Joint Optimization of Convolutional Neural
Network and Image Preprocessing Selection for
Embryo Grade Prediction in In Vitro
Fertilization?
Kento Uchida??1 , Shota Saito??1,3 , Panca Dewi Pamungkasari??1,2 , Yusei
Kawai1 , Ita Fauzia Hanoum4 , Filbert H. Juwono5 , and Shinichi Shirakawa1
1

Graduate School of Environment and Information Sciences, Yokohama National
University, Yokohama, Japan2
Department of Information and Communication Technology, Universitas Nasional,
Jakarta, Indonesia
3
SkillUp AI Co., Ltd., Tokyo, Japan
4
Infertility Laboratory of Permata Hati Program, RSUP DR Sardjito, Indonesia
5
Department of Electrical and Computer Engineering, Curtin University Malaysia,
Sarawak, Malaysia

Abstract. Convolutional neural networks (CNNs) are a standard toolfor image recognition. To improve the performance of CNNs, it is important to design not only the network architecture but also the preprocessing of the input image. Extracting or enhancing the meaningful featuresof the input image in the preprocessing stage can help to improve the
CNN performance. In this paper, we focus on the use of the well-known
image processing filters, such as the edge extraction and denoising, andadd the preprocessed images to the input of CNNs. As the optimal filter
selection depends on dataset, we develop a joint optimization methodof CNN and image processing filter selection. We represent the image
processing filter selection by a binary vector and introduce the probability distribution of the vector. To derive the gradient-based optimization
algorithm, we compute the gradients of weight and distribution parameters on the expected loss under the distribution. The proposed method
is applied to an embryo grading task for in vitro fertilization, where theembryo grade is assigned based on the morphological criterion. The experimental result shows that the proposed method succeeds to reduce
the test error by more than 8% compared with the naive CNN models.
Keywords: Convolutional Neural Network · Image Processing Filter ·Embryo Grading · In Vitro Fertilization?

This is an author version of the paper accepted to the 14th International Symposium
on Visual Computing (ISVC 2019). The final authenticated version is available online
at https://doi.org/10.1007/978-3-030-33723-0_2.
??
Equal contribution

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K. Uchida et al.

1

Introduction

Convolutional neural networks (CNNs) continue to update the state-of-the-art
performance of image classification and detection. The performance improvement of CNNs is not only caused by the architecture design but also preprocessing of input images. Traditional image processing filters, such as denoising andedge enhancement filters, help to remove unuseful noise or extract importantfeatures in input images. For instance, Calderon et al. [4] analyze the impact
of denoising, contrast, and edge enhancement as a preprocessing for CNN, andshow that such preprocessing has the potential to improve the performance of
CNN in X-ray image dataset.
Adequate preprocessing should be selected depending on the datasets to exploit the potential of image preprocessing for CNNs. We focus on the problem
to select the adequate image processing filters as preprocessing from candidates
prepared in advance. In this paper, we develop a method for optimizing the image processing filter selection during a single CNN training. In our method, abinary vector represents the selection of image processing filters, i.e., each bit
indicates that the corresponding filter is selected or not. It is difficult to optimize the binary vector by gradient method because it is discrete. To handle thisdifficulty, we consider the multivariate Bernoulli distribution as the underlying
distribution of the binary vector and introduce an alternative differentiable objective function parameterized by the distribution parameters and the weights ofa neural network. This relaxation technique is called stochastic relaxation, which
is used in the one-shot neural architecture search [1,13] and embedded feature
selection [14]. Instead of directly optimizing the binary vector, we optimize the
distribution parameters jointly with the weights. Figure 1 shows the conceptual
image of the proposed method. Since the proposed method requires the modeltraining only once, the increase of computational time is not significant.
We believe that the image processing filters, such as edge detection anddenoising, are useful for medical images rather than for general object images,
because a small difference in the edge or shape may be important in medical
images. To verify the effect of our selection scheme of image processing filters,
we apply the proposed method to the prediction of embryo grade for in vitro
fertilization (IVF) using day 3 embryo images. The experimental result showsthat the proposed method can reduce the test error by more than 8% comparedwith the naive CNN model without image processing filters.

2

Joint Optimization of CNN and Image Preprocessing
Filter Selection

We consider the general problem setting on supervised learning with a given
training image dataset D = {X, Y }. Let X = {x1 , . . . , xN } be the set of input
images, and Y = {y1 , . . . , yN } be the set of corresponding target variables. The
goal of a machine learning algorithm is to find a better-generalized model φ :x 7→ y that works well on unseen (test) data (x, y).

Joint Optimization of CNN and Image Preprocessing Selection
Sampling
Binary Vector

Image Filters

Bernoulli Distribution

Update Distribution

...
1 0

1 0

1 0

0

Sha3

Expected Loss

...

...

...

CNN Model

SobV5(Natural Gradient Descent)1

Update CNN weight(Gradient Descent)Update CNN and Distribution
Simultaneously

1

Nop

Image of
Embryo3

Selection of Image Filters

Fig. 1. Conceptual illustration of the proposed method.

In this paper, we consider a CNN model with image preprocessing denotedby φ(W, M ) parameterized by the weight vector W and binary vector M ∈M = {0, 1}d , where M represents the filter selection. Each bit in M determines
whether or not the preprocessed image by the corresponding filter appears in
the input images for CNN.
Specifically, we prepare the image processing filters, ψ1 , . . . , ψd , that transform an original image x into the filtered images x̄ = {ψ1 (x), . . . , ψd (x)}. Thesefilters are expected to extract or enhance the useful features of the original image. The filtered images are concatenated to the channel direction and used as
the input of CNN. We determine whether each filtered image is included in the
input of CNN by the binary vector. Therefore, the input of CNN can be obtainedby {m1 ψ1 (x), . . . , md ψd (x)}, where mi ∈ {0, 1} indicates i-th element of M . As
the useful image processing filters depend on datasets and the unmeaningful
filters may lead the performance deterioration, we develop the algorithm thatfinds the better binary vector in a single CNN training.
Given a loss function L(W, M ) to be minimized, such as the cross-entropy,
the gradient with respect to (w.r.t.) M cannot be obtained because M is discretevariable. We transform the original objective into the differentiable one by using the probability distributionof M . Let us consider the multivariate Bernoulli
Qd
distribution pθ (M ) = i=1 θimi (1 − θi )1−mi , where θ ∈ Θ ⊆ [0, 1]d is the distribution parameter. The value θi is the probability that mi becomes 1 and can be
regarded as the selection probability of the i-th filter. By taking the expectationof L(W, M ) under the distribution, we get an alternative objective function for
W and θ: G(W, θ) = Epθ [L(W, M )]. This transformation of objective function iscalled stochastic relaxation. Different from the original objective function L, thetransformed objective function G is differentiable w.r.t. both W and θ.
We adopt the optimization algorithm proposed in [13,14] to minimize theexpected loss G(W, θ). The vanilla (Euclidian) gradient
P w.r.t. W and the natural gradient w.r.t. θ are given by ∇W G(W, θ) =M ∈M ∇W L(W, M )pθ (M )˜ θ G(W, θ) = P
˜ θ ln pθ (M )pθ (M ), respectively, where ∇
˜θ =
and ∇
L(W,
M
)
∇
M ∈M
F (θ)−1 ∇θ is the so-called natural gradient [3] that is the steepest direction of θ
w.r.t. the Kullback-Leibler divergence, and F (θ) is the Fisher information ma-

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K. Uchida et al.

trix of pθ . The training of the model φ is done by iteratively updating both W
and θ to the above gradient direction.
In practice, these gradients are approximated by Monte-Carlo using λ samples, M1 , . . . , Mλ , drawn from pθ . Also, the loss function is approximatedusing
P
N mini-batch data samples Z as L(W, M ) ≈ L̄(W, M ; Z) = N1 z∈Z l(z, W, M ),where l(z, W, M ) represents the loss of a datum. Consequently, the gradient w.r.t.
W is given byλ1X∇W G(W, θ) ≈∇W L̄(W, Mi ; Z) .
(1)
λ i=1
The gradient ∇W L̄(W, Mi ; Z) can be computed using back-propagation and we
can use any stochastic gradient descent (SGD) method for optimizing W .
Since we consider the Bernoulli distribution as pθ , the natural gradient of
˜ ln pθ (M ) = M − θ. Then,the log-likelihood can be analytically obtained as ∇˜ θ G(W, θ) ≈we can get the approximation of the natural gradient w.r.t. θ as ∇Pλ
1i=1 L̄(W, Mi ; Z)(Mi − θ). For the natural gradient estimate, we transformλthe loss value into the ranking-based utility as was done in [13,14] as follows:ui = 1 for best dλ/4e samples, ui = −1 for worst dλ/4e samples, otherwise
ui = 0. The ranking-based utility transformation makes the algorithm invariant
to the order preserving transformation of L. With this utility transformation,the θ update becomesλθ(t+1) = θ(t) +ηθ Xui (Mi − θ(t) ) ,
λ i=1

(2)

where ηθ is the learning rate for θ. We note that the minimization problem
is turned into the maximization problem due to the utility transforms. In thealgorithm implementation, we restrict the range of θi within [1/d, 1 − 1/d] tokeep the possibility of generating any binary vector. The training procedure issummarized in Algorithm 1.
After the model training, we choose the most likely binary vector to predicta new data as M̂ = argmaxM pθ (M ) such that mi = 1 if θi ≥ 0.5, otherwise
mi = 0. Then, we predict new data using the image processing filters decidedby M̂ .

3

Embryo Grading Task and Dataset

IVF is the most common fertility treatment which assists a woman for getting
pregnancy with genetic technology. The low success rate of IVF has become amajor issue to date. According to [6], embryo grading is responsible for around
one-third of implantation failures. Hence, the determination of the morphological embryo grading for the base of the selection is very important. Currently,
the embryo selection is done through a manual grading by embryologist using a
microscope. The manual selection makes the process dependent on the embryologist’s skills and experiences. Therefore, embryo grading is subjective and theJoint Optimization of CNN and Image Preprocessing Selection

5

Algorithm 1: The training procedure of the proposed method.
Input: Training data D and hyperparameters {λ, ηθ }Output: Optimized parameter of W and θ
1 begin2
Initialize the connection weights of CNN and Bernoulli distribution
parameter as W (0) and θ(0)3t←04while not stopping criterion is satisfied do
5
Get N mini-batch samples from D
6
Sample M1 , . . . , Mλ from pθ(t)7Compute the loss L̄(W, Mi ) for each sample
8
Update the distribution parameter to θ(t+1) using (2)9Force θ(t+1) ∈ [1/d, 1 − 1/d]d10Update the connection weights to W (t+1) using (1) by any SGD
11
t←t+1

fate of an embryo is determined only based on restricted information and observation. The machine learning techniques have been applied to embryo images toautomate and improve the embryo grading process. For instance, the number ofcells in day 3 embryo, one of the important criterion to determine the embryo
grade, was predicted using features extracted from embryo image by conditionalrandom fields [11] or Adaboost [19]. Khan et al. [8] showed that CNN could
improve the performance of cell counting in embryo image. Also, CNN was used
to predict the embryo grading from the fifth day’s embryo image directly [5,9].
In this paper, we use the day 3 embryo images that were collected from2016 to 2018 at the Infertility Clinic in Indonesia. The day 3 embryo grading ismore crucial than the day 5 embryo grading since it makes the decision whether
the embryo will be transferred to uterus or cultured until the blastocyst phase[2,12]. The grade of the embryo was categorized by an embryologist based on
the standard morphological criterion introduced by [18]. Due to the limitationof the dataset, the grades for embryos were adjusted to be 3 groups; they could
be either excellent, moderate, or poor. Table 1 shows the correspondence of ourgrading scheme with the grading of [18] and the morphological criterion. The
dataset consisted of 254, 599, and 533 images for excellent embryos, moderate
embryos, and poor embryos, respectively. The total number of images was 1386,
which was collected from 238 patients, and each patient had about 4 embryoson the 3rd day. Figure 2 shows the examples of the embryo for each grade.
The task is to classify the embryo images into three categories (grades). In theexperiment, the images were resized to 128 × 128 and converted to grayscale.
Then, we randomly assigned 80 % of all images as the training dataset, and 20% as the test dataset.

6

K. Uchida et al.

Table 1. Correspondence of the modified grading applied to our dataset with the grade
introduced by [18] and morphological criterion for the embryo on the 3rd day.
Grade [18]Modified Grade

Number of Cells

Blastomere

Fragmentation

1
2
3
4
5

Excellent
Moderate
Poor
Poor
Poor

7-8 cells
7-8 cells
6-8 cells
4-6 cells
4-5 cells

Similar
Similar
Fairly similar
Fairly similar
Not Similarless than 5%
5 − 15%15 − 25%
25 − 30%
more than 30%

Fig. 2. Examples of embryo image in excellent (left), moderate (center), and poor(right) grades.

4

Experiment and Result

4.1

Experimental Setting

The CNN architecture used in the experiment is based on the VGG-Net [15]consisting of 16 convolutional layers with 3 × 3 kernel. Different from the original VGG-Net, we add the batch normalization in the convolutional and fullyconnected layers and remove the dropout [16] in the fully-connected layers. In
addition, we insert the global average pooling [10] before the first fully-connected
layer. As our embryo grading task is classification, the loss function is the softmax cross-entropy.
We set the mini-batch size to 64 and the maximum number of epochs to
3,000 (about 54,000 training iterations). The weight parameters are initialized
by He’s initialization [7] and optimized by using Nesterov’s accelerated stochastic
gradient method [17] with a momentum of 0.9. We also use the weight decay of
10−4 for the training of the weight parameters. The learning rate for the weights
is initialized by 0.1 and divided by 10 at 1/2 and 3/4 of the maximum numberof epochs. These parameter settings are based on [13].
We prepare 15 image processing filters including no operation (Nop) listed
in Table 2. The sample size of the binary vector in each iteration is λ = 2, andthe learning rate for distribution parameters is set to ηθ = 1/15. The distribution parameters θ are initialized by 0.5. Each preprocessed image by the image
processing filters is standardized, i.e., each pixel value is subtracted by the mean

Joint Optimization of CNN and Image Preprocessing Selection

7

Table 2. Image processing filters used in the experiment.
Filter−Original image
Blur filter
Gaussian filter
Sharpening filter
Laplacian filter
Vertical-Sobel filter
Horizontal-Sobel filter
Median filter

Nop
−
−
−
−
−
−
−

Abbreviation(3x3 kernel)(5x5 kernel)
−
Blur3
Gau3
Sha3
Lap3
SobV3
SobH3
Med3

−
Blur5
Gau5
Sha5
Lap5
SobV5
SobH5
Med5

pixel value and divided by the standard deviation. Also, we apply the standard
data augmentation, i.e., shifting, flipping, and rotation, to the filtered images.
To investigate the effect of the proposed method, we compare the following
four models:
1. No Filter: the model without image preprocessing filters (naive CNN)
2. All Filters: the model using all preprocessed images as inputs
3. Random: the model with fixed filter selection probability of 0.5 (i.e., ourmethod without θ optimization)
4. Joint Optimization (ours): the model that are jointly optimized CNN
and the image preprocessing filter selection
We report the experimental results based on five trials with different random
seeds. For the compared models, No Filter, All Filters, and Random, we set themini-batch size to 128. The numbers of data samples used to the parameters
update become equal among all models by setting such batch size because ourmethod uses the doubled number of data samples (λ = 2) in each iteration.
4.2

Result and Discussion

Figure 3 shows the transitions of the median value and the inter-quartile rangeof test error for each model. Our method can reduce the test error than theother models after about 5000 iterations. The values of median (lower andupper quartile) of the test error at the final iteration are as follows; No Filter: 39.57% (37.05%, 39.93%), All Filters: 38.13% (38.13%, 42.45%), Random:
46.04% (44.24%, 50.72%), and Joint Optimization (ours): 28.78% (26.62%, 28.78%).
We observe that our method significantly reduces the test error at the final iteration by more than 8 % compared to No Filter and All Filters. This result
implies that the redundant image preprocessing has the potential to lead a adverse effect, but selecting appropriate filters can improve the performance of
CNN. The result of Random significantly worse than other models, suggestingthat the optimization algorithm of our method can work well. We note that the
total training time of all models is more or less the same. Thus, the proposed

8

K. Uchida et al.
65

No Filter
All Filters
RandomJoint Optimization

60

Test Error (%)

55
50
45
40
35
30
25
0

10000

20000

30000

40000

50000

Number of Iterations

Fig. 3. Transitions of test error for each model.

method can improve the prediction accuracy without additional computational
cost.
Figure 4 depicts the confusion matrices of test data for each model. We cansee that the recall obtained by our method is higher than others for moderate
and poor grades. For the excellent grade, the accuracy of all models is not sohigh, and the excellent embryo tends to be predicted incorrectly as the moderate
grade. According to Table 1, the difference between the excellent grade andmoderate grade is only the amount of fragmentation. We believe that this poor
accuracy for excellent embryo data is because the number of data graded as
excellent is not sufficient for learning such differences. We emphasize that theratio of the worst misclassification, where the excellent embryo is predicted aspoor, or the inverse case, is very low in our method. From the viewpoint of IVF,
this result is encouraging as both of the excellent and moderate embryos canbe transferred to the uterus. Moreover, distinguishing poor embryo is the mostimportant task because the worst situation is transferring the poor embryo tothe uterus. This improvement suggests that the selected image processing filters
can extract useful features for accurate grade prediction.
Figure 5 shows the preprocessed images and their selection probabilities at
the final iteration. We observe that the selection probability of Nop is not high,
implying that the preprocessed images are useful in embryo grade prediction
rather than the original image. The filters whose selection probability is morethan 0.8 are Sha3, Sha5, SobV3, SobV5, SobH3, SobH5, Med3, and Med5. Regarding the criterion of embryologist in Table 1, Med3 and Med5 contribute toeliminating the fragmentation, and Sha3 and Sha5 conversely emphasize them.
The edge detection filters (SobV3, SobV5, SobH3, and SobH5) are expected tohelp to count the embryo and to determine the similarity of blastomere.

5

Conclusion

We have proposed the method that jointly optimizes CNN and the image processing filter selection. We introduced the Bernoulli distribution as a law of

Joint Optimization of CNN and Image Preprocessing Selection
All Filters

excellent

0.400
(22)

0.582
(32)

0.018
(1)

0.491
(27)

0.491
(27)

0.018
(1)

moderate

0.139
(16)

0.617
(71)

0.243
(28)

0.113
(13)

0.635
(73)

0.252
(29)

poor

0.046
(5)

0.259
(28)

0.694
(75)

0.037
(4)

0.296
(32)

0.667
(72)

RandomJoint Optimization
0.000
(0)

moderate

0.139
(16)

0.513
(59)

0.348
(40)

0.061
(7)

0.774
(89)

0.165
(19)

poor

0.046
(5)

0.222
(24)

0.731
(79)

0.009
(1)

0.204
(22)

0.787
(85)

m

ex

m

ex

po
or

0.564
(31)

od
er
at
e

0.436
(24)

ce
lle
nt

0.182
(10)

po
or

0.600
(33)

od
er
at
e

0.218
excellent
(12)

ce
lle
nt

True GradeNo Filter

9

Predicted GradeFig. 4. Confusion matrices of test data for each model. The values in each cell indicate
the ratio of data samples classified into each category, and the values in parentheses
indicate the number of data samples. We report the confusion matrix of the trial thatrecorded the median of test error for each model.

binary vector for filter selection. The distribution parameter and the connection
weight of CNN were jointly updated to the gradient directions. We applied the
proposed method to the embryo grading prediction for IVF, where the labels of
the dataset were given by an embryologist based on the morphological criteria.
We have shown that the test error of the proposed method can be reduced bymore than 8 % compared to naive CNN.
The different types of image processing filters are often applied several times
to extract and enhance meaningful features. In our method, each image processing filter is employed only once to the original image. Optimizing the combination of image processing filter sequences is one of the future works. In theembryo image dataset, we consider that the prediction of the excellent grade
directly is difficult because its criteria are similar to those of moderate grade.
Therefore, constructing the CNN that predicts the criteria for embryo grading,i.e., cell number, the similarity of blastomere and amount of fragmentation, may
contribute to the improvement of the prediction accuracy for embryo grading.
In the experiment of this paper, most of the prepared filters were linear filtersand can be represented by a convolution operation in CNNs. Nevertheless, we
confirmed that the proposed method is useful in our embryo dataset. Although
the evaluation of our method on other datasets, such as large scale dataset,

10

K. Uchida et al.

Nop (0.27)

Blur3 (0.40)

Blur5 (0.20)

Gau3 (0.07)

Gau5 (0.10)

Sha3 (0.90)

Sha5 (0.93)

Lap3 (0.37)

Lap5 (0.07)

SobV3 (0.93)

SobV5 (0.93)

SobH3 (0.93)

SobH5 (0.93)

Med3 (0.93)

Med5 (0.93)

Fig. 5. Preprocessed images of the embryo by the image processing filters. The values
in the parentheses are the selection probability of each filter, where the bold font means
the selection probability is higher than 0.8. The result is the trial that recorded the
median of test error.

is another important future work. In addition, as our method can adopt nonlinear and non-differentiable image preprocessing, adding such non-linear filters
is promising future work.

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