2011 20th European Conference on Circuit Theory and Design (ECCTD)

Four-Layer Cellular Neural Networks in
Consideration of Color and Luminosity
Yoshihiro Kato, Yasuhiro Ueda, Yoko Uwate and Yoshifumi Nishio
Department of Electrical and Electronic Engineering, Tokushima University,
2-1 Minami Josanjima, Tokushima 770-8506, Japan
Email: {kkato, yasuhiro, uwate, nishio}@ee.tokushima-u.ac.jp

Abstract—Human’s retina has the capability to identify colorand luminosity. The cell identifies color is called a cone celland identifies luminosity is called a rod cell. The color imageprocessing using CNN was proposed by Roska et al. Additionally,Inoue et al. have used three-layer CNN based on cone cell, andperformed edge enhancement. They have confirmed that edge
had been detected under three-layer CNN influencing each other.
However, the edge of a low luminosity portion is not detected.
In this study, we propose four-layer cellular neural networks
in consideration of three primary colors of light and luminosity,respectively. In this research, we show some edge detection results
and confirm that the proposed CNN is effective compared withthe conventional CNN and the existing CNN.

I. I NTRODUCTION
In recent years, our life teems with information by growth ofhigh information society. Generally, digital circuit is used formany information processing. However, digital circuit cannot
perform real time processing. Therefore, the neural networks
were devised based on the human’s nervous system. The
neural networks can design of analog circuit. Additionally,
the neural networks can perform expression of nonlinear
operating characteristics. Hence, the neural networks can express complicated processing easily. In fact, neural networks
are used in every direction, such as an associative memory,pattern recognition, image processing, and so on. Then in1988, Cellular Neural Networks (CNN) [1] were introducedby L. O. Chua and L. Yang. The idea of the CNN wasinspired from the architecture of the cellular automata andthe neural networks. A different point from the conventional
neural networks is that CNN has local connectivity property.
Since, the structure of CNN resembles that of animals’ retina.
Therefore, CNN can be used for various image processing
applications [2]-[5] including pattern formation [6].
Human’s retina has the capability to identify color andluminosity. The cell identifies color is called a cone cell. Conecell consists of cells which react to the three primary colorsof light which are red, green and blue, respectively. Conecell often functions in bright place. However, cone cell hardly
functions in dark place. On the other hand, the cell reacting
to luminosity is called a rod cell. Rod cell often functions indark place. However, rod cell cannot identify a color. The color
image processing using CNN was proposed by Roska et al [7].
Additionally, Inoue et al. have used three-layer CNN based oncone cell which processes the three primary colors of light (R,G, B), and performed edge enhancement in [8]. The three-layer

978-1-4577-0616-5/11/$26.00 ©2011 IEEE

CNN is called RGB-CNN. They have confirmed that edge had
been detected under three-layer CNN influencing each other.
However, the edge of a low luminosity portion is not detected.
In this study, we propose the four-layer cellular neuralnetworks considering cone cell and rod cell which process
the three primary colors of light and the luminosity (CRCNN: Cone and Rod CNN). Before the processing, a color
image is converted to four gray-scale images. They correspondto red value, green value, blue value and luminosity value,
respectively. This preprocessing corresponds to the functionof the cone and rod cells of the human’s retina. These fourgray-scale images are inputted to each layer in the proposedfour-layer CNN.
The rest of this paper is structured as follows. In Sec. II, we
propose the CR-CNN. In Sec. III, we show some simulation
results. The section IV concludes the article.

II. CR-CNN
A. Cellular Neural Networks
The CNN has 𝑀 by 𝑁 processing unit circuits calledcells. The cell contains linear and nonlinear circuit elements
which are typically linear capacitors, linear resistors, linear andnonlinear controlled sources. Cells are arranged in a reticularpattern to 𝑀 line 𝑁 row. We represent a cell 𝐶(𝑖, 𝑗) using
a variable 𝑖 which denotes vertical position and a variable 𝑗which denotes horizontal position. The CNN is an array ofcells. Each cell is connected to its neighboring cells according
to a template. Usually, the template is the same for all cells
except for boundary cells. The CNN has the features of time
continuity, spatial discreteness, nonlinearity and parallel processing capability. Additionally, the local connectivity property
makes the CNN tailor made for VLSI implementation.
B. Structure of the CR-CNN
In this subsection, we explain the structure of the CRCNN as shown in Fig. 1. The CR-CNN is constructed byfour single-layer CNNs. Each layer corresponds to the three
primary colors of light which are red, green and blue andluminosity, respectively. Each layer is combined by connection
template which are 𝐶𝑅 , 𝐶𝐺 , 𝐶𝐵 , 𝐶𝐿 , 𝐶𝐿𝑅 , 𝐶𝐿𝐺 and 𝐶𝐿𝐵 .
The state equation and the output equation of each layer areshown as follows.

874

𝑖+𝑟
∑

+𝑗+𝑟
∑

𝐶𝐺(𝑖,𝑗;𝑘,𝑙) 𝑣𝑦𝐺𝑘𝑙 (𝑡)𝑘=𝑖−𝑟 𝑙=𝑗−𝑟𝑖+𝑟
∑

+𝑗+𝑟
∑

𝐶𝐿(𝑖,𝑗;𝑘,𝑙) 𝑣𝑦𝐿𝑘𝑙 (𝑡) + 𝐼𝐵(3)

𝑘=𝑖−𝑟 𝑙=𝑗−𝑟State equation of luminosity-layer :𝑑𝑣𝑥𝐿𝑖𝑗𝑑𝑡=𝑖+𝑟∑−𝑣𝑥𝐿𝑖𝑗 +𝑗+𝑟∑

𝐴𝐿(𝑖,𝑗;𝑘,𝑙) 𝑣𝑦𝐿𝑘𝑙 (𝑡)𝑘=𝑖−𝑟 𝑙=𝑗−𝑟𝑖+𝑟
∑

+𝑗+𝑟
∑

𝐵𝐿(𝑖,𝑗;𝑘,𝑙) 𝑣𝑢𝐿𝑘𝑙 (𝑡)𝑘=𝑖−𝑟 𝑙=𝑗−𝑟𝑖+𝑟
∑

+𝑗+𝑟
∑

𝐶𝐿𝑅(𝑖,𝑗;𝑘,𝑙) 𝑣𝑦𝑅𝑘𝑙 (𝑡)𝑘=𝑖−𝑟 𝑙=𝑗−𝑟

Fig. 1.

𝑖+𝑟∑

Structure of the CR-CNN.

+𝑗+𝑟∑

𝐶𝐿𝐺(𝑖,𝑗;𝑘,𝑙) 𝑣𝑦𝐺𝑘𝑙 (𝑡)𝑘=𝑖−𝑟 𝑙=𝑗−𝑟State equation of red-layer :𝑑𝑣𝑥𝑅𝑖𝑗𝑑𝑡=𝑖+𝑟∑−𝑣𝑥𝑅𝑖𝑗 +𝑗+𝑟
∑

+𝑗+𝑟
∑

𝐴𝑅(𝑖,𝑗;𝑘,𝑙) 𝑣𝑦𝑅𝑘𝑙 (𝑡)𝐵𝑅(𝑖,𝑗;𝑘,𝑙) 𝑣𝑢𝑅𝑘𝑙 (𝑡)+𝑗+𝑟∑𝐶𝐵(𝑖,𝑗;𝑘,𝑙) 𝑣𝑦𝐵𝑘𝑙 (𝑡)𝑘=𝑖−𝑟 𝑙=𝑗−𝑟+𝑖+𝑟∑𝑗+𝑟∑

𝐶𝐿(𝑖,𝑗;𝑘,𝑙) 𝑣𝑦𝐿𝑘𝑙 (𝑡) + 𝐼𝑅State equation of green-layer :=𝑖+𝑟∑−𝑣𝑥𝐺𝑖𝑗 +𝑗+𝑟
∑𝑖+𝑟
∑𝑗+𝑟
∑

𝐴𝐺(𝑖,𝑗;𝑘,𝑙) 𝑣𝑦𝐺𝑘𝑙 (𝑡)𝐵𝐺(𝑖,𝑗;𝑘,𝑙) 𝑣𝑢𝐺𝑘𝑙 (𝑡)𝑘=𝑖−𝑟 𝑙=𝑗−𝑟+𝑖+𝑟
∑𝑗+𝑟
∑

+𝑗+𝑟
∑

𝐶𝐿(𝑖,𝑗;𝑘,𝑙) 𝑣𝑦𝐿𝑘𝑙 (𝑡) + 𝐼𝐺

𝑘=𝑖−𝑟 𝑙=𝑗−𝑟State equation of blue-layer :𝑑𝑣𝑥𝐵𝑖𝑗𝑑𝑡=𝑖+𝑟∑−𝑣𝑥𝐵𝑖𝑗 +𝑗+𝑟∑𝐴𝐵(𝑖,𝑗;𝑘,𝑙) 𝑣𝑦𝐵𝑘𝑙 (𝑡)𝑘=𝑖−𝑟 𝑙=𝑗−𝑟+𝑖+𝑟∑𝑗+𝑟∑1(∣𝑣𝑥𝑅𝑖𝑗 (𝑡) + 1∣ − ∣𝑣𝑥𝑅𝑖𝑗 (𝑡) − 1∣)2(5)𝑣𝑦𝐺𝑖𝑗 (𝑡) =1(∣𝑣𝑥𝐺𝑖𝑗 (𝑡) + 1∣ − ∣𝑣𝑥𝐺𝑖𝑗 (𝑡) − 1∣)2(6)𝑣𝑦𝐵𝑖𝑗 (𝑡) =1(∣𝑣𝑥𝐵𝑖𝑗 (𝑡) + 1∣ − ∣𝑣𝑥𝐵𝑖𝑗 (𝑡) − 1∣)2(7)𝑣𝑦𝐿𝑖𝑗 (𝑡) =1(∣𝑣𝑥𝐿𝑖𝑗 (𝑡) + 1∣ − ∣𝑣𝑥𝐿𝑖𝑗 (𝑡) − 1∣)2(8)III. S IMULATION R ESULTS

𝐶𝑅(𝑖,𝑗;𝑘,𝑙) 𝑣𝑦𝑅𝑘𝑙 (𝑡)𝑘=𝑖−𝑟 𝑙=𝑗−𝑟𝑖+𝑟∑𝑣𝑦𝑅𝑖𝑗 (𝑡) =where 𝑣𝑥 , 𝑣𝑦 and 𝑣𝑢 represent a state, an output and an input
value of cell, respectively. In the each state equation, 𝐴 isthe feedback template, 𝐵 is the control template, 𝐶 is theconnection template from other layer and 𝐼 is the constantbias. The output equation has the feature of piece-wise linear
function. In fact, the output value of the CR-CNN is withinof −1 to 1.

𝑘=𝑖−𝑟 𝑙=𝑗−𝑟+(4)(1)

𝑘=𝑖−𝑟 𝑙=𝑗−𝑟

𝑑𝑣𝑥𝐺𝑖𝑗𝑑𝑡

𝐶𝐿𝐵(𝑖,𝑗;𝑘,𝑙) 𝑣𝑦𝐵𝑘𝑙 (𝑡) + 𝐼𝐿

Output equation :𝑘=𝑖−𝑟 𝑙=𝑗−𝑟
𝑖+𝑟
∑𝑗+𝑟
∑

𝑘=𝑖−𝑟 𝑙=𝑗−𝑟

𝑘=𝑖−𝑟 𝑙=𝑗−𝑟𝑖+𝑟∑𝑖+𝑟∑+𝐵𝐵(𝑖,𝑗;𝑘,𝑙) 𝑣𝑢𝐵𝑘𝑙 (𝑡)(2)

In this section, we show some simulation results for edge
detection by using the CR-CNN. For this simulation, we usesome general color images. Figure 2 shows an example ofthe dissolution of a color image to four gray-scale images.
Figure 2 (a) is the original color image. Also Figs. 2 (b), (c),(d) and (e) are the gray-scale images corresponding to theluminosity, red, green and blue values of the color image,respectively. They are used as input image of each layer,respectively.
Templates for edge detection by using the CR-CNN are
shown as follows.

𝑘=𝑖−𝑟 𝑙=𝑗−𝑟875⎡0
𝐶𝐺 = ⎣ 00⎡0𝐶𝐵 = ⎣ 00⎡(a)0
𝐶𝐿 = ⎣ 00⎡0
𝐶𝐿𝑅 = ⎣ 00⎡(b)0
𝐶𝐿𝐺 = ⎣ 00(c)⎡0
𝐶𝐿𝐵 = ⎣ 000𝑏0⎤00 ⎦00𝑏0⎤00 ⎦00𝑏0⎤00 ⎦0⎤0𝑏000 ⎦00𝑏0⎤00 ⎦00𝑏0⎤00 ⎦0{{{𝑏 = 0.9
𝑏=0if 𝑣𝑦𝐺𝑖𝑗 ≥ 0otherwise𝑏 = 0.9𝑏=0

if 𝑣𝑦𝐵𝑖𝑗 ≥ 0otherwise

𝑏=1
𝑏=0

if 𝑣𝑦𝐿𝑖𝑗 ≥ 0otherwise⎧𝑏 = 0.9⎨⎩⎧𝑏 = 0.9⎨⎩(e)Fig. 2. Gray-scale image. (a) Original color image. (b) Gray-scale image forluminosity value. (c) Gray-scale image for red value. (d) Gray-scale imagefor green value. (e) Gray-scale image for blue value.

Edge detection template in the CR-CNN :⎡⎤0 0 0
𝐴𝑅 = 𝐴𝐺 = 𝐴𝐵 = 𝐴𝐿 = ⎣ 0 1 0 ⎦0 0 0⎤−1 −1 −1
𝐵𝑅 = 𝐵𝐺 = 𝐵𝐵 = 𝐵𝐿 = ⎣ −1 8 −1 ⎦−1 −1 −1

𝑏=0⎧
𝑏 = 0.9⎨⎩𝐼𝑅 = 𝐼𝐺 = 𝐼𝐵 = 𝐼𝐿 = −1,(d)𝑏=0𝑏=0if 𝑣𝑦𝑅𝑖𝑗 ≥ 0,𝑣𝑦𝑅𝑖𝑗 > 𝑣𝑦𝐺𝑖𝑗 and𝑣𝑦𝑅𝑖𝑗 > 𝑣𝑦𝐵𝑖𝑗
otherwise
if 𝑣𝑦𝐺𝑖𝑗 ≥ 0,𝑣𝑦𝐺𝑖𝑗 > 𝑣𝑦𝑅𝑖𝑗 and𝑣𝑦𝐺𝑖𝑗 > 𝑣𝑦𝐵𝑖𝑗
otherwise
if 𝑣𝑦𝐵𝑖𝑗 ≥ 0,𝑣𝑦𝐵𝑖𝑗 > 𝑣𝑦𝑅𝑖𝑗 and𝑣𝑦𝐵𝑖𝑗 > 𝑣𝑦𝐺𝑖𝑗otherwise(9)

where 𝐴, 𝐵 and 𝐼 of each layer are the same as existingedge detection template in [9]. Red, green and blue layers
are influenced through connection template (𝐶𝐵 , 𝐶𝑅 , 𝐶𝐺 and𝐶𝐿 ) from blue, red and green layers, respectively and luminosity layer. Luminosity layer is influenced though connectiontemplate (𝐶𝐿𝑅 , 𝐶𝐿𝐺 and 𝐶𝐿𝐵 ) only from the cell whose
value is the large among red, green and blue layer when thevalue is lager than zero. In the case of each cell are the sameoutput value, luminosity layer is influenced through connection
template only from one of them. In this simulation result, theoutput images of all the layers became almost the same image.

⎡⎡0
𝐶𝑅 = ⎣ 000𝑏0⎤
00 ⎦0{𝑏 = 0.9
𝑏=0if 𝑣𝑦𝑅𝑖𝑗 ≥ 0otherwise

A. Pepper Image
Figure 3 shows the simulation results of edge detection.
The input images of each layer are Figs. 2 (b) to (e). In
Fig. 3 (b), using the RGB-CNN, edge is more detected thanthe conventional CNN like Fig. 3 (a). However, the edge of alow luminosity portion remains as black. In Fig. 3 (c), we cansee that the CR-CNN can detect the edges more effectively
than the conventional CNN and the RGB-CNN.

876

(a)

(b)

(c)

(a)

(b)

(c)

(d)

Fig. 3. Simulation results 1. (a) Edge detection result using the conventional
CNN for the input image converted to gray-scale image. (b) Edge detection
result using the RGB-CNN. (c) Edge detection result using the CR-CNN(output image of blue layer).

Fig. 4. Simulation results 2. (a) Input image. (b) Edge detection result using
the conventional CNN for the input image converted to gray-scale image.
(c) Edge detection result using the RGB-CNN. (d) Edge detection result using
the CR-CNN (output image of blue layer).

B. Couple Image[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.

Figure 4 shows the simulation results of edge detection.
In Fig. 4 (a), this input image is a low luminosity image.
In Fig. 4 (b), using the conventional CNN, most edge is notdetected. In Fig. 4 (c), using the RGB-CNN, this output image
is not edge detection image which would appear that the input
image is a low luminosity. In Fig. 4 (d), we can see that
the CR-CNN can detect the edges more effectively than theconventional CNN and the RGB-CNN.
The simulation results by using the CR-CNN arise from thestructure which consideration of three primary colors of lightand luminosity.
IV. C ONCLUSION
In this study, we have proposed four-layer CNN in consideration of three primary colors of light and luminosity. From
some simulation results, we have confirmed that the CR-CNN
could detect the edge of color images more effectively than theconventional CNN and the RGB-CNN. In the future work, wewould like to use the CR-CNN for other task of color image
processing.

[3] M. Namba and Z. Zhang, “Cellular Neural Network for Associative Memory and Its Application to Braille Image Recognition,” Proc. of IJCNN’06,pp. 4716-4721, Jul. 2006.
[4] H. Koeppl and L. O. Chua, “An Adaptive Cellular Nonlinear Network 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.
[6] K. R. Crounse and L. O. Chua, “Methods for Image Processing and Pattern Formation in Cellular Neural Networks: A Tutorial,” IEEE Trans.
Circuits Syst., vol. 42, no. 10, pp. 583-601, Oct. 1995.
[7] T. Roska, A. Zarandy and L. O. Chua, “Color Image Processing by CNN,”
Proc. of ECCTD’93, pp. 57-62, Aug. 1993.
[8] T. Inoue and Y. Nishio, “Edge Enhancement of Color Image by ThreeLayer Cellular Neural Network Considering Three Primary Colors,” Proc.
of NOLTA’08, pp. 540-543, Sep. 2008.
[9] Cellular Sensory Wave Computers Laboratory Computer and Automation Research Institute Hungarian Academy of Sciences, “Cellular wave Computing Library (Template, Algorithms, and Programs)
Version 2.1”

R EFERENCES[1] L. O. Chua and L. Yang, “Cellular Neural Networks: Theory,” IEEE
Trans. Circuits Syst., vol. 32, pp. 1257-1272, Oct. 1988.

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