CLINICAL STUDY
Quantitative Analysis of Face Symmetry Abraham Tamir, MD Abstract: The major objective of this article was to report quantitatively the degree of human face symmetry for reported images taken from the Internet. From the original image of a certain person that appears in the center of each triplet, 2 symmetric combinations were constructed that are based on the left part of the image and its mirror image (left-left) and on the right part of the image and its mirror image (right-right). By applying a computer software that enables to determine length, surface area, and perimeter of any geometric shape, the following measurements were obtained for each triplet: face perimeter and area; distance between the pupils; mouth length; its perimeter and area; nose length and face length, usually below the ears; as well as the area and perimeter of the pupils. Then, for each of the above measurements, the value C, which characterizes the degree of symmetry of the real image with respect to the combinations right-right and left-left, was calculated. C appears on the right-hand side below each image. A high value of C indicates a low symmetry, and as the value is decreasing, the symmetry is increasing. The magnitude on the left relates to the pupils and compares the difference between the area and perimeter of the 2 pupils. The major conclusion arrived at here is that the human face is asymmetric to some degree; the degree of asymmetry is reported quantitatively under each portrait.
FIGURE 1. Caricatures describe different persons using exaggeration of their faces and looking that is also more increased by their symmetrical images.
(J Craniofac Surg 2015;26: 1268–1269)
hands, wrists, and ears are equal in width) is more likely to be viewed as attractive by women. Scientists discovered that people with a high level of face symmetry, when the left side of the face is very similar to the right side, have lower chances of having psychologic problems when they are 79 to 83 years old. According to Cogprints,2 right-right composites of women’s faces were judged as significantly healthier than left-left composites, whereas in men’s faces, no significant left-left difference emerged.2
S
QUANTITATIVE RESULTS OF FACE SYMMETRY AND MAJOR CONCLUSIONS
Key Words: Face symmetry
ymmetry is what occurs when 1 side of something mirrors the other. If you were to draw a midline, called a line of symmetry, from the top of your forehead, down the middle of your nose, over your lips, and to the bottom of your chin, you could see that your eyes, ears, nostrils, and teeth all mirror each other on either side of the line. Thus, symmetry may also be defined as the ‘‘exact reflection of form on opposite sides of a dividing line or plane.’’ Facial symmetry is 1 of a number of traits associated with health, physical attractiveness, and beauty of a person or animal. According to Wikipedia,1 symmetric faces, namely those that have the same dimensions and patterns on both sides of the face, are typically seen as more attractive than unsymmetric ones.1 Symmetry is apparently important throughout the body and not simply in the face. A man who has greater overall symmetry (whose feet, ankles, elbows,
From the Ben-Gurion University of the Negev, Beer-Sheba, Israel. Received October 4, 2014. Accepted for publication January 21, 2015. Address correspondence and reprint requests to Abraham Tamir, Ben-Gurion University of the Negev, Beer-Sheba, Israel; E-mail: [email protected] The author reports no conflict of interest. Copyright # 2015 by Mutaz B. Habal, MD ISSN: 1049-2275 DOI: 10.1097/SCS.0000000000001610
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Pictures of triplets of 37 images arranged in an increasing order of symmetry demonstrate the results of our quantitative survey
FIGURE 2. Eleven real faces located in the center of each triplet and consisting of 17 important people. All faces are distorted due to their right-right and leftleft combination creating symmetrical non-real images.
The Journal of Craniofacial Surgery
Volume 26, Number 4, June 2015
Copyright © 2015 Mutaz B. Habal, MD. Unauthorized reproduction of this article is prohibited.
The Journal of Craniofacial Surgery
Volume 26, Number 4, June 2015
FIGURE 3. Twelve real faces located in the center of each triplet and consisting of 17 people. All faces are distorted due to their right-right and left–left combination creating symmetrical non-real images.
(Figs. 1–3). Two kinds of pictures are presented. The caricatures were painted by the very famous Israeli caricaturist Shlomo Cohen that was selected from his book.3 The 23 real faces are pictures of images found in the Internet. In selecting the pictures, special attention was paid that they are exact front views of the image. For each original image of a certain person that appears in the center of each triplet, 2 symmetric combinations were constructed that are based on the left part of the image and its mirror image (left-left) and on the right part of the image and its mirror image (right-right). By applying a computer software, the Jar program, that enables to determine length, surface area, and perimeter of any geometric shape, the following measurements were obtained for each triplet: face perimeter and area; distance between the pupils; mouth length; its perimeter and area; nose length and face length, usually below the ears; as well as the area and perimeter of the pupils. Then, for each of the above measurements, the ratio C was
#
2015 Mutaz B. Habal, MD
Quantitative Analysis of Face Symmetry
calculated using the following formula: C ¼ [(B A)/A] 100, where A is the numerical magnitude of each of the above quantities in the original image, B corresponds to the symmetric image, and C is the relative deviation. In the pictures reported, each image is characterized by 2 numerical quantities written below. On the right appears the mean of all measured C quantities that characterizes the degree of symmetry of the real image with respect to the combinations right-right and left-left. The magnitude on the left relates to the pupils and compares the difference between the area and perimeter of the 2 pupils. The major conclusions drawn from the study are summarized as follows: (1) All images have some degree of asymmetry. The reasons for this phenomenon are the following: (a) The fact that each half of our brain has a different function is probably a reason for the facial asymmetry. (b) The chance is almost zero that all milliards of cells that build our faces will be distributed in a complete symmetry from our birth to death. (2) In addition to faces, eyes and pupils are also asymmetric with respect to their area and perimeter. In general, the asymmetry of the pupils is lower than that of the faces. (3) In general, the reported asymmetry of the 3 babies and the 1 child is lower than that of the adults. These results agree with the results of Ref. 4, in which higher asymmetry has been shown in the elderly (those aged > 80 y) compared with people between the ages of newborn and 45 years.4 (4) The following mean results were obtained based on the measurements of 103 images: (a) 31% is the degree of asymmetry of the real image with respect to the combinations right-right and left-left; (b) 13% is the degree of asymmetry between the area and perimeter of the 2 pupils; and (c) the total mean of a þ b is 44%.
REFERENCES 1. Wikipedia. Facial Symmetry. Available at: http://en.wikipedia.org/wiki/ Facial_symmetry. Accessed April 21, 2015 2. Available at: http://cogprints.org/1715/0/LateralityHealth.pdf. Accessed April 21, 2015 3. Cohen S. Overview [in Hebrew]. Israel: Arigent, 2008 4. NHS Choices. Facial Symmetry Decline. Available at: http://www.nhs. uk/news/2009/08August/Pages/FacialSymmetryDecline.aspx. Accessed April 21, 2015
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Copyright © 2015 Mutaz B. Habal, MD. Unauthorized reproduction of this article is prohibited.
Quantitative Analysis of Face Symmetry Abraham Tamir, MD Abstract: The major objective of this article was to report quantitatively the degree of human face symmetry for reported images taken from the Internet. From the original image of a certain person that appears in the center of each triplet, 2 symmetric combinations were constructed that are based on the left part of the image and its mirror image (left-left) and on the right part of the image and its mirror image (right-right). By applying a computer software that enables to determine length, surface area, and perimeter of any geometric shape, the following measurements were obtained for each triplet: face perimeter and area; distance between the pupils; mouth length; its perimeter and area; nose length and face length, usually below the ears; as well as the area and perimeter of the pupils. Then, for each of the above measurements, the value C, which characterizes the degree of symmetry of the real image with respect to the combinations right-right and left-left, was calculated. C appears on the right-hand side below each image. A high value of C indicates a low symmetry, and as the value is decreasing, the symmetry is increasing. The magnitude on the left relates to the pupils and compares the difference between the area and perimeter of the 2 pupils. The major conclusion arrived at here is that the human face is asymmetric to some degree; the degree of asymmetry is reported quantitatively under each portrait.
FIGURE 1. Caricatures describe different persons using exaggeration of their faces and looking that is also more increased by their symmetrical images.
(J Craniofac Surg 2015;26: 1268–1269)
hands, wrists, and ears are equal in width) is more likely to be viewed as attractive by women. Scientists discovered that people with a high level of face symmetry, when the left side of the face is very similar to the right side, have lower chances of having psychologic problems when they are 79 to 83 years old. According to Cogprints,2 right-right composites of women’s faces were judged as significantly healthier than left-left composites, whereas in men’s faces, no significant left-left difference emerged.2
S
QUANTITATIVE RESULTS OF FACE SYMMETRY AND MAJOR CONCLUSIONS
Key Words: Face symmetry
ymmetry is what occurs when 1 side of something mirrors the other. If you were to draw a midline, called a line of symmetry, from the top of your forehead, down the middle of your nose, over your lips, and to the bottom of your chin, you could see that your eyes, ears, nostrils, and teeth all mirror each other on either side of the line. Thus, symmetry may also be defined as the ‘‘exact reflection of form on opposite sides of a dividing line or plane.’’ Facial symmetry is 1 of a number of traits associated with health, physical attractiveness, and beauty of a person or animal. According to Wikipedia,1 symmetric faces, namely those that have the same dimensions and patterns on both sides of the face, are typically seen as more attractive than unsymmetric ones.1 Symmetry is apparently important throughout the body and not simply in the face. A man who has greater overall symmetry (whose feet, ankles, elbows,
From the Ben-Gurion University of the Negev, Beer-Sheba, Israel. Received October 4, 2014. Accepted for publication January 21, 2015. Address correspondence and reprint requests to Abraham Tamir, Ben-Gurion University of the Negev, Beer-Sheba, Israel; E-mail: [email protected] The author reports no conflict of interest. Copyright # 2015 by Mutaz B. Habal, MD ISSN: 1049-2275 DOI: 10.1097/SCS.0000000000001610
1268
Pictures of triplets of 37 images arranged in an increasing order of symmetry demonstrate the results of our quantitative survey
FIGURE 2. Eleven real faces located in the center of each triplet and consisting of 17 important people. All faces are distorted due to their right-right and leftleft combination creating symmetrical non-real images.
The Journal of Craniofacial Surgery
Volume 26, Number 4, June 2015
Copyright © 2015 Mutaz B. Habal, MD. Unauthorized reproduction of this article is prohibited.
The Journal of Craniofacial Surgery
Volume 26, Number 4, June 2015
FIGURE 3. Twelve real faces located in the center of each triplet and consisting of 17 people. All faces are distorted due to their right-right and left–left combination creating symmetrical non-real images.
(Figs. 1–3). Two kinds of pictures are presented. The caricatures were painted by the very famous Israeli caricaturist Shlomo Cohen that was selected from his book.3 The 23 real faces are pictures of images found in the Internet. In selecting the pictures, special attention was paid that they are exact front views of the image. For each original image of a certain person that appears in the center of each triplet, 2 symmetric combinations were constructed that are based on the left part of the image and its mirror image (left-left) and on the right part of the image and its mirror image (right-right). By applying a computer software, the Jar program, that enables to determine length, surface area, and perimeter of any geometric shape, the following measurements were obtained for each triplet: face perimeter and area; distance between the pupils; mouth length; its perimeter and area; nose length and face length, usually below the ears; as well as the area and perimeter of the pupils. Then, for each of the above measurements, the ratio C was
#
2015 Mutaz B. Habal, MD
Quantitative Analysis of Face Symmetry
calculated using the following formula: C ¼ [(B A)/A] 100, where A is the numerical magnitude of each of the above quantities in the original image, B corresponds to the symmetric image, and C is the relative deviation. In the pictures reported, each image is characterized by 2 numerical quantities written below. On the right appears the mean of all measured C quantities that characterizes the degree of symmetry of the real image with respect to the combinations right-right and left-left. The magnitude on the left relates to the pupils and compares the difference between the area and perimeter of the 2 pupils. The major conclusions drawn from the study are summarized as follows: (1) All images have some degree of asymmetry. The reasons for this phenomenon are the following: (a) The fact that each half of our brain has a different function is probably a reason for the facial asymmetry. (b) The chance is almost zero that all milliards of cells that build our faces will be distributed in a complete symmetry from our birth to death. (2) In addition to faces, eyes and pupils are also asymmetric with respect to their area and perimeter. In general, the asymmetry of the pupils is lower than that of the faces. (3) In general, the reported asymmetry of the 3 babies and the 1 child is lower than that of the adults. These results agree with the results of Ref. 4, in which higher asymmetry has been shown in the elderly (those aged > 80 y) compared with people between the ages of newborn and 45 years.4 (4) The following mean results were obtained based on the measurements of 103 images: (a) 31% is the degree of asymmetry of the real image with respect to the combinations right-right and left-left; (b) 13% is the degree of asymmetry between the area and perimeter of the 2 pupils; and (c) the total mean of a þ b is 44%.
REFERENCES 1. Wikipedia. Facial Symmetry. Available at: http://en.wikipedia.org/wiki/ Facial_symmetry. Accessed April 21, 2015 2. Available at: http://cogprints.org/1715/0/LateralityHealth.pdf. Accessed April 21, 2015 3. Cohen S. Overview [in Hebrew]. Israel: Arigent, 2008 4. NHS Choices. Facial Symmetry Decline. Available at: http://www.nhs. uk/news/2009/08August/Pages/FacialSymmetryDecline.aspx. Accessed April 21, 2015
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Copyright © 2015 Mutaz B. Habal, MD. Unauthorized reproduction of this article is prohibited.
