JP4575619B2 - Real age estimation method - Google Patents
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- JP4575619B2 JP4575619B2 JP2001136792A JP2001136792A JP4575619B2 JP 4575619 B2 JP4575619 B2 JP 4575619B2 JP 2001136792 A JP2001136792 A JP 2001136792A JP 2001136792 A JP2001136792 A JP 2001136792A JP 4575619 B2 JP4575619 B2 JP 4575619B2
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- age
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【0001】
【発明の属する技術分野】
本発明は、実年齢の推定方法に関する。
【0002】
【従来の技術】
人は社会的動物であり、人が生きてゆくためには他人との交わりは避けて通ることができない。この様な人人との交わりにおいて、相手の属性を知ることは必要不可欠なことであるが、年齢などの情報は、上下関係或いはどの様な敬語を用いるかなどの交際上欠くべからざる情報であるが、それ自体がタブーであるため、なかなか情報として得ることは難しく、推定の元に対処するしか方法がなかった。この様な推定は多くの場合正確さに欠き、的確な実年齢の推定方法が求められていた。又、年齢と外的容貌の間には因果関係があることは誰しも知っていることではあるが、どの様な因果律があるかは全く知られておらず、外的容貌の変化には個体差も大きく、従ってその大きなばらつきのため、外的容貌を指標に的確な実年齢の推定を行うことは極めて困難であると考えられていた。
【0003】
他方、映画、演劇などの分野においては、俳優が実年齢とはかけ離れた役をこなすことが少なくなく、この様な場合には、設定上の年齢に合わせてメークアップなどによる印象年齢の調整を行っているが、時としてこの調整がうまく行かず、ストーリーに支障を来すことが少なくなかった。この様な場合において、設定年齢に見えるメークを行うことは重要なことであり、形態的な変化を具現化する、いわゆる特殊メーク技術そのものは発達しており、問題はどの様にメークするかの指針の欠如が大きな原因であると考えられている。この様な指針の策定が望まれていた。
【0004】
前記の印象年齢の調整方法は映画、演劇の分野のみならず、例えば、美容形成外科などの分野においても、しわやタルミを除く手技は知られていても、どこの部位のしわやタルミをどの様に強制するべきかの指針が明確ではないため的確な手術が行えないことがあることも否めず、印象年齢の的確な調整方法の開発は、社会全般に関わる問題であるといえる。
【0005】
【発明が解決しようとする課題】
本発明は、この様な状況下為されたものであり、的確な実年齢の推定或いは印象年齢の的確な調整の礎になる、外的容貌の形態と実年齢との間の因果律を明らかにすることを課題とする。
【0006】
【課題を解決するための手段】
本発明者らは、この様な状況に鑑みて、外的容貌の形態と実年齢との間の因果律を求めて、鋭意研究努力を重ねた結果、しわの形態と実年齢の間に非常によい相関性を見いだし、これが外的容貌の形態と実年齢の因果律であることに気づき、発明を完成させるに至った。即ち、本発明は、以下に示す、技術に関するものである。
(1)しわの程度の存在部位ごとのスコアを指標とする実年齢の推定方法であって、
被験者のしわの程度を、目尻、口周囲、鼻唇溝及び額の4種の存在部位ごとに、基準写真との比較によりスコア化し、
得られたスコアから、実年齢が既知の標本について得られたしわの程度の前記存在部位ごとのスコアと実年齢との関係を表す回帰式を用いて、推定年齢を算出することを特徴とする、実年齢の推定方法。
(2)前記スコア化が、5段階評定尺度の基準写真との比較により行われることを特徴とする、(1)に記載の実年齢の推定方法。
以下、本発明について、実施の形態を中心に更に詳細に説明を加える。
【0007】
本発明の実年齢の推定方法は、しわの程度の存在部位ごとのスコアを指標とすることを特徴とする。存在部位は、目尻、口周囲、鼻唇溝及び額の4種である。これらの位置のイメージを図1に示す。これらを的確に判定することにより、実年齢が的確に推定できる。これらの判定には、通常化粧料の分野で行われているしわの評価の基準を適用し、最も軽微なものをスコア1、最も重篤なものをスコア5とする5段階基準が好ましく例示できる。この様な基準は、具体的な基準写真を予め作成し、これとの比較によって判定する。この様な基準写真の1例を図2及び図3に示す。これらのスコアに重みをつけて計算することにより、より正確な実年齢の推定ができる。
【0008】
推定のための重さ付けは統計的な処理により行うことができる。即ち、年齢に広がりのある標本を、上記の判定基準に合わせて各部位のしわのスコアを判定し、重回帰分析を行えば、回帰式を得ることができ、この式を元に的確な実年齢の推定を行うことができる。後記の実施例に、この様な例を示す。
【0009】
又、印象年齢の調整法としては、上記のしわが実年齢によく相関していることを利用したものであり、実年齢に関与の大きいしわをなくしたり、見えにくくしたり或いは逆にしわを付与して歳を多めに見せたりすることができる。この様なしわの付与の順位は、上記のしわの寄与度への順位や回帰式や重相関回帰式を利用して、しわのスコアを試行錯誤で代入して外観年齢(印象年齢)をフィッティングさせて行けば、相当する年齢のしわの形状がシミュレートでき、これに基づいて顔の形状を調整すればよい。この様な技術は美容形成の処置の指針や特殊メークアップの指針とすることができる。この様な変化はコンピューターグラフィックを利用すれば、バーチャルに再現できるので、美容形成などに於いて的確な術後の予想を患者に提示できる。
【0010】
【実施例】
以下に、実施例を挙げて、本発明について、更に詳細に説明を加えるが、本発明が、かかる実施例にのみ限定されないことは言うまでもない。
【0011】
<実施例1>
(重回帰分析例)
40〜70代の日本人女性73名を標本として、美容専門家3名が標本の顔写真と図2及び図3に示す基準写真と比較し、目視によりしわのスコアを付した。このスコア値を説明変数として、目的変数を実年齢として重回帰分析を行った。変数はステップワイズ法により4個選択した。この結果、説明変数としては目尻のしわ、口周囲のしわ、鼻唇溝及び額のしわの4つが残った。これらの重相関係数は0.900で決定係数は0.811であった。これらの値は、1に極めて近く、しわのスコアが、実年齢と極めて良い相関関係にあることを示し、従って、かかるしわのスコアを評定することにより、実年齢を的確に推定できることがわかる。回帰式は以下の通り。
推定年齢(実年齢)=目尻のしわのスコア×3.642+鼻唇溝のスコア×2.244+口周囲のしわのスコア×2.448+額のしわのスコア×1.739+22.838
又、標準偏回帰係数は、目尻のしわが0.416、口周囲のしわが0.249、鼻唇溝が0.224及び額のしわが0.188であり、この順に実年齢への寄与度が高い。即ち、言い換えれば、外観年齢(印象年齢)を調整するには、これらの寄与度の高い部位のしわを調整することにより、容易に外観年齢の調整が行えることがわかる。
【0012】
<実施例2>
47名の女性の顔写真をモーフィングにより混合し、60歳の混合顔を作成した。この顔より各部位のしわを除去したしわ除去顔を102名のパネラーにより年齢を判定してもらった。又、別途平均顔のしわのスコアを判定したところ、目尻のしわが4.5、鼻唇溝が4、口の周囲が3.5及び額のしわが4であった。これを実施例1の推定式に代入し、推定年齢を計算すると63.72歳であり、極めて正確な推定が出来たことが判明した。更に、この推定式のしわスコアに1を代入して各しわ除去顔の推定年齢を算出した。結果を、パネラーの判定値と推定値の比較として、表1に示す。これより本発明の推定方法が適切であることが判る。これらの60歳の平均顔としわ除去顔を図4に示す。
【0013】
【表1】
【0014】
【発明の効果】
本発明によれば、的確な実年齢の推定或いは印象年齢の的確な調整の礎になる、外的容貌の形態と実年齢との間の因果律を明らかにすることが出来る。
【図面の簡単な説明】
【図1】しわの位置のイメージを示す図である。
【図2】しわ判定の基準写真を示す図である。(図面代用写真)
【図3】しわ判定の基準写真を示す図である。(図面代用写真)
【図4】60歳の平均顔とそのしわ除去顔を示す図である。(図面代用写真)[0001]
BACKGROUND OF THE INVENTION
The present invention also relates to estimate how the actual age.
[0002]
[Prior art]
A person is a social animal, and in order for a person to live, it is impossible to avoid fellowship with others. It is indispensable to know the attributes of the other person in the relationship with such people, but information such as age is information that is essential for companionship, such as hierarchical relationship or what honorifics are used. However, because it is a taboo in itself, it was difficult to obtain it as information, and there was no other way but to deal with the estimation. Such estimation is often inaccurate, and an accurate method for estimating the actual age has been required. Also, everyone knows that there is a causal relationship between age and external appearance, but what kind of causality is not known at all, and changes in external appearance Individual differences are also large, and therefore, due to their large variations, it was considered extremely difficult to accurately estimate the actual age using the external appearance as an index.
[0003]
On the other hand, in the fields of movies, theater, etc., actors often play roles that are far from the actual age. In such cases, adjustment of impression age by make-up etc. is adjusted according to the set age. I did, but sometimes this adjustment did not go well, and it often caused trouble for the story. In such cases, it is important to make makeup that looks like the set age, so-called special make-up technology that embodies morphological changes has developed, and the problem is how to make it. The lack of guidance is considered to be a major cause. The development of such guidelines was desired.
[0004]
The impression age adjustment method described above is not only in the field of movies and theater, but also in the field of cosmetic plastic surgery, for example, even if techniques other than wrinkles and tarmi are known, Since there is no clear guideline on how to enforce this, there is a case where accurate surgery may not be performed, and the development of an accurate method for adjusting impression age is a problem for society in general.
[0005]
[Problems to be solved by the invention]
The present invention has been made under such circumstances, and reveals the causality between the form of external appearance and the actual age, which is the basis for accurate estimation of actual age or accurate adjustment of impression age. The task is to do.
[0006]
[Means for Solving the Problems]
In light of this situation, the present inventors have sought for a causality between the external appearance form and the actual age, and as a result of earnest research efforts, I found a good correlation and realized that this was the causality of the form of external appearance and real age, and completed the invention. That is, the present invention relates to the following technologies.
(1) A method for estimating an actual age using a score for each site where wrinkles are present as an index,
The degree of wrinkle of the subject was scored by comparison with the reference photograph for each of the four types of existence sites of the corner of the eye, the circumference of the mouth, the nasal cleft and the forehead
From the obtained score, the estimated age is calculated using a regression equation that represents the relationship between the actual age and the score for each existing part of the degree of wrinkles obtained for a sample whose actual age is known , Real age estimation method.
(2) The method for estimating an actual age according to (1), wherein the scoring is performed by comparison with a reference photograph of a five-level rating scale.
Hereinafter, the present invention will be described in more detail with a focus on embodiments.
[0007]
The method for estimating the actual age according to the present invention is characterized in that the score for each site where wrinkles are present is used as an index. There are four types of sites: the corner of the eye, the periphery of the mouth, the nasal cleft and the forehead. Images of these positions are shown in FIG. By accurately determining these, the actual age can be accurately estimated. These decision to apply the criteria for evaluation of wrinkles taking place in the field of ordinary cosmetics, score those most minor 1, the most serious ones and score 5 out criteria preferably exemplified it can. Such criteria creates specific criteria photograph advance, you determined by comparison to this. An example of such a reference photograph is shown in FIGS. By calculating these scores with weights, it is possible to estimate the actual age more accurately.
[0008]
Weighting for estimation can be performed by statistical processing. In other words, if a wrinkle score is determined for a specimen with a wide range of age according to the above criteria and a multiple regression analysis is performed, a regression equation can be obtained. Age estimation can be performed. Such an example is shown in the examples described later.
[0009]
In addition, as the method of adjustment of impression age, is obtained by utilizing the fact that correlates well with my real age and above, or eliminate the sum to greater involvement in the actual age, it was in or or reverse difficult to see it is possible to show them a little longer the old to impart. Grant of the order of such wrinkles, using the rank and regression equation and multiple correlation regression equation to the contribution of the above wrinkle, appearance age by substituting a score of wrinkles by trial and error (the impression age) if you go by fitting, can simulate the shape of the wrinkles of the corresponding age, it is sufficient to adjust the shape of the face on the basis of this. Such a technique can be used as a guideline for cosmetic treatment or a special make-up guideline. Such changes can be reproduced virtually by using computer graphics, so that accurate postoperative predictions can be presented to the patient in cosmetic formation.
[0010]
【Example】
Hereinafter, the present invention will be described in more detail with reference to examples, but it is needless to say that the present invention is not limited to such examples.
[0011]
<Example 1>
(Example of multiple regression analysis)
As a sample a Japanese woman 73 people of 40 to 70 generations, beauty three experts is compared with a reference photograph showing the face photograph and FIGS. 2 and 3 of the specimen, was given the score of wrinkles by visual observation. The multiple regression analysis was performed with the score value as the explanatory variable and the objective variable as the actual age. Four variables were selected by the stepwise method. As a result, there remained four explanatory variables: the corners of the corners of the eyes, the wrinkles around the mouth, the nasal lip and the wrinkles of the forehead. These multiple correlation coefficients were 0.900 and the determination coefficient was 0.811. These values are very close to 1, the score of the wrinkles may indicate a very good correlation between the actual age, therefore, by assessing the score of such Shi Wa, it can be accurately estimated real age Recognize. The regression equation is as follows.
Estimated age (actual age) = score of eye wrinkle score x 3.642 + nose lip score x 2.244 + wrinkle score around mouth x 2.448 + forehead wrinkle score x 1.739 + 22.838
The standard partial regression coefficient is 0.416 for the corner of the corner of the eye, 0.249 for the wrinkle around the mouth, 0.224 for the nasal lip and 0.188 for the forehead. High degree. That is, in other words, to adjust the appearance age (impression age) by adjusting a ring of these high contribution site, it can be seen that can be performed easily look age-adjusted.
[0012]
<Example 2>
The face photos of 47 women were mixed by morphing to create a 60-year-old mixed face. The wrinkle-removed face obtained by removing wrinkles from each part from this face was judged by 102 panelists for age. Further, when the score of wrinkles on the average face was determined separately, it was 4.5 for the corners of the corners of the eyes, 4 for the nostril, 3 for the circumference of the mouth, and 4 for the forehead. When this was substituted into the estimation formula of Example 1 and the estimated age was calculated, it was 63.72 years old, and it was found that an extremely accurate estimation was possible. Furthermore, the estimated age of each wrinkle-removed face was calculated by substituting 1 into the wrinkle score of this estimation formula. The results are shown in Table 1 as a comparison between panel decision values and estimated values. This shows that the estimation method of the present invention is appropriate. The average face and wrinkle removal face of these 60 years is shown in FIG.
[0013]
[Table 1]
[0014]
【The invention's effect】
According to the present invention, it is possible to clarify the causality between the form of the external appearance and the actual age, which is the basis for the accurate estimation of the actual age or the accurate adjustment of the impression age.
[Brief description of the drawings]
FIG. 1 is a diagram illustrating an image of a wrinkle position.
FIG. 2 is a view showing a reference photograph for wrinkle determination. (Drawing substitute photo)
FIG. 3 is a view showing a reference photograph for wrinkle determination. (Drawing substitute photo)
FIG. 4 is a diagram showing an average face of 60 years old and its wrinkle-removed face. (Drawing substitute photo)
Claims (2)
被験者のしわの程度を、目尻、口周囲、鼻唇溝及び額の4種の存在部位ごとに、基準写真との比較によりスコア化し、
得られたスコアから、実年齢が既知の標本について得られたしわの程度の前記存在部位ごとのスコアと実年齢との関係を表す回帰式を用いて、推定年齢を算出することを特徴とする、実年齢の推定方法。A method for estimating the actual age using the score for each site of wrinkle as an index,
The degree of wrinkle of the subject was scored by comparison with the reference photograph for each of the four types of existence sites of the corner of the eye, the circumference of the mouth, the nasal cleft and the forehead
From the obtained score, the estimated age is calculated using a regression equation that represents the relationship between the actual age and the score for each existing part of the degree of wrinkles obtained for a sample whose actual age is known , Real age estimation method.
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JP2006023953A (en) * | 2004-07-07 | 2006-01-26 | Fuji Photo Film Co Ltd | Information display system |
JP2006081846A (en) * | 2004-09-17 | 2006-03-30 | Inforward Inc | Method and apparatus for estimating facial wrinkle |
US7972788B2 (en) | 2005-08-23 | 2011-07-05 | Fancl Corporation | Skin aging marker and technique for use thereof |
EP1920714A4 (en) | 2005-09-02 | 2010-03-10 | Pola Chem Ind Inc | Method of evaluating skin conditions and method of estimating skin thickness |
JP4273359B2 (en) | 2007-09-28 | 2009-06-03 | Necソフト株式会社 | Age estimation system and age estimation method |
CN102870136B (en) | 2010-06-21 | 2017-05-10 | 宝丽化学工业有限公司 | Age estimation method |
US20120148119A1 (en) * | 2010-12-14 | 2012-06-14 | Dayan Steven H | Method and system for estimating the perceived age of an individual |
JP5981113B2 (en) * | 2011-09-14 | 2016-08-31 | 株式会社 資生堂 | Evaluation method for sagging of jaw |
DE102014226858A1 (en) * | 2014-12-22 | 2016-06-23 | Robert Bosch Gmbh | Method for operating an activatable locking device for a door and / or a window, securing device for a vehicle, vehicle |
WO2023112718A1 (en) * | 2021-12-17 | 2023-06-22 | 株式会社 資生堂 | Wrinkle evaluation method, wrinkle evaluation system, fat infiltration evaluation method, fat infiltration evaluation system, computer program, skin sensing method for wrinkle evaluation purposes, recommendation method on basis of wrinkle evaluation, and method for predicting future state of fat infiltration and/or future state of wrinkles |
Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JPH06333023A (en) * | 1993-05-26 | 1994-12-02 | Casio Comput Co Ltd | Age presuming device |
JP2000083954A (en) * | 1998-09-09 | 2000-03-28 | Pola Chem Ind Inc | Method for estimating age of skin |
-
2001
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Patent Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JPH06333023A (en) * | 1993-05-26 | 1994-12-02 | Casio Comput Co Ltd | Age presuming device |
JP2000083954A (en) * | 1998-09-09 | 2000-03-28 | Pola Chem Ind Inc | Method for estimating age of skin |
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