3D face modeling은 high-end와 low-end의 quality gap이 매우 크다.
High-end models : Photo-realistic but require manual labor
Low-end models : Simple but lack realism
FLAME aims to move low-ends to high-end by a generic 3D face models that are compact, can fit to data, capture realistic details, and enable animation.

$$ M(\vec{\beta}, \vec{\theta}, \vec{\psi}): \mathbb{R}^{|\vec{\beta}| \times|\vec{\theta}| \times|\vec{\psi}|} \rightarrow \mathbb{R}^{3 N} $$
where inputs $\vec{\beta} \in \mathbb{R}^{|\vec{\beta}|}$, $\vec{\theta} \in \mathbb{R}^{|\vec{\theta}|}$, $\vec{\psi} \in \mathbb{R}^{|\vec{\psi}|}$ are each coefficient for shape, pose and expression