We present a differentiable representation, DMesh, for general 3D triangular
meshes. DMesh considers both the geometry and connectivity information of a
mesh. In our design, we first get a set of convex tetrahedra that compactly
tessellates the domain based on Weighted Delaunay Triangulation (WDT), and
formulate probability of faces to exist on our desired mesh in a differentiable
manner based on the WDT. This enables DMesh to represent meshes of various
topology in a differentiable way, and allows us to reconstruct the mesh under
various observations, such as point cloud and multi-view images using
gradient-based optimization. The source code and full paper is available at:
this https URL

我们提出了一种可导表示 DMesh，用于一般的三维三角网格。DMesh 考虑了网格的几何和连通性信息。在我们的设计中，我们首先基于加权 Delaunay 三角剖分 (WDT) 获得一组紧凑的凸四面体，并基于 WDT 以可导的方式提出面存在的概率，从而使得 DMesh 能够以可导的方式表示各种拓扑的网格，并利用基于梯度的优化方法在各种观测条件下，例如点云和多视角图像，进行网格的重建。完整论文和源代码可在此 https URL 找到。

DMesh: 一种通用网格的可微表示

DMesh: A Differentiable Representation for General Meshes

Recently, there has been an increased interest in NeRF methods which
reconstruct differentiable representation of three-dimensional scenes. One of
the main limitations of such methods is their inability to assess the
confidence of the model in its predictions. In this paper, we propose a new
neural network model for the formation of extended vector representations,
called uSF, which allows the model to predict not only color and semantic label
of each point, but also estimate the corresponding values of uncertainty. We
show that with a small number of images available for training, a model
quantifying uncertainty performs better than a model without such
functionality. Code of the uSF approach is publicly available at
this https URL

提出了一种新的神经网络模型 uSF，用于形成扩展向量表示，通过评估模型的预测不确定性，实现了对三维场景的可微分重建和不确定性估计，并证明了具有不确定性功能的模型在训练样本有限的情况下表现更好。