ARTICLES

Sci. Rep. Kanazawa Univ.
Vol. 63, pp. 67–78, 2019

Convolutional Neural Network to Classify Capillaries of
Images in Human Fingertips
Mochammad H AFIIZH1,2, *1 Graduate School of Natural Science and Technology, Kanazawa University

Kakuma, Kanazawa, 920-1192, Japan
2 Department of Mathematics, Universitas Negeri Malang

Malang, 65145, Indonesia(Received June 26, 2019, and accepted in revised form August 28, 2019)

Abstract In this paper, we report on training an image classiﬁer implemented as a convolutional neural network (CNN) to judge the state of human capillaries from microscope
photographs. This work is motivated by medical research that suggests that their shape andother features are linked to other health measures. Instead of medical doctor’s diagnosis andtherefore to possibly lower the cost and consistency of the diagnosis, we propose a CNN classiﬁer. To overcome the difﬁculty of obtaining a large number of training images, we utilize
the transfer learning approach. We base our model on a pre-trained VGG16 model for the
lower layers of the network and our implementation uses Python and the Torch library. Abnormal types of capillaries are divided into several patterns and appropriate pre-processing
is performed including a partial differential equation approach. The trained CNN has been
applied to actual capillary patterns to verify its performance.
Keywords.

1

Image, capillaries, CNN, transfer learning

Introduction

Prevention is important in medicine. According to private discussion with medical experts, there
is a medical research that suggests that the shape and other features of human capillaries arelinked to other health measures. Ogawa [10] outlined that the health of a person affects the shapeof capillaries at the root of a ﬁngernail. The reference [15] also reported that the structure ofcapillaries is strongly related to serious diseases: connective tissue disease, diabetic Mellitus, andcancer. Hence, examining the capillaries status is important as a diagnostic tool.
Capillaries are the smallest-diameter blood vessels which connect arteries to veins. The size ofcapillaries is about 5 to 10 micrometers in diameter and their diameter averages 8 micrometers [3].
In general, checking capillaries directly is not easy, for example, when examining the capillaries at
eye’s fundus, the dilation of the pupil is required. However, by assuming the capillary is the trackof red blood cells, then capturing the image of capillaries around the root part of a ﬁngernail canbe conducted just by a microscope with magniﬁcation around 700-900. Thus, it is possible even to* Email:moch.haﬁish.fmipa@um.ac.id

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Convolutional Neural Network to Classify Capillaries of Images in Human Fingertips

Figure 1: The ﬁrst two columns are the images of actual capillaries on human ﬁngertip taken by amicroscope. The last two columns are the images of artiﬁcial capillaries drawn by a hand.

conduct the observations with a cheap microscope and record the changes of patterns easily. The
ﬁrst two columns in Figure 1 show examples of capillaries on human ﬁngertips taken by 700-900
magniﬁcation of a microscope. The lens of microscope were located on the skin near the root of aﬁngernail.
However, diagnosis based on these images is not an easy task because it requires the skill of
medical experts (doctors). This skill is unique and not every doctor can perform this diagnosis.
Different doctors might give different diagnosis results. The problem is how to learn diagnosis
from the skilled doctors and how to develop a consistent diagnosis. To overcome these problems,
we propose a CNN classiﬁer. We believe this approach can also possibly lower the cost.
CNN is a mapping from a set of inputs to a set of outputs determined by a set of adjustableparameters. It is the most powerful tool used for a large-scale image recognition [8], [12], and[13]. It is also applied to other classiﬁcation problems, for example, in [9] and [14]. In addition,
it is applied to medical images [2], [6], [11], and [16]. These are the main reasons for choosing
CNN.
Generally, CNN requires a large number of images in training data. All these images determine
the adjusted parameters during training, which is the process of updating parameters. However,this can be overcome by utilizing the transfer learning approach. The transfer learning means wecopy the model and its optimum parameters. This model is a so-called pre-trained. We base ourmodel on a pre-trained VGG16 model for the lower layers of the network. Hence, the input of
the images is feeding up to the pre-trained model ﬁrst, and then the output becomes input to our
network. We use Python and the Torch library to implement our CNN model.
The purpose of this research is to train an image classiﬁer implemented as a CNN to judge
the state of human capillaries from microscope photographs according to medical motivation. We
present two models of CNN. The ﬁrst model has two categories. The second model has nine
categories.
The ﬁrst CNN model has two categories because the starting point of this paper is the research
work by Hung, Nakane, and Hashimoto [5] which developed a judgment category by measuring
curve oscillation. Their trial was the following: (i) detecting the edge of the object of capillaries
by image processing, (ii) measuring the curvature of the edge, and (iii) calculating the oscillation
density. Edge refers to the boundary of the object in the image. Thus, they deﬁned meander
category. They presented the images of capillaries related to either healthy or unhealthy persons.
According to those images, the simple structure of capillaries which looks like the U-conﬁgurationis related to the healthy person. If it has a complicated structure, such as meaningless meandering,
it is related to the unhealthy person. The dissertation [4] implemented the partial differential
equation approach by applying the Fourier transform on the signed curvature of the edge to classify
the status of images of the capillaries into straight and wiggly categories. The straight category isof the simple structure while the wiggly category is of the complicated structure.
Unfortunately, the meaning of complicated structures is very difﬁcult to transfer the infor-

Mochammad H AFIIZH

69

Figure 2: The images of artiﬁcial capillaries of each category in the second CNN model. From left
to right: the ﬁrst row is the straight ﬁne, straight 1 branch, straight 2 branches, straight jump, andstraight sharp, while the second row is the wiggly ﬁne, wiggly 1 branch, and wiggly 2 branches,
and wiggly jump.

mation or technique to other doctors. The ﬁrst model of CNN can distinguish the structure ofcapillaries into two categories, but no further information can be added by this model. We think it
is insufﬁcient because (i) skill cannot be transferred to other doctors, (ii) the causes and effects are
not clear, which is not good for further research, and (iii) new detail explanation cannot be found.
To overcome these problems, the ﬁrst is that we divide the abnormal types of capillaries into
several patterns such as meandering, unexpected separation pattern, and branch appearing. The
second is by deﬁning a mathematical category for each pattern. The third is by creating artiﬁcial
data for training. The last is to train the CNN model.
For each pattern, the stage number is given. We give the meandering category by performing
the pre-processing which is the partial differential equation approach as in [4]. For the case of
unexpected separation pattern and branch appearing, we count the number of ’separation’ and’branch’ points and give the indicator. Therefore, we present the second CNN model which hasnine categories: straight ﬁne, straight 1 branch, straight 2 branches, straight jump, straight sharp,
wiggly ﬁne, wiggly 1 branch, wiggly 2 branches, and wiggly jump. The ﬁrst category is the simple
structure without any abnormal type. The second category is the simple structure with a branch
point. The third category is the simple structure with two branch points. The fourth category is
the simple structure with a jump. The ﬁfth category is the simple structure with sharp oscillation.
The sixth category is the meandering pattern without any separation and branch. The seventh toninth category is similar to the second to fourth category respectively except the pattern which ismeandering type.
We create artiﬁcial data and give indicators to each category. These artiﬁcial data created byhand-drawing or computer software are mainly used for training. We perform the appropriate preprocessing including a partial differential equation approach to obtain the indicators, especiallyfor dividing the artiﬁcial data into straight and wiggly category. We use artiﬁcial data to train
the ﬁrst and second CNN model. The last two columns in Figure 1 show artiﬁcial data for eachcategory in the ﬁrst CNN model. Figure 2 shows the artiﬁcial data of nine categories in the second
CNN model. Thus, both trained CNN have been applied to actual capillary patterns to verify its
performance.

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Convolutional Neural Network to Classify Capillaries of Images in Human Fingertips

The beneﬁt of this approach is the possibility to train CNN by a small number of test data.
The other merit is not only the capillaries are classiﬁed into straight and wiggly, but the damage
patterns of capillaries are also classiﬁed. The output is expressed by numbers (score) for eachcategory. This score means how close the input image to the training data of each category. We
consider this score when applying the trained model to the images of actual capillary patterns.
Finally, this paper is organized as follows. The ﬁrst section is introduction. The CNN approachis brieﬂy described in the second section of this paper. The last section shows the results.

2

Convolutional Neural Network

The basis of CNN is a neural network model. Generally, this model is a mapping from a set of
inputs to a set of outputs determined by a set of adjustable parameters. This mapping consists ofseveral composed functions known as the layers. Each layer contains several nodes, whereas eachnode has some parameters. For more detailed explanation of neural networks and CNN, refer to[1].
Training, validation, and test data in this research is based on hand-drawn images. The quantity
is increased by stretching, rotating, and adding noise to each image. The angles of rotation arelimited because we assume that the input images are not ﬂipped up and down. Each image islabeled by the category where the image belongs to.
All images as the input of VGG16 model are pre-processed, including the partial differential
equation approach. These images are resized such that they satisfy the requirement of VGG16.
The average of pixel values of each image is subtracted such that it is around zero due to the ReLU
5
activation function. The pixel values are multiplied by 255
to make its pixel values become dense.
The denominator is 255 because the original range value of the pixel is integer between 0 and 255.
The numerator can be speciﬁed by the other number, ﬁve is not the only option.
Transfer learning means that the model and its optimum parameters after being trained by theothers on a huge amount of training data is being copied. That model is a so-called pre-trainedmodel. The pre-trained model in this research is VGG16. More layers are then added at the endof that model.
VGG is the abbreviation for Visual Geometry Group. This VGG16 model was developed by
Simonyan and Zisserman from Department of Engineering Science, University of Oxford. It is avery deep CNN model. It was the basis of their ImageNet Challenge 2014 submission, where theirteam secured the ﬁrst and second places in the localization and classiﬁcation tracks respectively[13]. VGG16 classiﬁes images into 1000 categories. Among these categories, some examples
are snakes, spoons, microphones, and paintbrushes. We assume that the complicated structures ofcapillaries are similar to snakes and that the simple structures are similar to spoons, microphones,
or paintbrushes. The input images of VGG16-model are in RGB format of ﬁxed 224 × 224-size.
We use the ﬁrst 37 layers of this pre-trained model, as shown in Table 1. The output of this pretrained model becomes the input of our proposed model. Figure 3 shows a summary of the CNN
model in this paper.
We propose a model of fully connected layer consisting of ﬁve layers. The ﬁrst layer consistsof 256 nodes. Consequently, this layer requires 1,048,832 parameters because the output from thepre-trained model has 4,096 nodes. Let the output of pre-trained model be y(37) ∈ R4096 . Thus,
the output of layer p1 is(p )y(p1 ) = w(p1 ) y(37) + w(0)1

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Mochammad H AFIIZH

Layer-p1

Layer-p2

Layer-p3

Layer-p4Layer-p5

..
.

..
.

output-1
output-2
output-3
output-4
Input the color image

Ouput

VGG16
output-5
output-6
..
.

..
.

..
.

..
.

output-4096

Figure 3: The ﬂow chart of CNN model. The proposed model is in the dashed rectangle.

(p )where y(p1 ) , w(0)1 ∈ R256 and w(p1 ) ∈ M256×4096 . The output of layer p2 is


(p )
(p )
y(i)2 = max y(i)1 , 0
where i = 1, 2, . . . , 256. The Dropout in layer p3 has factor 0.2 which means 20% of the output of
this layer in each channel is deactivated randomly. The output of layer p3 is( (p )
if node-i is activated
y 2
(p3 )
y(i) = (i)0
if node-i is deactivatedwhere i = 1, 2, . . . , 256. Let n be the number of categories. Layer p4 has output as follows,(p )y(p4 ) = w(p4 ) y(p3 ) + w(0)4(p )where y(p3 ) ∈ R256 is the output of layer p3 , y(p4 ) , w(0)4 ∈ Rn , and w(p1 ) ∈ Mn×256 .
The last layer is LogSoftmax, an activation function, where the output of this layer p5 is

 

(p )
exp y(i)4(p )
y(i)5 = log (p4 )n∑ j=1 exp y( j)for i = 1, 2, . . . , n. We propose two CNN models. The ﬁrst model is of n = 2 and the second model
is of n = 9.
The loss function, in this case, is Average Negative Log Likelihood. Since the ﬁnal layer scoreis already LogSoftmax-layer, we need to multiply the output from the ﬁnal layer by negative one.
We deﬁne T as the set of targeted output. Let M ∈ Z+ be the number of images in training,y(p5 ,m) ∈ Rn be the output of the layer p5 for mth -image, and tm ∈ T be the targeted output ofmth -image. Since the ﬁnal layer is LogSoftmax, then the negative log-likelihood is deﬁned as
L(y(p5 ) , t, w, M) =1 M
(p ,m)−y(i)5∑M m=1

i=argmax tm

where y(p5 ) is the set of the output of layer p5 for all M images, t is the set of the targeted output
for all M images, and w is the set of trainable parameters.

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Convolutional Neural Network to Classify Capillaries of Images in Human Fingertips

Table 1: The model of VGG16 up to layer 37.
Layer (type)Output shape# Parameters

Conv2d-1[64, 224, 224]

1,792

ReLU-2[64, 224, 224]

0Conv2d-3[64, 224, 224]

36,928

ReLU-4[64, 224, 224]

0

MaxPool2d-5[64, 112, 112]0

Conv2d-6[128, 112, 112]

73,856

ReLU-7[128, 112, 112]0

Conv2d-8[128, 112, 112]

147,584

ReLU-9[128, 112, 112]0

MaxPool2d-10[128, 56, 56]

0

Conv2d-11[256, 56, 56]

295,168

ReLU-12[256, 56, 56]

0

Conv2d-13[256, 56, 56]

590,080

ReLU-14[256, 56, 56]

0

Conv2d-15[256, 56, 56]

590,080

ReLU-16[256, 56, 56]

0MaxPool2d-17[256, 28, 28]0

Conv2d-18[512, 28, 28]

1,180,160

ReLU-19[512, 28, 28]0

Conv2d-20[512, 28, 28]

2,359,808

ReLU-21[512, 28, 28]0

Conv2d-22[512, 28, 28]

2,359,808

ReLU-23[512, 28, 28]0

MaxPool2d-24[512, 14, 14]0

Conv2d-25[512, 14, 14]

2,359,808

ReLU-26[512, 14, 14]0

Conv2d-27[512, 14, 14]

2,359,808

ReLU-28[512, 14, 14]0

Conv2d-29[512, 14, 14]

2,359,808

ReLU-30[512, 14, 14]0

MaxPool2d-31[512, 7, 7]

0Linear-32[4096]

102,764,544

ReLU-33[4096]

0

Dropout-34[4096]0Linear-35[4096]

16,781,312

ReLU-36[4096]

0

Dropout-37[4096]

0

Total params: 134,260,544
Trainable params: 0
Non-trainable params: 134,260,544

1

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Mochammad H AFIIZH

Training

Test

Validation

Figure 4: All the hand-drawn images grouped into three blocks: Training, Validation, and Test.
The ﬁrst row of each block is labeled by straight while the second row of each block is labeled by
wiggly.

For the ﬁrst CNN model, the number of categories are two. Thus, the set of the targeted output
is T = { (1, 0) , (0, 1) } where (1, 0) belongs to the ﬁrst category and (0, 1) belongs to the second
category. The second CNN model has nine categories. Thus, the targeted output for the category-i
is t(i) ∈ R9 where the ith -component is 1 and the other components are 0.
Adam method is implemented to ﬁnd the minimizer of L with respect to the trainable parameters. The name of this method is derived from the adaptive moment estimation. This method
computes individual adaptive learning rates for different parameters from the estimation of theﬁrst and second moments of the gradients [7].
The output of CNN model is the score of each category. This score means how close the input
image to the training data of each category. Increasing the number of training images might getbetter results. From this score, we determine that the input image is classiﬁed to the highest scorecategory. We also state that the image is classiﬁed correctly if the highest score category is thesame as the label of that image. We deﬁne average accuracy bymc
× 100%,
M
where mc is the number of images classiﬁed correctly and M is the number of input images.

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Convolutional Neural Network to Classify Capillaries of Images in Human Fingertips

Figure 5: The result of the process of updating parameters of the ﬁrst CNN model.

3 Results
For the ﬁrst CNN model, we created 12 hand-drawn images for each category, as shown in Figure
4. Six of them were applied during training, the other three were applied as validation data, while
the rests were applied as test data. The number of images was increased by stretching, rotating,and adding noise. The stretch factors were 1.2, 1, and 0.7. These stretch factors are restricted to
avoid a wiggly capillary to look like a straight capillary. The angles of rotation were -18, -9, 0,
9, and 18. By this small number of angles, we expect to lower the computational time keeping
higher accuracy. We added noise to the copy of each image. Hence, the total number of images
in the training data were 360, while the total images in both validation and test data are the same,
180 images.
Figure 5 shows the accuracy and the loss function of training and validation in each time step
(epoch) of the ﬁrst CNN model. The initial parameters are given randomly such that the accuracy
is the lowest, whereas the loss is the highest. The accuracy at epoch 2 increases while the loss
decreases. After epoch 2, the accuracies are stable above 90%, and the loss is less than 0.2. The
parameters at epoch 11 are called the optimum parameters. The accuracy of the training at lastepoch is around 95%. It means around 18 of 360 images are classiﬁed incorrectly.
The accuracy of the ﬁrst trained CNN model implemented to the artiﬁcial test data is 97%.
Out of 180 images, ﬁve are classiﬁed incorrectly. All these incorrect classiﬁcations are from thestraight category, as shown in the second row in Figure 6. The ﬁrst row of Figure 6 shows someexamples of the correct classiﬁcation of the test data from both categories.
From this result, we show that the ﬁrst CNN model to classify the capillaries into straight andwiggly patterns works successfully. The implementation of this model to the validation data also
works similarly to the training results. In addition, when we apply this model to the test data which
are different with the training data, the accuracy is similar to the training result. Therefore, it isacceptable to train the large number of parameters by the small number of images in training. The
other merit is that the computational cost during the training is reduced.
The ﬁrst trained CNN model is applied to images of real capillaries. We present eight images of
the capillaries in Figure 7. Instead of showing the accuracy, we present the score of each category.
The straight category at the top images in Figure 7 has higher score than the wiggly category. The
ﬁrst three columns of the bottom images in Figure 7 have higher scores for the wiggly category.
The higher score for the last column of this below image is the straight category, although thecapillary has more than two turning points.

75

Mochammad H AFIIZH

0.2

0.4

0.6

0.8

1.0

0.0

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0.00

wiggslytraightwiggslytraight

0.0

1.00

wiggslytraightwiggslytraight

Figure 6: Some images in the test data which the incorrect classiﬁcation is shown in the second
row and the correct classiﬁcation is shown in the ﬁrst row.

0.0

0.94
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Figure 7: The results of ﬁrst CNN model applied to the images of capillaries taken by a microscope. The score in each category is presented by the horizontal bar below each image.

For the second CNN model, we create more images for each category. Each image is stretched,rotated, and noise is added. The total is 7,200 images in the training set and each category has 800
images. The total number of images for validation is 2,250.
We perform 24 iterations to train the second CNN model. The accuracies and losses can beseen in Figure 8. The graph of accuracy increases and the loss decreases, but after 3 epochs, bothchange slowly. The trend of the graph of validation follows the training.
The training accuracy trend of the last six iterations seems ﬂat at around 70%. There is also adecreasing trend of the validation accuracy from the nineteenth to twenty-ﬁrst iteration. Therefore,
the training is stopped after 24 iterations.

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Convolutional Neural Network to Classify Capillaries of Images in Human Fingertips

Figure 8: The result of the process of updating parameters of the second CNN model.

The highest training accuracy is 70.8% at the nineteenth, twenty-ﬁrst, and twenty-third iterations. Among these iterations, the highest validation accuracy occurs at the nineteenth iteration.
Hence, we choose the result of the nineteenth iteration as the optimum parameters.
The test data contain 9 × 750 = 6, 750 images. The accuracy when we applied the model tothe test data is 63.98%. Table 2 shows the details of the accuracy and loss of each category in thesecond CNN model. The accuracies of the four categories are more than 87%, but the other four
categories have less than 50% accuracy. The lowest accuracy is the category of the wiggly jump,that is 18.93%.
Figure 9 shows the results when the second trained CNN model is applied to the images ofactual capillaries. The horizontal bars in the second column show the score of each category. The
right vertical axis shows the precise number of each bar. The left vertical axis shows the category
number related to Table 2.
The images in the ﬁrst three rows of Figure 9 show that the second category is the highest
score. The ﬁfth image has the highest score for the wiggly ﬁne category. The category of thestraight 2 branches has the highest score for the rest images.
Table 2: The accuracy and loss of each category from the second CNN model.

No.

Category

Accuracy

Loss

1Straight fine

38.13

1.040

2

Straight 1 Branch

95.87

0.161

3

Straight 2 Branches

87.73

0.284

4

Straight Jump

96.53

0.130

5

Straight Sharp

99.87

0.003

6

Wiggly fine

65.47

1.097

7

Wiggly 1 Branch

27.33

1.415

8

Wiggly 2 Branches

46.00

1.215

9

Wiggly Jump

18.93

1.483

Average

63.98

0.759

1

Conclusions According to the results, we successfully train the ﬁrst CNN model such that it canclassify the images of capillaries into two categories: straight and wiggly. Transfer learning can
support the limitation of the number of images in training. For the second CNN model, although

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Mochammad H AFIIZH
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Figure 9: The results of the second CNN model applied to the images of capillaries taken by amicroscope. The score in each category is presented by the horizontal bar next to each image.

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Convolutional Neural Network to Classify Capillaries of Images in Human Fingertips

the average accuracy of nine categories on the artiﬁcial test data is 63%, the accuracies of the four
categories are less than 50%. We also present the score of each category from both trained CNN
models to the actual capillaries. For future research, a large number of values for the angles ofrotation would be implemented, and the other pre-trained models would be tested and compared.

Acknowledgements
This research is ﬁnancially supported by LPDP (Lembaga Pengelola Dana Pendidikan) which is
the Indonesia Endowment Fund for Education established by the Ministry of Finance, Republic ofIndonesia. The author would like to thank Prof. Seiro Omata as the author’s Ph.D. supervisor forthe great advice and discussion during the process of completing this paper.

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