978-4-9905392-1-4, pp. 87-91.
10. D. Kutsuna, T. Hattori, Y. Kawakami, H. Matsushita, Y.
Imai, T. Izumi, Color image arrangement by elastictransform based on histogram matching, in Proceedingsof 18th International Symposium on Artificial Life andRobotics (CD) (Yuseong, Daejeon, 2013)，ISBN978-49902880-7-5, pp. 280-283.

Published by Atlantis Press
Copyright: the authors
67