Proceedings of International Joint Conference on Neural Networks, Atlanta, Georgia, USA, June 14-19, 2009

Applications of Color Image Processing Using
Three-Layer Cellular Neural Network Considering HSB Model
Takashi Inoue and Yoshifumi Nishio

Abstract— In this study, we propose a three-layer cellularneural network dealing with color images considering the HSB
model. Firstly, the conversion method of color images to threegrayscale images using the HSB model is explained. Secondly,
the structure of the proposed three-layer cellular neural network considering the HSB model is explained. Simulation
results of some color image processing show the basic propertiesof the proposed network and its effectiveness.

I. I NTRODUCTIONCELLULAR Neural Networks (CNN) [1] were introduced by Chua and Yang in 1988. The idea of the CNN
was inspired from the architecture of the cellular automata
and the neural networks. Unlike the conventional neuralnetworks, the CNN has local connectivity property. Since
the structure of the CNN resembles the structure of animals’
retina, the CNN can be used for various image processing
application [2]-[4] including character extractions [5][6].
Further, the CNN can be utilized to produce some kinds ofpattern generation [7][8] and the texture segmentation [9].
The humans retina have an ability distinguishing colors
and consist of three types of cells called “cone” responding
to the three primary colors and a cell called “rod” responding
to the amount of light. The humans can recognize colors by
the function of the cone cells. Roska et al. have proposed
a concept using a three-layer CNN processing the three
primary colors in [10]. They have confirmed that the threelayer CNN could produce half-toned images of color images.
However, after their pioneering work, there have not been
many researches on the CNN dealing with color images
effectively.
In the previous study, we have proposed the three-layer
cellular neural networks considering three primary colors(RGB-CNN) [11]. Before the processing, a color image isdivided into three primary colors and they are converted tothree grayscale images using RGB model. This preprocess
corresponds to the function of the cone cells of the retina.
These three images are inputted to the three-layer cellularneural networks. In our RGB-CNN, the connections between
the three layers play an important role. Namely, the threelayers do not operate independently but all the outputs influence to the other layers. By using RGB-CNN, we obtained
the effective edge detection results and interesting output
characteristics. However, we think that the RGB-CNN isdifferent from the perception of human. In the RGB model,
the blue-element value of yellow is zero. However, when

Department of Electrical and Electronic Engineering, Tokushima University, 2-1 Minami-Josanjima, Tokushima 770-8506, Japan (email: {takashi,
nishio}@ee.tokushima-u.ac.jp).

978-1-4244-3553-1/09/$25.00 ©2009 IEEE

human recognize the color of yellow, the blue-element may
have some amount of value. Additionally, the color of whitein RGB model has the value of (R: 255, G: 255, B: 255). On
the flip side, the pure colors of R, G and B have values of(R: 255, G: 0, B: 0), (R: 0, G: 255, B: 0) and (R: 0, G: 0, B:
255), respectively. Namely, we can not distinct white fromred by using only the red-element value in the RGB model.
The color image processing using CNN imitating the humans
recognition method of color may have more powerful color
image processing applications.
In this study, we concentrate on the HSB model inconversion from color image to grayscale image. The HSB
model comprises three components of “Hue”, “Saturation”
and “Brightness”. The color in the RGB model is defined by
combination of three primary colors. On the other hand, theprinciple of the HSB model is similar to the perception ofhuman, and human recognize color as “What is a color ?”, “How much is vibrant ?”, “ How much is bright ?”. Namely,
the CNN considering the HSB model (HSB-CNN) may be
more similar to the processing of human than the CNN
considering the RGB model. We carry our some examples ofcolor image processing using the proposed HSB-CNN andconfirm its basic properties and the effectiveness.
In the Sec. 2, we review the basic of the standard CNN. In
the Sec. 3, we show the conversion method of color images
using the HSB model and the structure of the proposed HSBCNN. In the Sec. 4, simulation results of some color image
processing are shown. Section 5 concludes the article.

II. C ELLULAR NEURAL NETWORKS [1]In this section, we describe the basic structure of the
CNN. The CNN has M by N processing unit circuits
called cells. Cells are arranged in a reticular pattern to M
line N row. We represent a cell C(i, j) using a variable
i which denotes vertical position and a variable j which
denotes horizontal position. The cell contains linear andnonlinear circuit elements. The CNN is an array of cells.
Each cell is connected to its neighboring cells according toa template. Usually, the template is the same for all cells
except for boundary cells. The CNN has the features oftime continuity, spatial discreteness, nonlinearity and parallel
processing capability.
The state equation and the output equation of the cell are
shown as follows.

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State equation:
dvxij
dt

2) Saturation:

=

i+r


−vxij +j+r
S(i, j) (0 ≤ S ≤ 1.0).

A(i,j;k,l) vykl (t)k=i−r l=j−r
i+r


j+r


B(i,j;k,l) vukl (t) + I(1)1(|vxij (t) + 1| − |vxij (t) − 1|)
2

(2)

+

k=i−r l=j−r(5)

The Saturation S is shown by a positive value between 0.0
and 1.0. Figure 2 shows the aspect of the saturation. Whenthe value of S is near 1.0, color looks a pure color, whilenear 0.0, color looks a muddy color.

Output equation:vyij (t) =where vx , vy and vu represent a state, an output and an inputof cell, respectively. In the equation (1), A is the feedback
template and B is the control template. These and bias I arecollectively called general template.
The r − neighborhood of the cell C(i, j) in the CNN isdefined by
N r(i, j) = {C(k, l) | max { |k − i| , |l − j| } ≤ r,
1 ≤ k ≤ M;

1 ≤ l ≤ N}

Fig. 2.

Saturation.

(3)

where r is a positive integer number. In our study, we fix thevalue of r as 1.
III. P ROPOSED COLOR IMAGE PROCESSING METHOD(HSB-CNN)
In the original CNN, color images are converted tograyscale images before the processing. The grayscale images do not have color information. Therefore, the conventional CNN is impossible to consider color information. The
proposed HSB-CNN is a three-layer CNN considering HSB
model.

3) Brightness:
B(i, j) (0 ≤ B ≤ 1.0).

(6)

The Brightness B is shown by a positive value between 0.0
and 1.0. Figure 3 shows the aspect of the brightness. Whenthe value of B is near 1.0, color becomes bright, while near
0.0, color becomes dark.

Fig. 3.

Brightness.

A. HSB Model
The HSB model comprises of the three components “Hue”,“Saturation” and “Brightness”.
1) Hue:In the HSB model, any colors are represented by thesethree values H, S and B.

H(i, j) (0◦ ≤ H ≤ 360◦ ).

B. Conversion method from a color image to grayscale
images(4)

The Hue H is shown by a degree between 0◦ and 360◦ .
Figure 1 shows the hue circle in the HSB model. In thehue circle, the three primary colors red, green and blue arerepresented by 0◦ (= 360◦), 120◦ and 240◦, respectively.

In this subsection, we describe the conversion method
using HSB model from a color image to grayscale images.
First, we consider the conversion from a color image tograyscale images corresponding to the hue value. Because agrayscale image cannot be represented by a value of degree,
the hue value needs to be converted from degree to a realvalue in a certain interval. Further, the hue value is divided
into three components corresponding to the three primarycolors, in order to make it easy to process color images. The
conversion equations of the hue are shown as follows.
Conversion Equation of Hue:
Hue for Red:HR (i, j) = cos(H(i, j)◦ )Fig. 1.

Hue circle.

(−1.0≤HR ≤1.0).

(7)

HG (i, j) = cos(H(i, j)◦ + 120◦ ) (−1.0≤HG ≤1.0).

(8)

Hue for Green:

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Hue for Blue:
HB (i, j) = cos(H(i, j)◦ + 240◦ ) (−1.0≤HB ≤1.0).

(9)Note that we use the cosine function in Eqs. (7), (8) and (9)in order to extract the three-color components. This means
that, for example, even ”green” color includes some ”red”
component.
Second, we combine the three values of H, S and B. The
combination equations are shown as follows.
Combination Equation for Red:GR (i, j) =+HR (i, j) × 0.6((S(i, j) − 0.5) × 2) × 0.2+((B(i, j) − 0.5) × 2) × 0.2.
(−1.0 ≤ GR ≤ 1.0).

(a)

(b)

(c)

(d)

(10)

Combination Equation for Green:
GG (i, j) = HG (i, j) × 0.6+ ((S(i, j) − 0.5) × 2) × 0.2+ ((B(i, j) − 0.5) × 2) × 0.2.
(−1.0 ≤ GG ≤ 1.0).

(11)

Fig. 4. Example of conversion to grayscale images using RGB model.
(a) Color input image. (b) Grayscale image for red. (c) Grayscale image forgreen. (d) Grayscale image for blue.

Combination Equation for Blue:GB (i, j)= HB (i, j) × 0.6+ ((S(i, j) − 0.5) × 2) × 0.2+ ((B(i, j) − 0.5) × 2) × 0.2.
(−1.0 ≤ GB ≤ 1.0).

(12)After the combination in Eqs. (10), (11) and (12), GR , GG
and GB become the values of the cells in three grayscale
images. The S and B have values between 0.0 and 1.0.
However, the value of grayscale images and the hue value
after the conversion are between −1.0 and 1.0. Therefore,
we need to convert the values of S and B to values between−1.0 and 1.0. Additionally, the values of H, S and B should
be weighted before the combination. Because we consider
some image processing in which the difference of colors isimportant, we consider that H is most important and that theweight of H should be larger than the other two.
1) Example of conversion to grayscale images: Figure 4
shows an example of the conversion of a color image to threegrayscale images using the conventional RGB model. In thisconversion, a color value is divided into three primary colors(red, green and blue) and they are represented by grayscale
images.
In Figs. 4(b), (c) and (d), we can see that the threegrayscale images are similar except only very pure colors(e.g. red bridge handrails). This is because the RGB model
does not consider the effect of the brightness and hencecolors with similar brightness give similar values to the threecomponents.
Figure 5 shows an example of the conversion of the samecolor image to three grayscale images using the proposed
HSB model Eqs. (4)-(12). In Figs. 5(b), (c) and (d), we cansee large difference of the grayscale images. Namely, redparts (bridge handrails) have large values in Fig. 5(b), green
parts (trees) have large values in Fig. 5(c), and blue parts(sky) have large values in Fig. 5(d). We can say that theconversion using the HSB model is more effective than the
RGB model in color image processing.
C. Structure of Three-Layer CNN (HSB-CNN)
In this subsection, we describe the structure of a threelayer CNN processing the three grayscale images prepared by
the proposed HSB model, called HSB-CNN. Figure 6 shows
the structure of the proposed HSB-CNN. The HSB-CNN
consists of three single-layer CNNs. Each layer is coupled toanother layer with the connection template (CR , CG , CB ).
Because of these connection templates, the red layer has adirect influence to the green layer. Also, the green layer has
a direct influence to the blue layer, and the blue to the red.
We can say that all layers have mutual influences each other.
The dynamical system equations associated with the HSBCNN are described by the following equations:(1) Three first-order differential equations:
dvxR,ijdti+r
= −vxR,ij +j+r

AR(i,j;k,l) vyR,kl (t)k=i−r l=j−r

+

i+r


j+r


BR(i,j;k,l) vuR,kl (t)k=i−r l=j−r

+

i+r


j+r


CB(i,j;k,l) vyB,kl (t) + IR(13)

k=i−r l=j−r

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dvxB,ijdti+r= −vxB,ij +j+r

AB(i,j;k,l) vyB,kl (t)k=i−r l=j−r

+

i+r


j+r


BB(i,j;k,l) vuB,kl (t)k=i−r l=j−r

+
(a)

i+r


j+r


CG(i,j;k,l) vyG,kl (t) + IB(15)

k=i−r l=j−r(b)(2) Three output equations:
vyR,ij (t) =1(|vxR,ij (t) + 1| − |vxR,ij (t) − 1|) (16)2vyG,ij (t) =1(|vxG,ij (t) + 1| − |vxG,ij (t) − 1|) (17)21(|vxB,ij (t) + 1| − |vxB,ij (t) − 1|) (18)2where vx , vy , and vu represent a state, an output and an inputof cell, respectively. In the equations (13), (14) and (15), C
are the connection templates introduced to couple the threelayers.
Figure 7 shows the processing of the HSB-CNN. Before the processing, a color image is converted into threegrayscale images using the proposed HSB model Eqs. (4)(12). These three images are inputted to the HSB-CNN asvuR , vuG , and vuB . Finally, we can obtain three possible
output images from the HSB-CNN.
vyB,ij (t) =

(c)

(d)

Fig. 5. Example of conversion to grayscale images using HSB model.
(a) Color input image. (b) Grayscale image for red. (c) Grayscale image forgreen. (d) Grayscale image for blue.

Fig. 6.

Structure of HSB-CNN.
Fig. 7.

Processing of HSB-CNN.

IV. S IMULATION RESULTS
dvxG,ijdti+r
= −vxG,ij +j+r

AG(i,j;k,l) vyG,kl (t)k=i−r l=j−r

+

i+r


j+r


A. Task 1: Color binarization

BG(i,j;k,l) vuG,kl (t)k=i−r l=j−r

+

i+r


j+r


k=i−r l=j−r

CR(i,j;k,l) vyR,kl (t) + IG

In this section, we show the applications of color image
processing using HSB-CNN by computer simulation. All theoriginal templates in this section are found in [12].

(14)First, we consider the task of color binarization, namely acolor image is converted to a binary image as follows. Only
colors near pure red, pure green or pure blue are extracted
as a black pixels.

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We use the following template from the template library [12].
Grayscale to Binary Threshold Template:
⎤
⎤
⎡
⎡
0 0 0
0 0 0
(19)
A = ⎣ 0 2 0 ⎦ , B = ⎣ 0 0 0 ⎦ , I.
0 0 0
0 0 0
In the original CNN, by using this template, grayscale images
can be converted to binary images according to the thresholdvalue which is given as the value of I.
Color Binarization Template of HSB-CNN:
Template of Red layer: Template (19).
Template of Green layer : Template (19).
Template of Blue layer : Template (19).
Coupling template:⎡

0 0
CR = ⎣ 0 b
0 0⎡0
CG = ⎣ 00⎡0
CB = ⎣ 0
0

⎤
0
0 ⎦
0

⎤
0 0
b 0 ⎦
0 0
⎤
0 0
b 0 ⎦
0 0







b=4
b=0

if vyR,ij ≥ 0.9
otherwiseb=4
b=0

if vyG,ij ≥ 0.9
otherwiseb=4
b=0

if vyB,ij ≥ 0.9
otherwise

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(20)
Remark: The HSB-CNN usually gives three different output
images from the three layers. However, in this task, only one
output image is needed. Therefore, we apply threshold typefunction to the coupling templates in HSB-CNN. By using
this threshold type of template (20), output images of alllayers in HSB-CNN become the same.
Figure 8 shows the simulation results of color binarizationof “mandrill” image using template (20) in HSB-CNN. In
this simulation, we change the threshold value of I in thetemplates of the three layers. From these results, we cansee that the regions near pure colors of red, green and blue
remain in the output and the area is changed according to
the threshold value. Namely, we can say that the conversion
from grayscale images to binary images is expanded to color
images using the proposed HSB-CNN.
B. Task 2: Color edge detection
Secondly, we consider the task of color edge detection,
namely edges of a three primary colors are extracted.
We use the following template from the template library [12].
Edge detection :⎤⎤⎡⎡−1 −1 −10 0 0
−1 ⎦ , I = −1.
A = ⎣ 0 1 0 ⎦ , B = ⎣ −1 8
−1 −1 −1
0 0 0
(21)

Fig. 8. Task 1 (mandrill): Color binarization using template (20) in HSBCNN. (a) Input color image. (b) Output image for I = −0.3. (c) I = −0.4.
(d) I = −0.5. (e) I = −0.6. (f) I = −0.7. (g) I = −0.8. (h) I = −0.9.

The “Edge Detection” template can detect the edges of binary
images in the original CNN.
In this simulation, we set the template (19) or the template(21) to each layer. For example, we set the template (19) as
the template of red, and the template (21) as the templatesof green and blue layers. The threshold value of “Grayscale
to Binary Threshold” template (template (19)) is set as1339

I = −0.4. By the above template setting, we expect that theregion near pure red in color input image becomes black,and the edges of color input image can be detected at thesame time.
Color Edge Detection Template of HSB-CNN:
Template of Red layer: Template (19) or (21).
Template of Green layer : Template (19) or (21).
Template of Blue layer : Template (19) or (21).
Coupling template:⎡0
CR = ⎣ a0⎡0
CG = ⎣ a0⎡0
CB = ⎣ a
0

a
b
a

⎤

0
a = 1, b = 4 if vyR,ij ≥ 0.9
⎦
a
a=b=0
otherwise
0

a
b
a

⎤

0
a = 1, b = 4 if vyG,ij ≥ 0.9
⎦
a
a=b=0
otherwise
0

⎤

a 0
a = 1, b = 4 if vyB,ij ≥ 0.9
b a ⎦
a=b=0
otherwisea 0(22)

Remark: In general, edge detection results include somespot noises. In order to solve this problem, we add the noise
removal effect to the coupling templates.
Figure 9 shows the simulation results of color edge detection of “bridge” image using template (22) in HSB-CNN. In
this simulation, we set the “Grayscale to Binary Threshold”
template to the red layer, and “Edge Detection” template to
the green and the blue layers. In Fig. 9, we can see that theoutput images of all layers are slightly different. In Figs. 9(c)and (d), the region of “road” have some noise. However, by
the noise removal effect of the coupling templates, the output
image of the red layer Fig. 9(a) has few noise. From theseresults, we can say that the output image from the layer with
“Grayscale to Binary Threshold” template in HSB-CNN has
few noise and becomes the optimal output image in edge
detection.
Figure 10 shows the effect of changing the layer with
“Grayscale to Binary Threshold” template. Namely, we set
that the one of three layers has “Grayscale to Binary Threshold” template and the other two layers have “Edge Detection”
template. Figure 10(b) shows the simulation result when the
red layer has “Grayscale to Binary Threshold” template.
Hence, the result is the same as Fig. 9(b). Figures 10(c)and (d) show the simulation results when the green and theblue layers have “Grayscale to Binary Threshold” template,respectively. We can see that green region and blue region
can be detected respectively and the edges of color input
image can be detected. Also, output images have few noises
by the noise removal effect of the coupling templates.
Figure 11 shows the simulation results for another color
image “Venice”. We can confirm that the regions of red,

(a)

(b)

(c)

(d)

Fig. 9. Task 2a (bridge): Color edge detection using template (22) in HSBCNN. (a) Input color image. (b) Output image of red layer (“Grayscale
to Binary Threshold” template). (c) Output image of green layer (“Edge
Detection” template). (d) Output image of blue layer (“Edge Detection”
template).

green and blue can be successfully detected and edges ofcolor input image can be detected in all output images.
C. Task 3: Color parts extraction
In this subsection, we apply the results in the previous
subsections (Task 1: Color binarization or Task 2: Coloredge detection) to extract the color parts. Some images
may have regions as sky, sea, forest, human, building andso on, and one may need to extract only these specificregions. Regardless of the purposes, extracting some regionsof images is one of the most important tasks in image processing. When human recognize some regions, informationsof texture, color and perspective of objects are considered.
In these information, color is easier to recognize than otherinformation. For example, we consider the region of sea as
blue region instead of wave pattern, the region of forest is
green instead of the shape of a tree.
Figures 12 and 13 show the simulation results obtained
from the results of Figs. 10 and 11 (Task 2: Color edge
detection). For example, Fig. 12(b) is the image extracted
from the original input image Fig. 10(a) such that only the
pixels corresponding to the black pixels in Fig. 10(b). As aresult, Fig. 12(b) includes only the red part “bridge handrails”
and all the edges of the input image. Similarly, Figs. 12(c)and 12(d) include the green part “forest” and the blue part“sky” with all the edges, respectively.
Next, Fig. 14 shows the simulation results obtained fromthe results of Fig. 8 (Task 1: Color binarization). In this

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(a)

(b)

(a)

(b)

(c)

(d)

(c)

(d)

Fig. 10. Task 2b (bridge): Color edge detection with different templatecombinations. (a) Input color image. (b) Output image (red layer: template(19), green and blue layers: template (21)). (c) Output image (green layer:
template (19), red and blue layers: template (21)). (d) Output image (bluelayer: template (19), red and green layers: template (21)).

Fig. 11. Task 2b (Venice): Color edge detection with different templatecombinations. (a) Input color image. (b) Output image (red layer: template(19), green and blue layers: template (21)). (b) Output image (green layer:
template (19), red and blue layers: template (21)). (b) Output image (bluelayer: template (19), red and green layers: template (21)).

simulation, because we use the results of Fig. 8, the results
include parts near three pure colors. Also, only small regions
very close to pure colors remain when the threshold value issmall.

[3] M. Namba and Z. Zhang, “Cellular Neural Network for Associative
Memory and Its Application to Braille Image Recognition,” Proc. of
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and its Application,” Proc. of NOLTA’07, pp. 15-18, Sep. 2007.
[5] T. Kozek, K.R. Crounse, T. Roska and L.O. Chua, “Smart Image
Scanning Algorithms for the CNN Universal Machine,” Proc. of
NOLTA’95, vol. 2, pp. 707-712, 1995.
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V. C ONCLUSIONSIn this study, we have proposed a three-layer CNN dealing
with color images considering the HSB model. The principleof the HSB model is similar to the perception of human. We
realize the CNN with the structure similar to the human’srecognition method by considering the HSB model. By
computer simulation of some processing tasks for color
images, we have confirmed that the HSB-CNN is effective
for color image processing. Although this article reports only
some examples of applications, we consider that the HSBCNN can be available to various color image processing.
ACKNOWLEDGMENT

The authors would like to thank Prof. Kristina Kelberof University of Applied Sciences Dresden for her valuablecomments.
R EFERENCES[1] L.O. Chua and L. Yang, “Cellular Neural Networks:Theory,” IEEE
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[2] F. Dirk and T. Ronald, “Coding of Binary Image Data using Cellular
Neural Networks and Iterative Annealing,” Proc. of ECCTD’03, vol. 1,
pp. 229-232, Sep. 2003.

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(a)

(c)

(b)

(c)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(d)

Fig. 12. Task 3 (bridge): Color parts extraction from images in Fig. 10.
(a) Input color image. (b) Red color extraction using simulation result of
Fig. 10(b). (c) Green color extraction using simulation result of Fig. 10(c).
(d) blue color extraction using simulation result of Fig. 10(d).

(a)

(a)

(b)

(d)

Fig. 13. Task 3 (Venice): Color parts extraction from images in Fig. 11.
(a) Input color image. (b) Red color extraction using simulation result of
Fig. 11(b). (c) Green color extraction using simulation result of Fig. 11(c).
(d) Blue color extraction using simulation result of Fig. 11(d).

Fig. 14. Task 3 (mandrill): Color parts extraction from images in Fig. 8.
(a) Input color image. (b) Extraction result using simulation result of Fig.
8(b). (c) Extraction result using simulation result of Fig. 8(c). (d) Extraction
result using simulation result of Fig. 8(d). (e) Extraction result using
simulation result of Fig. 8(e). (f) Extraction result using simulation resultof Fig. 8(f). (g) Extraction result using simulation result of Fig. 8(g).
(h) Extraction result using simulation result of Fig. 8(h).

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