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.
翻译:3D 面部之间的高顶对顶对顶通信是3D & 2D 面部分析的一个根本性和具有挑战性的问题。 虽然稀疏的地标具有解剖式地面真实通信, 但大多数面部区域的密集顶层通信并不为人所知。 在这种观点中, 当前文献通常产生合理但多样的解决办法, 与最佳的3D 面临密集的注册问题不同。 在本文中, 我们重新审视密集的注册, 遇到一个维度下降的问题, 即线条比例分解, 并采用迭代分化和吸附方法, 以唯一达到最终解决方案。 这个方法随后扩大到 3D 表面。 这个方法通过制定用于分解的本地注册问题, 以及具有固定特征的线性最小的顶点问题。 在这个基础上, 我们进一步提出一个多分辨率的算法, 以加速计算进程。 拟议的方法与新的本地缩放度指标相关, 我们在这里说明3D 面形细胞的面部位重新排列的物理含义。 在公共数据集上进行的广泛实验, 显示在常规 3D 3L 上应用的方法将具有高度的精确的正交式格式, 。一般的注册将带来许多方面。