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Edited by: Rashmi Gupta, Indian Institute of Technology Bombay, India

Reviewed by: Jay Friedenberg, Manhattan College, United States; Federica Marcolin, Polytechnic University of Turin, Italy

This article was submitted to Cognitive Science, a section of the journal Frontiers in Psychology

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

There is a close relationship between the attractiveness of the face and the facial features. The shape of the facial features determines the level of attractiveness, in which the eyes and eyebrows are particularly vital. In this article, we proposed a method to study the facial attractiveness by combining global face shape and local geometric features of eye and eyebrow and using computer big data analysis for assistance. Firstly, we collected 300 images of East Asian female and use machine learning methods to evaluate the attractiveness scores of face images. Secondly, geometric models were constructed separately for the eyebrows and the eyes to obtain their geometric and shape features. Correlation analysis was performed on the obtained data to study their shape matching of different facial attractiveness rating levels. Finally, the relationship between the shape of face and eyebrows was analyzed by combining the facial ratio and the geometric features of the eyebrows. The research in this article can provide reference for medical and beauty institutions and women’s makeup, and further study in the field of facial aesthetic analysis based on geometric features.

Beauty has always been the center of countless topics. Maslow believes that human beings always have a yearning for beauty. Appreciation of beautiful things is an instinctive pursuit of human beings, and beautiful things are refreshing. Face is a special aesthetic object, and people’s evaluation of the attractiveness of others’ faces often occurs in daily life (

Among the factors affecting the attractiveness of the face, the geometric features of the face are essential. There are many kinds of judgment standards for the beauty of the face in ancient and modern China and foreign countries (

Female demand more cosmetics than male, which means that compared with male, “beauty” is more important for female, so there are many studies on the attractiveness of female’s faces.

Although there are many methods to study facial features and attractiveness, many studies focus on the distance and proportion between the facial features, without considering the shape features and matching degree of them. Face attractiveness can also be measured more comprehensively by the connection between local and global of the face. Previous studies have concentrated on one of the facial features associated with facial attractiveness, while eyebrows and eyes are very close to each other in the face, so we predict that there is a certain relationship between the combination of the two features and facial attractiveness. In this article, our contributions can be summarized as follows:

Firstly, we collect 300 Asian female images on the Internet and use machine learning to evaluate the attractiveness scores of all face images;

Secondly, construct geometric models of the eyebrows and eyes, and calculate the parameters of the eyebrows and eyes according to the characteristics of them, including the length, area, average width, curvature of the eyebrows, the size of the eyes and pupils, and the proportion of iris to whole eye. Combine the obtained data of geometric and shape features to analyze the relationship between the shape matching of the two and the facial attractiveness; and

Finally, extract the feature points of the face image, and analyze the relationship between the shape of face and eyebrow according to the distance between the feature points, combined with the face proportion and the geometric and shape features of the eyebrows.

In the next section we will introduce the materials and methods used in this work. Then the experimental results and discussion are given. The final section summarizes this article.

In this study, we used an image dataset containing 300 East Asian female face images publicly downloaded at

In today’s image processing field, due to the rapid development of science and technology and artificial intelligence, machine learning is occupying an increasingly important position. To accurately classify the beauty of 300 East Asian female’s faces, we used machine learning to evaluate the attractiveness scores of these facial images. The evaluation model is divided into two modules: training and testing. In the training process, the 68 feature points of the face image are extracted firstly, then the face feature vectors are extracted, and finally the training is performed according to the obtained feature vectors. The label of the average attractiveness score assessed by real-life evaluators cited in the classification model is from the article (

Prediction process of facial attractiveness score (Clarification: the training images were obtained from the SCUT-FBP dataset, which is publicly available at

The frontal_face_detector of dlib library in Python is primarily used as a face extractor and finally the facial landmark is written into the file. The obtained facial marked point image is shown in

Facial marked point image (Clarification: written informed consent was obtained from the individual for the publication of this image).

The four facial ratio features are calculated from each training image by using the feature points, and the obtained features are saved to a file.

The input data used in the training model are the features of the images and the artificial score label. In the process of training, PCA algorithm is used to reduce the dimension of the feature, and then the random forest training model is adopted.

According to the data and model obtained above, a CNN is designed for predicting the attractiveness score of self-selected images.

Network architecture of CNN.

The common shapes of eyebrows are shown in

Common shapes of eyebrow.

Firstly, the unilateral eyebrow image is taken from the frontal face image to normalize the size of 100 × 50, and then adaptively thresholded. Since the binary image after the adaptive thresholding has noise, the Blob analysis is used to eliminate the noise and a small amount of hair interference, a binary image of the normalized eyebrow area is obtained. For the value

where

where

Through adaptive thresholding, eyebrow regions can be accurately segmented, as shown in

The first line is the original image of the eyebrows, the second line is the binary image of the eyebrows after threshold segmentation and denoising, and the third line is the curve of the eyebrows.

Since the eyebrow images have been normalized, the area of the eyebrow varies among individuals. It can be obtained by dividing the binary eyebrow image by threshold and counting the number of pixels in the eyebrow area, that is, the number of white pixels in the binary image.

To calculate the length of eyebrows, first extract the curve of eyebrows. The curve diagram of eyebrows can be obtained from the binary graph of eyebrows, and the process is as follows: Firstly after obtaining the eyebrow binaries, the eyebrow area was detected; Secondly take the intermediate value of the maximum and minimum values of the ordinate on each abscissa of the eyebrow region, and traverse all abscissa values to obtain a series of points; Thirdly connect the points to get the curve of the eyebrows. As shown the third row in

It is defined as the area of the eyebrows divided by the length of the eyebrows.

The curve of eyebrow is a crucial parameter of eyebrow appearance, it is the important basis that people differentiates eyebrow. We need to get the curve of eyebrows first, and calculate the bending degree of eyebrows through the curve of eyebrows. The steps to calculate eyebrow curvature are as follows: Firstly, calculate the linear equation of two ends of eyebrow curve; Secondly, the distance from the point to the straight line is used to calculate the distance from all points on the eyebrow curve to the line equation except two end points; Thirdly, the furthest distance is defined as the degree of eyebrow curvature.

The calculation formula of distance

When we observe the shape of the eye, we can find that the eye can be approximately elliptical and the iris can be approximately circular. Therefore, in this article, we use least-squares fitting of ellipse and circle to obtain the geometric parameters of eyes and irises. Firstly, the image of the eye area is normalized to the size of 100 × 50, and then the edge detection and processing of the eye area are carried out with sobel operator to obtain the edge of the eye and iris, and the contour lines of the two are obtained by ellipse and circle fitting. Finally, the contour equation coefficient is used to calculate the area of eyes and irises.

Firstly, the normalized eye image is processed by edge detection with sobel operator, and the edges of eyes and irises are extracted and binarized. In the edge image processed in the previous step, there are both edge points of the eye contour and edge points of the non-eye contour. The true contours of the eye and iris are extracted by searching for the connected area with the largest edge pixel and making interference correction. The result of these two steps is shown in

These four are images of eye after normalized, processed by edge detection with sobel operator, searched for the connected area with the largest edge pixel and made interference correction.

In this article, the direct least-square method is used for fitting. The core of least squares technique is to find parameter sets that minimize the distance measure between data points and ellipses (

The general equation of the plane quadratic curve of an ellipse can be expressed by Eq. 5:

where _{i}) is called the “algebraic distance” of a point [_{i}, _{i}] to the conic ^{2} = 1, the general quadratic equation represented by the above formula is ellipse. Therefore, the ellipse fitting problem is transformed to find the minimum sum of squared algebraic distances between points and quadratic curves ^{2} = 1:

where

where ^{2} subject to the constraint ^{T}

This may be rewritten as:

where ^{T}^{+},(λi, μi

According to the proof in the literature (^{-1}^{-1} and conditional constraint matrix ^{2}.

Since the eigenvalue of _{i} are the solutions of ellipse fitting. The only solution:

After obtaining the six parameters of the elliptic equation, the geometric center of the ellipse is:

The long and short half axes are:

Then the area of the eye after ellipse fitting is:

The iris is approximately circular, so use the least-square circle to fit the iris profile. The basic principle of least square circle method (

The center (

The general Eq. 18 of the circle is a linear equation of

Take the partial derivative of

By solving the above equation

Based on the above method of least squares ellipse and circle fitting for eyes and irises, the final fitting results are shown in

The fitting results of eyes and irises.

Face shape is the most intuitive feature of face image, and the information of face shape is more stable, so people pay special attention to the face shape. Common face shapes include heart, round, oval, square and so on. In order to study the relationship between the shape of face and eyebrow, we used the facial transverse/longitudinal ratio D1/D2 shown in

D1/D2 is the transverse/longitudinal ratio of face. The green rectangle marks the point of the hairline after adding hairline detector (Clarification: written informed consent was obtained from the individual for the publication of this image).

Examples of four typical facial shapes: from left to right are square, oval, round, and heart. And the facial transverse/longitudinal ratio D1/D2 are 0.754, 0.791, 0.872, and 0.736, respectively (Clarification: written informed consents were obtained from the individuals for the publication of these images).

The 300 facial attractiveness scores obtained by machine learning method are: 92 images in the range of 2–3 scores, 146 images in the range of 3–4 scores, and 62 images in the range of 4–5 scores (the entire score range is 1–5, with a maximum of 5 points). Faces with higher attractiveness scores accounted for a larger proportion in order to promote effective researching of beautiful faces.

The distributions of eyebrow parameters obtained by using the geometric feature model of eyebrows constructed in the previous section are shown in

The four figures are length, curvature, area, average width distribution of eyebrow, respectively. The horizontal axis is the interval of the described parameter. The vertical axis is the number of images in the parameter interval.

The three figures are distributions of area of iris, proportion of iris to whole eye, area of eye, respectively. The horizontal axis is the interval of the described parameter. The vertical axis is the number of images in the parameter interval.

Through analyzing the data, it is found that there is a relationship between eyebrow curvature and eye size. We have drawn the scatter diagram of the two when the attractiveness scores of face images are within the range of 2–3, 3–4, and 4–5, respectively, as shown in

The three figures are the scatter diagrams of the eye area and curvature of eyebrow when the attractiveness scores of face images are within the range of 2–3, 3–4, and 4–5, respectively.

Data analysis of D1/D2 and eyebrow parameters revealed that there is a relationship between the shape of face and eyebrow. D1/D2, which is the ratio of transverse to longitudinal of the face, can be used to characterize the change in face shape. The closer D1/D2 is to 1, the rounder the face shape is, while the smaller D1/D2 is, the longer the face shape is.

The D1/D2 of the longitudinal axis is the average value in each eyebrow curvature parameter interval. The three curves show the relationship of the two between the attractiveness score intervals in 2–3, 3–4, and 4–5, respectively.

Facial attractiveness is closely linked to our daily life and social interaction. In this article, we propose an approach to study the attractiveness by combining the geometric and shape features of the eyebrows and the eyes, and the shape of face. The data used are 300 Asian female face images and scored using machine learning methods. The geometric models of eyebrows and eyes are constructed separately, and the proportions of face are calculated. Combine these geometric features in the face of different attractiveness rating levels to research the matching degree of eyebrows, eyes and face shape. The results show that the high-bending eyebrows with small eyes and round face, low-bending eyebrows with large eyes and longer face will make the facial image have a higher attractiveness score. This method has certain value and practical significance for exploring the relationship between the matching degree of facial features and the attractiveness of face, and can be used as a reference for plastic surgery hospitals or beauty institutions.

JZ proposed the idea. JZ, MZ, and CH analyzed the data. All authors collected all images, designed the experiments, and drafted and revised the manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.