In 3D shape reconstruction based on template mesh deformation, a regularization, such as smoothness energy, is employed to guide the reconstruction into a desirable direction. In this paper, we highlight an often overlooked property in the regularization: the vertex density in the mesh. Without careful control on the density, the reconstruction may suffer from under-sampling of vertices near shape details. We propose a novel mesh density adaptation method to resolve the under-sampling problem. Our mesh density adaptation energy increases the density of vertices near complex structures via deformation to help reconstruction of shape details. We demonstrate the usability and performance of mesh density adaptation with two tasks, inverse rendering and non-rigid surface registration. Our method produces more accurate reconstruction results compared to the cases without mesh density adaptation.

翻译：在基于模板网格变形的三维形状重建中，通常采用平滑能量等正则化项来引导重建过程向理想方向进行。本文指出正则化中一个常被忽视的特性：网格顶点密度。若未对顶点密度进行精细控制，重建结果可能在形状细节处因顶点采样不足而受损。我们提出一种新颖的网格密度自适应方法来解决欠采样问题。该方法通过变形增加复杂结构区域的顶点密度，从而辅助形状细节的重建。通过逆渲染与非刚性表面配准两项任务，我们验证了网格密度自适应的实用性与性能。实验结果表明，与未采用网格密度自适应的情形相比，我们的方法能获得更精确的重建结果。