3D face registration is an important process in which a 3D face model is
aligned and mapped to a template face. However, the task of 3D face
registration becomes particularly challenging when dealing with partial face
data, where only limited facial information is available. To address this
challenge, this paper presents a novel deep learning-based approach that
combines quasi-conformal geometry with deep neural networks for partial face
registration. The proposed framework begins with a Landmark Detection Network
that utilizes curvature information to detect the presence of facial features
and estimate their corresponding coordinates. These facial landmark features
serve as essential guidance for the registration process. To establish a dense
correspondence between the partial face and the template surface, a
registration network based on quasiconformal theories is employed. The
registration network establishes a bijective quasiconformal surface mapping
aligning corresponding partial faces based on detected landmarks and curvature
values. It consists of the Coefficients Prediction Network, which outputs the
optimal Beltrami coefficient representing the surface mapping. The Beltrami
coefficient quantifies the local geometric distortion of the mapping. By
controlling the magnitude of the Beltrami coefficient through a suitable
activation function, the bijectivity and geometric distortion of the mapping
can be controlled. The Beltrami coefficient is then fed into the Beltrami
solver network to reconstruct the corresponding mapping. The surface
registration enables the acquisition of corresponding regions and the
establishment of point-wise correspondence between different partial faces,
facilitating precise shape comparison through the evaluation of point-wise
geometric differences at these corresponding regions. Experimental results
demonstrate the effectiveness of the proposed method.

该研究提出了一种基于深度学习和拟共形几何的方法，用于处理局部人脸数据的三维人脸注册，其通过使用曲率信息检测面部特征并估计其对应的坐标，从而建立局部人脸和模板表面之间的密集对应关系，实现点对点的几何差异估计及形状比较。