To better understand the human face, its salient features must be extracted. One of the most common ways to extract facial features is to find feature points on face images. Most facial features are based on geometry, shape, and distribution; such as the eyes, nose, and mouth. Lanitis et al. [11] developed a statistical model of facial appearance based on the active appearance model as a basis for obtaining a parametric description of facial images. In general, AAM-based approaches can consider shape and texture rather than facial geometry. AAM (Active Appearance Model) [12] is a common face descriptor that uses the PCA technique for dimensions reduction while preserving important elements including the template and texture of the face image structure. This model can simultaneously extract changes in the shape and texture of the human face, changes that reflect the aging process in the face. The AAM method offers two models of gray surfaces and the overall shape of the face. The use of AAM for face description causes age characteristics to appear in the gray surface model and race and gender characteristics to appear in the shape model [13]. In [14], AAM is used to extract the desired features for teaching the proposed algorithm. For a face image presented by the AAM method, two series of extensions must be calculated; a shape model and a texture model. Making a shape model similar to the ASM model is taken from a collection of face images. Let denote a set of landmark points by a 2n*1 vector as:
\(\text{s}={\left({\text{x}}_{1},\dots {,\text{x}}_{\text{i}},\dots ,{\text{x}}_{\text{n}},{\text{y}}_{1},..,{\text{y}}_{\text{i}},\dots ,{\text{y}}_{\text{n}}\right)}^{\text{T}}\)
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(1)
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Where \(\left({\text{x}}_{\text{i}},{\text{y}}_{\text{i}}\right)\) denotes the location of the i-th reference point where n is the number of reference points. This description does not provide any clear information about connectivity. By applying PCA, an active appearance model similar to the ASM can be provided [12]. Therefore, the shape of a face is modeled as follows [12]:
\(\text{s}=\overline{\text{s}}+{\text{P}}_{\text{s}}{\text{b}}_{\text{s}}\)
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(2)
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Which s and \(\overline{\text{s}}\) (2n*1) denote the shape of face and the mean of the face shapes in the same age group respectively. \({\text{P}}_{\text{s}}\) (2n*t, matrix whose columns are unit vectors along principle axes or basis vector) is a set of orthogonal modes of deformation and bs (t*1, vector: b1, …., bt) is a set of parameters for the face shape model. Similarly, the face texture is represented using a vector of intensity values for the face pixels [12]:
\(\text{g}={\left({\text{g}}_{1},\dots ,{\text{g}}_{\text{m}}\right)}^{\text{T}}\)
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(3)
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m is the number of pixels on the face image. To build a texture model, all training faces must be written in the mean shape frame to collect texture information from landmark points. The result is shape-free textures [12];
\(\text{g}=\overline{\text{g}}+{\text{P}}_{\text{g}}{\text{b}}_{\text{g}}\)
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(4)
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Here \(\overline{\text{g}}\) (m*1, vector) is the mean of the texture, \({\text{P}}_{\text{g}}\) (m*M, the M eigenvectors corresponding to the M largest eigenvalues) is the orthogonal Variation mode derived from the training set, and \({\text{b}}_{\text{g}}\) (bg= b1, b2, ..., bm) contains a combination of texture parameters in the texture subspace. Finally, a combination of shape and texture is provided using PCA on the data as follows and created the appearance subspace [12].
\(\text{b}=\left(\begin{array}{c}{\text{w}}_{\text{s}}{\text{b}}_{\text{s}}\\ {\text{b}}_{\text{g}}\end{array}\right)=\left(\begin{array}{c}{\text{w}}_{\text{s}}{\text{P}}_{\text{s}}^{\text{T}}\left(\text{s}-\overline{\text{s}}\right)\\ {\text{P}}_{\text{g}}^{\text{T}}\left(\text{g}-\overline{\text{g}}\right)\end{array}\right)\)
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(5)
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\({\text{w}}_{\text{s}}\) is a diagonal matrix through which the appropriate weight between the pixel distance and the pixel intensity is obtained. After applying PCA we have [12]:
\(\text{b}=\text{Q}\text{c}\)
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(6)
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Q are the eigenvectors (shape and texture model) and c is a vector consists of appearance parameters that control both the shape and texture of the model [12]. PCA can eliminate the relationship between shape and texture parameters in the model. Moreover, it provides a more compact model in which the shape and texture of the face are represented as a function of\(\text{c}:\)
\(\text{s}=\overline{\text{s}}+{\text{P}}_{\text{s}}{\text{W}}_{\text{s}}{\text{Q}}_{\text{s}}\text{c}\)
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(7)
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\(\text{g}=\overline{\text{g}}+{\text{P}}_{\text{g}}{\text{Q}}_{\text{g}}\text{c}\)
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(8)
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which:
\(\text{Q}=\left(\begin{array}{c}{\text{Q}}_{\text{s}}\\ {\text{Q}}_{\text{g}}\end{array}\right)\)
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(9)
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Accordingly, a face template is obtained for each age group using the AAM method.
For each age group, the face template is a good representation of the age group. The number of landmark points and the way that the points are arranged is crucial. We tested a different number of landmarks and their position on the face suggested in the literature. Finally, we suggested using 66 and 92 landmark points with the most appropriate way of arranging the points to represent the face. Figure 1 shows the suggested landmarks for the samples of man and women's faces. In Table 1, the number of landmarks suggested in the literature is compared with the number of feature points. Each of these references has a different number and patterns in terms of the arrangement of feature points on the face.
Table 1
References and number of key points
References
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number of key points
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year
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[8]
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68
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2016
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[9]
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68
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2018
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[15]
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68
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2019
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[16]
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68
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2016
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[17]
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79
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2018
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[12&18]
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122
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2001&1998
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This work
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66
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-
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This work
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92
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-
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Figure 2 shows the landmark points due to the number of feature points are known and also the arrangement pattern of these points (right), in a specific age group (65–67, man gender), by selecting the same and the similar number of face images, we implemented the arrangement patterns and the number of points presented in each of these references on these images(left).
As shown in Fig. 2(f), the suggested landmarks with 92 points, takes into account smile lines, chin lines (both sides from the corners of the lips to the chin), bags under the eyes (lines under the eyes), which appear in the face of adulthood. This is a more appropriate and comprehensive choice in comparison with the other landmarks in the literature. Figure 3 (a) shows the obtained templates with the proposed layout pattern (92 feature points) for 10 age groups.
Figure 3 (b) shows the templates (79 feature points and different layouts) presented in [17]. As shown, especially in the age group over 45, the details of the elderly person's face, including bags under the eyes, smile lines, as well as lines on both sides of the mouth to the chin, are of lower quality than the suggested 92-point pattern. Examples of the suggested template, layout, and texture model are presented in Fig. 4.
For each age group, we suggested the proper locations for 92 landmark points to provide a suitable representation for the face template of the group.