# 3D Morphorble Model

[3d-face

3dmm

flame

FaceScape

FaceWareHouse

]
This notebooks describes the models which could represent animatable 3D face mesh, which is usually referred 3D morphorble model (3DMM).

# FaceWareHouse

FaceWareHouse is a database of 3D facial expressions for visual computing applications. Some highlights:

- learned from data captured from Kinect includes 159 subjects and 20 expressins each. The quality and resolution of Kinect depth camea is at millimeter level;
- bilinear model with identity and expression on different axis \(V=C_r\times W_{id}\times W_{exp}\), with \(W_{id}\in\mathbb{R}^{150}\) and \(W_{exp}\in\mathbb{R}^{47}\);

# FLAME

FLAME parametrizes the 3D face mesh by identity \(\beta\in\mathbb{R}^{100}\), expression \(\psi\in\mathbb{R}^{50}\) and head pose \(\theta\in\mathbb{R}^{15}\)). Some highlights of FLAME:

- learned from 33000 3D scans of several hertergenous dataset including about 3800 identities, 8000 scans for poses and 69000 frames for expressions;
- strictly linear model for identity, expression and pose;
- the idenity and expression basis are orthornomal and computed from data. The number of basis are configurable;
- pose contains global pose, neck pose, jaw pose and two pupil poses;
- FLAME also supports different rendering to output the 2D image.

FLAME could be written as:

\[M(\beta,\theta,\psi)=W(T+B_S(\beta,S)+B_p(\theta,P)+B_E(\psi,E),J(\beta),\theta)\]This figure shows the coverage of variability given different number of basis.

# FaceScape

FaceScape provides large-scale high-quality 3D face datasets, parametric models, docs and toolkits about 3D face related technology. It is published in CVPR 2020 and code is available in github. FaceScape utilizes a bilinear model instead of linear model in FLAME.

Some highlights of FaceScape:

- learned from 18760 scans from 938 subjects and 20 expressions each;
- bilinear model with identity and expression on different axis \(V=C_r\times W_{id}\times W_{exp}\), with \(W_{id}\in\mathbb{R}^{938}\) and \(W_{exp}\in\mathbb{R}^{52}\);
- captured with high quality multi-view systemconsists of 68 DSLR cameras, 30 of which capture 8K images focusing on front side, and the other cameras capture 4K level images for the side part.