Table 1 Upper (distances 1–10) and lower (distances 11–15) face geometric distance

left inner brow-left inner eye corner

${\text{P}}_1=\frac{{\text{d}}_3\text{E}-{\text{d}}_3\text{N}}{{\text{d}}_3\text{N}}$

right eye height

${\text{P}}_6=\frac{\left({\text{d}}_6\text{E}+{\text{d}}_8\text{E}\right)-\left({\text{d}}_6\text{N}+{\text{d}}_8\text{N}\right)}{\left({\text{d}}_6\text{N}+{\text{d}}_8\text{N}\right)}$

right inner brow-right inner eye corner

${\text{P}}_2=\frac{{\text{d}}_4\text{E}-{\text{d}}_4\text{N}}{{\text{d}}_4\text{N}}$

left top eye point-line connecting left eye corners

${\text{P}}_7=\frac{{\text{d}}_5\text{E}-{\text{d}}_5\text{N}}{{\text{d}}_5\text{N}}$

left top brow-line connecting left eye corners

${\text{P}}_3=\frac{{\text{d}}_1\text{E}-{\text{d}}_1\text{N}}{{\text{d}}_1\text{N}}$

right top eye point-line connecting right eye corners

${\text{P}}_8=\frac{{\text{d}}_6\text{E}-{\text{d}}_6\text{N}}{{\text{d}}_6\text{N}}$

right top brow-line connecting right eye corners

${\text{P}}_4=\frac{{\text{d}}_2\text{E}-{\text{d}}_2\text{N}}{{\text{d}}_2\text{N}}$

left bottom eye point-line connecting left eye corners

${\text{P}}_9=\frac{{\text{d}}_7\text{E}-{\text{d}}_7\text{N}}{{\text{d}}_7\text{N}}$

left eye height

${\text{P}}_5=\frac{\left({\text{d}}_5\text{E}+{\text{d}}_7\text{E}\right)-\left({\text{d}}_5\text{N}+{\text{d}}_7\text{N}\right)}{\left({\text{d}}_5\text{N}+{\text{d}}_7\text{N}\right)}$

right bottom eye point-line connecting right eye corners

${\text{P}}_{10}=\frac{{\text{d}}_8\text{E}-{\text{d}}_8\text{N}}{{\text{d}}_8\text{N}}$

Mouth height

${\text{P}}_{11}=\frac{\left({\text{d}}_{12}\text{E}+{\text{d}}_{13}\text{E}\right)-\left({\text{d}}_{12}\text{N}+{\text{d}}_{13}\text{N}\right)}{\left({\text{d}}_{12}\text{N}+{\text{d}}_{13}\text{N}\right)}$

Mouth width

${\text{P}}_{12}=\frac{{\text{d}}_{11}\text{E}-{\text{d}}_{11}\text{N}}{{\text{d}}_{11}\text{N}}$

left lip corner-line connecting left eye corners

${\text{P}}_{13}=\frac{{\text{d}}_9\text{E}-{\text{d}}_9\text{N}}{{\text{d}}_9\text{N}}$

right lip corner-line connecting right eye corners

${\text{P}}_{14}=\frac{{\text{d}}_{10}\text{E}-{\text{d}}_{10}\text{N}}{{\text{d}}_{10}\text{N}}$

top lip-line connecting lip corners

${\text{P}}_{15}=\frac{{\text{d}}_{13}\text{E}-{\text{d}}_{13}\text{N}}{{\text{d}}_{13}\text{N}}$