Journal of Robotics, Networking and Artificial Life, Vol. 3, No. 1 (June 2016), 17-23

Medical Image Analysis of Brain X-ray CT Images By Deep GMDH-Type Neural Network

Tadashi Kondo†
Graduate School of Health Sciences, Tokushima University
3-18-15 Kuramoto-cho Tokushima 770-8509 Japan
Email: †kondomedsci@gmail.com
Junji Ueno
Graduate School of Health Sciences, Tokushima University
3-18-15 Kuramoto-cho Tokushima 770-8509 Japan
Shoichiro Takao
Graduate School of Health Sciences, Tokushima University
3-18-15 Kuramoto-cho Tokushima 770-8509 JapanAbstract
The deep Group Method of Data Handling (GMDH)-type neural network is applied to the medical image analysisof brain X-ray CT image. In this algorithm, the deep neural network architectures which have many hidden layers
and fit the complexity of the nonlinear systems, are automatically organized using the heuristic self-organization
method so as to minimize the prediction error criterion defined as Akaike’s Information Criterion (AIC) orPrediction Sum of Squares (PSS). The learning algorithm is the principal component-regression analysis and theaccurate and stable predicted values are obtained. The recognition results show that the deep GMDH-type neuralnetwork algorithm is useful for the medical image analysis of brain X-ray CT images.
Keywords: Deep neural networks, GMDH, Medical image recognition, Evolutionary computation, X-ray CT image.

1. Introduction
The deep GMDH-type neural network algorithms
were proposed in our early works1~4 and can
automatically organize the neural network architecturesusing heuristic self-organization method5,6 which is a
type of the evolutionary computation. In this study, deep
GMDH-type neural network algorithm1 is applied to themedical image analysis of brain X-ray CT images. The
learning calculations of the weights is the principal
component-regression analysis and the accurate andstable predicted values are obtained. In this GMDH-type
neural network, two types of neurons such as thesigmoid function neuron and the polynomial neuron areused to organize the deep neural network and very
complex nonlinear systems can be identified using thisdeep GMDH-type neural network. In our previouswork2, we have applied the deep multilayered GMDHtype neural network to the medical image recognition ofbrain and blood vessels. This deep multi-layered
GMDH-type neural network selected the sigmoid
function neural network architectures from the three
types of neural network architectures such as the
sigmoid function neural network, the radial basis
function (RBF) neural network and the polynomial
neural network architecture. The brain and blood vessel
regions are recognized and extracted accurately using
the sigmoid function neural network architectures. In
this study, the deep logistic GMDH-type neural network
algorithm is applied to the medical image analysis ofbrain X-ray CT images and the skull and the bloodvessel regions in the brain are recognized and extracted.
The recognition results are compared with thoseobtained using the conventional neural networks trained

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17Tadashi Kondo, Junji Ueno, Shoichiro Takaousing the back propagation algorithm and it is shownthat this deep neural network is accurate and useful forthe medical image analysis of the brain X-ray CT
image.

2. Deep GMDH-type neural network1
The GMDH-type neural network architecture isshown in Fig.1. Here, nonlinear function gi is describedby the following Kolmogorov-Gabor polynomial:gi (x1,x2,⋅⋅⋅,xp)= a0+∑aixi+∑∑aijxixj+⋅⋅⋅iij(1)

This nonlinear function is automatically organized
by using the polynomial neurons. The architecture of
the GMDH-type neural network is automaticallyorganized using the heuristic self-organization and isproduced as follows:
In the GMDH-type neural network, the original data
are not separated into training and test sets because
AIC7 or PSS8 can be used as the test errors.

gi (x1,x2,⋅⋅⋅,xp)∑ : (Nonlinear function)zk = ∑ wi gi (x1,x2,⋅⋅⋅,xp)
f : (Nonlinear function)
φ =1/(1+exp ( - zk))Fig.1 Architecture of the deep GMDH-type neural network

2.1 The first layer(2)
uj=xj (j=1,2,⋅⋅⋅,p)where xj (j=1,2,⋅⋅⋅,p) are the input variables of thesystem, and p is the number of input variables.
2.2 The second layer
All combinations of two variables (ui,uj) are generated.
For each combination, the neuron architecture isdescribed by the following equations:∑: (Nonlinear function)(3)
zk=w1ui+w2uj+w3uiuj+w4ui2+w5uj2 –w0θ1
f : (Linear function)(4)
yk= zkwhere θ1 =1 and wi ( i=0,1,2,⋅⋅⋅,5) are weights between
the first and second layer. The weights wi (i=0,1,2,⋅⋅⋅,5)
are estimated by using the principal componentregression analysis. This procedure is as follows:First, the values of zk are calculated using thefollowing equation:(5)
zk=loge (φ’/(1-φ’))
where φ’ is the normalized output variable. Then theweights wi (i=0,1,2,⋅⋅⋅,5) are estimated by using theprincipal component-regression analysis.
[Principal component-regression analysis]
In the GMDH-type neural network, the multicolinearity is generated in the function Σ of the neurons
because heuristic self-organization method is used. In
this study, the function Σ is calculated using theprincipal component-regression analysis.
In the case of Eq.(3), orthogonal vector v is calculated .
v=C⋅u
(6)
Here,
v=(v1,v2,…,v5)
u=(ui uj, uiuj, ui2, uj2)
v is orthonormal vectors and C is orthonormal matrix. Cis calculated using the following eigenvalue equation.
R・C＝C・Λ
(7)
Here, R is a correlation matrix. Then, variable zk iscalculated using orthogonal regression analysis.
zk = wT⋅ v=w1v1+w2v2+…+w5v5(8)
Using the principal component-regression analysis,
variable zk in the function Σ is calculated without multicolinearity. In (8), useful orthogonal variables νi(i=1,2,…,5) are selected by stepwise regression
analysis9 using AIC or PSS criterion.
From these generated neurons, L neurons which
minimize AIC7 or PSS8 values are selected. The output
values (yk) of L selected neurons are set to the input
values of the neurons in the third layer.
2.3 The third and succeeding layers
In the third and succeeding layers, the same
computation of the second layer is iterated until AIC or

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Medical image analysis ofPSS values of L neurons are not decreased. When theiterative computation is terminated, the following
calculation of the output layer is carried out.
2.4 The output layer
In the output layer, the output values of the neuralnetwork are calculated from zk as follows:(9)
yk= 1/(1+exp ( - zk))
So, in the output layer, the neuron architecture becomes
as follows:∑: (Nonlinear function)(10)
zk = ∑ wi gi (x1,x2,⋅⋅⋅,xp)
f : (Nonlinear function)
φ =1/(1+exp ( - zk))(11)
The complete neural network architecture is produced
by selected neurons in each layer.
In this algorithm, the principal componentregression analysis is used for the learning calculationof the neural network and the accurate and stableprediction values are obtained. The structuralparameters such as the number of layers, the number ofneurons in hidden layers and useful input variables areautomatically selected to minimize prediction errorcriterion defined as AIC or PSS. The GMDH-type
neural network is organized with two types of neurons
which are the sigmoid function neuron and thepolynomial neuron and this neural network can identify
very complex nonlinear system.

variation of PSS values in each layer. The PSS values
were decreased gradually through the layers and small
PSS value was obtained in the seventh layer. The deep
GMDH-type neural network output the skull image(Fig.4) and the post-processing analysis of the output
skull image was carried out. Fig.5 shows the output
image after the post-processing. The output image after
the post-processing was overlapped to the originalimage (Fig.2) as shown in Fig.6. The recognized skull
region are very accurate. The skull region was extracted
from the original image as shown in Fig.7. These image
processing were carried out for all slices by theorganized deep GMDH-type neural network and the 3dimensional skull image was generated as shown inFig.8. A conventional neural network trained using theback propagation algorithm was applied to the same
recognition problem. The output images, when thenumbers of neurons in the hidden layer (m) are 5, 7 and
9, are shown in Fig.9. These images contain moreregions which are not part of the skull.

3. Application to the medical image analysis ofbrain X-ray CT images.
In this study, the regions of the skull and the bloodvessels in the brain were recognized and extracted
automatically. Multi-detector row CT (MDCT) imagesof the brain are used in this study.

Fig. 2 Original image of the brain

3.1 Extraction of the skull regions
An brain MDCT image shown in Fig.2 was used fororganizing the deep GMDH-type neural network. The
statistics of the image densities and x and y coordinatesin the neighboring regions, the N×N pixel regions, wereused as the image features. The neural networks wereorganized when the values of N were from 3 to 10.
When N was equal to 3, the neural network architecture
had the smallest recognition error. Fig.3 shows theLayer

Fig. 3 Variation of PSS values in each layer (1)Published by Atlantis Press
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Tadashi Kondo, Junji Ueno, Shoichiro Takao

Fig.8 The 3-dimensional skull imageFig. 4 Output image (1)(a) m=5

Fig. 5 Output image after the post processing (1)(b) m=7

Fig.6 Overlapped image (1)Fig.7 Extracted gray scale image (1) of the skull(c) m=9
Fig.9 Output images of the conventional neural network (1)Published by Atlantis Press
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20Medical image analysis of3.2 Extraction of the blood vessel regions
Another deep GMDH-type neural network wasorganized and applied to the recognition of the bloodvessel regions in the brain using the MDCT image
shown in Fig.10 which was extracted from the originalimage in Fig.2. Fig.11 shows the variation of PSS
values in each layer. Very small PSS values wereobtained in the seventh layer. The deep GMDH-type
neural network output the blood vessel image as shownin Fig.12. The output image after the post-processing(Fig.13) was overlapped as shown in Fig.14. The
recognized blood vessel regions were very accurate. The
blood vessel regions were extracted from the original
image as shown in Fig.15. These image processing werecarried out for all slices by the organized deep GMDHtype neural network and the 3-dimensional blood vessel
image was generated as shown in Fig.16. A
conventional neural network trained using the backpropagation algorithm was applied and the output
images, when the numbers of neurons in the hidden
layer (m) are 5, 7 and 9, are shown in Fig.17. These
images contained many noise compared with the output
image of the deep GMDH-type neural network which isshown in Fig.12.

Fig.13 Output image after the post-processing (2)Fig.10 Original image of blood vessels extracted from Fig.2

Fig.14 Overlapped image (2)LayerFig. 11 Variation of PSS values in each layer (2)Fig.12 Output image (2)Fig.15 Extracted gray scale image (2) of blood vessels

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Tadashi Kondo, Junji Ueno, Shoichiro Takao(a) m=5
Fig.16 The 3-dimensional blood vessel image

4. Conclusions
In this paper, the deep GMDH-type neural network
algorithm using principal component-regression
analysis was applied to the medical image analysis ofthe brain X-ray CT image, and the skull and the bloodvessel regions in the brain were recognized andextracted accurately. The deep neural networkarchitectures which had six hidden layers wereorganized for both skull and blood vessel regions so as
to minimize the prediction error criterion defined as
PSS. PSS values were gradually decreased through thehidden layers and these PSS values converged on verysmall PSS value in the seventh layer. The recognition
results were compared with those obtained using theconventional neural networks trained using the backpropagation algorithm and it was shown that this deepneural networks with many hidden layers were accurate
and useful for the medical image analysis of the brain
X-ray CT image.

(b) m=7(c) m=9Fig.17 Output images of the conventional neural network (2)Acknowledgment
This work was supported by (JSPS) KAKENHI
26420421.

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