3D shape representations that accommodate learning-based 3D reconstruction
are an open problem in machine learning and computer graphics. Previous work on
neural 3D reconstruction demonstrated benefits, but also limitations, of point
cloud, voxel, surface mesh, and implicit function representations. We introduce
Deformable Tetrahedral Meshes (DefTet) as a particular parameterization that
utilizes volumetric tetrahedral meshes for the reconstruction problem. Unlike
existing volumetric approaches, DefTet optimizes for both vertex placement and
occupancy, and is differentiable with respect to standard 3D reconstruction
loss functions. It is thus simultaneously high-precision, volumetric, and
amenable to learning-based neural architectures. We show that it can represent
arbitrary, complex topology, is both memory and computationally efficient, and
can produce high-fidelity reconstructions with a significantly smaller grid
size than alternative volumetric approaches. The predicted surfaces are also
inherently defined as tetrahedral meshes, thus do not require post-processing.
We demonstrate that DefTet matches or exceeds both the quality of the previous
best approaches and the performance of the fastest ones. Our approach obtains
high-quality tetrahedral meshes computed directly from noisy point clouds, and
is the first to showcase high-quality 3D tet-mesh results using only a single
image as input. Our project webpage: this https URL

介绍 Deformable Tetrahedral Meshes (DefTet) 作为一种特殊的参数化，利用容积四面体网格用于重建问题，该方法可以同时达到高精度、容积、可学习神经架构，并且可以产生比替代容积方法小得多的网格大小的高保真重建。

学习可变形四面体网格用于 3D 重建

Learning Deformable Tetrahedral Meshes for 3D Reconstruction

We are seeing a Cambrian explosion of 3D shape representations for use in
machine learning. Some representations seek high expressive power in capturing
high-resolution detail. Other approaches seek to represent shapes as
compositions of simple parts, which are intuitive for people to understand and
easy to edit and manipulate. However, it is difficult to achieve both fidelity
and interpretability in the same representation. We propose DualSDF, a
representation expressing shapes at two levels of granularity, one capturing
fine details and the other representing an abstracted proxy shape using simple
and semantically consistent shape primitives. To achieve a tight coupling
between the two representations, we use a variational objective over a shared
latent space. Our two-level model gives rise to a new shape manipulation
technique in which a user can interactively manipulate the coarse proxy shape
and see the changes instantly mirrored in the high-resolution shape. Moreover,
our model actively augments and guides the manipulation towards producing
semantically meaningful shapes, making complex manipulations possible with
minimal user input.

提出 DualSDF 表示法，它使用两个层次的粒度对形状进行表达，并使用修正的变分目标通过共享的潜空间实现两个表示之间的紧密耦合。该模型不仅可以进行形状编辑和操作，而且能够指导用户进行语义感知的形状生成和变换。