Age Progression During Formative Years in .NET

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11.2 Age Progression During Formative Years
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Figure 11.10. (i) The growth rates observed on different facial measurements across ages in men.
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(ii) The growth rates observed on different facial measurements in women. The data help identify the growth spurts observed across different facial features in men and women.
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Learning Facial Aging Models: A Face Recognition Perspective
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Generic Growth Model: Computational Aspects
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We propose a facial growth model that is built using average facial measurements extracted across individuals of the same age, gender, and ethnicity (tabulated in reference 33). The facial growth model characterizes population-speci c growth patterns and hence is termed generic. With the objective of characterizing the age-based ow observed over different facial features, we detail the computational aspects involved in developing the generic growth model in the following subsections.
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Identifying the Origin of Reference
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First, we build prototype faces for each of the ages (for boys and girls) using agebased average facial measurements provided in reference 33. Let the age-based facial (i) (i) (i) measurements be denoted as i = ( 1 , 2 , . . . , N ), where i corresponds to the age (1 i 18) and N corresponds to the number of facial measurements used in our study. Building prototype faces amounts to identifying the coordinates of the 24 facial landmarks of interest for each of the ages: ( i (xi , yi ), 1 i 18). Subsequently, the facial feature drifts observed on the prototype faces (average faces) across different ages are used to determine the optimal origin of reference for the proposed craniofacial growth model. The following cues help in identifying the origin of reference for the proposed model. r The craniofacial growth model de ned in Eq. (11.2) is such that the facial features with angular coordinates = 0 remain static and features with such that | | , where is a small number, grow minimally. Furthermore, from Eq. (11.2) we observe that facial feature growth is directly proportional to the radial coordinates of feature points. r Relative total increment, RTI (%), is a measure that quanti es the growth observed across different landmarks. It is de ned as l18l l1 100, where l1 , l18 1 correspond to the facial measurements extracted across a pair of facial landmarks at ages 1 and 18 years. Farkas [33] cites that the relative total increment computed across landmarks tr and n (in the forehead region) is much less than that computed across other pairs of facial landmarks. The above cues suggest that the origin of reference for the craniofacial growth model should ideally be located between landmarks tr and n on the axis of bilateral symmetry. Figure 11.11 illustrates the ow of facial features across prototype faces at different ages. The optimal origin of reference for the craniofacial growth model is estimated as explained below. Let (xij , yij ) correspond to the coordinates of the ith feature at age j years (1 i 24 , 1 j 18). Let (x0 , y0 ) correspond to the origin of reference for the growth model. y0 corresponds to the facial mid-axis and hence is known a priori. The origin of reference for the craniofacial growth model is to be identi ed such that the growth constraints imposed on the radial and angular coordinates of facial features
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11.2 Age Progression During Formative Years
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Figure 11.11. The gure illustrates prototype faces at different ages and helps visualize the ow of
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facial features with increase in age.
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are best accounted for. The growth constraints imposed on the angular coordinates of facial features imply that the x and y coordinates of facial features across age follow a linear relationship. We compute x0 and mi , 1 i 24, the slopes of lines that best t the facial feature coordinates across years, by solving the underlying least squares problem: m n min (xij mi (yij y0 ) x0 )2 . (11.3) w.r.t mi , x0
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While solving Eq. (11.3), we observe that the optimal origin of reference for the model is located between landmarks tr and n (on the forehead). The low rates of growth observed on forehead regions for boys (11.8%) and girls (2.25%) [33] further validate the above solution. Figure 11.12 illustrates the growth observed over different facial features for boys and girls and illustrates the located origin of reference.
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