Towards Fine-grained 3D Face Dense Registration: An Optimal Dividing and Diffusing Method

Dense vertex-to-vertex correspondence between 3D faces is a fundamental and challenging issue for 3D&2D face analysis. While the sparse landmarks have anatomically ground-truth correspondence, the dense vertex correspondences on most facial regions are unknown. In this view, the current literatures commonly result in reasonable but diverse solutions, which deviate from the optimum to the 3D face dense registration problem. In this paper, we revisit dense registration by a dimension-degraded problem, i.e. proportional segmentation of a line, and employ an iterative dividing and diffusing method to reach the final solution uniquely. This method is then extended to 3D surface by formulating a local registration problem for dividing and a linear least-square problem for diffusing, with constraints on fixed features. On this basis, we further propose a multi-resolution algorithm to accelerate the computational process. The proposed method is linked to a novel local scaling metric, where we illustrate the physical meaning as smooth rearrangement for local cells of 3D facial shapes. Extensive experiments on public datasets demonstrate the effectiveness of the proposed method in various aspects. Generally, the proposed method leads to coherent local registrations and elegant mesh grid routines for fine-grained 3D face dense registrations, which benefits many downstream applications significantly. It can also be applied to dense correspondence for other format of data which are not limited to face. The core code will be publicly available at https://github.com/NaughtyZZ/3D_face_dense_registration.