Manipulation of elastoplastic objects like dough often involves topological
changes such as splitting and merging. The ability to accurately predict these
topological changes that a specific action might incur is critical for planning
interactions with elastoplastic objects. We present DoughNet, a
Transformer-based architecture for handling these challenges, consisting of two
components. First, a denoising autoencoder represents deformable objects of
varying topology as sets of latent codes. Second, a visual predictive model
performs autoregressive set prediction to determine long-horizon geometrical
deformation and topological changes purely in latent space. Given a partial
initial state and desired manipulation trajectories, it infers all resulting
object geometries and topologies at each step. DoughNet thereby allows to plan
robotic manipulation; selecting a suited tool, its pose and opening width to
recreate robot- or human-made goals. Our experiments in simulated and real
environments show that DoughNet is able to significantly outperform related
approaches that consider deformation only as geometrical change.

利用 DoughNet，这是一个基于 Transformer 的架构，可以准确预测弹塑性物体中可能引发的拓扑变化，从而帮助计划弹塑性物体的相互作用和机器人操作。

DoughNet: 一个用于变形物体拓扑操作的视觉预测模型

DoughNet: A Visual Predictive Model for Topological Manipulation of  Deformable Objects

Neural fields are receiving increased attention as a geometric representation
due to their ability to compactly store detailed and smooth shapes and easily
undergo topological changes. Compared to classic geometry representations,
however, neural representations do not allow the user to exert intuitive
control over the shape. Motivated by this, we leverage boundary sensitivity to
express how perturbations in parameters move the shape boundary. This allows to
interpret the effect of each learnable parameter and study achievable
deformations. With this, we perform geometric editing: finding a parameter
update that best approximates a globally prescribed deformation. Prescribing
the deformation only locally allows the rest of the shape to change according
to some prior, such as semantics or deformation rigidity. Our method is
agnostic to the model its training and updates the NN in-place. Furthermore, we
show how boundary sensitivity helps to optimize and constrain objectives (such
as surface area and volume), which are difficult to compute without first
converting to another representation, such as a mesh.

利用边界敏感度表达参数的扰动如何移动形状边界，实现几何编辑并最优化约束目标，同时不需要转换为另一种表示方法（如网格结构），可用于神经网络的训练与更新。

使用边界敏感性进行神经隐式形状编辑

Neural Implicit Shape Editing using Boundary Sensitivity

Neural radiance fields (NeRF) achieve highly photo-realistic novel-view
synthesis, but it's a challenging problem to edit the scenes modeled by
NeRF-based methods, especially for dynamic scenes. We propose editable neural
radiance fields that enable end-users to easily edit dynamic scenes and even
support topological changes. Input with an image sequence from a single camera,
our network is trained fully automatically and models topologically varying
dynamics using our picked-out surface key points. Then end-users can edit the
scene by easily dragging the key points to desired new positions. To achieve
this, we propose a scene analysis method to detect and initialize key points by
considering the dynamics in the scene, and a weighted key points strategy to
model topologically varying dynamics by joint key points and weights
optimization. Our method supports intuitive multi-dimensional (up to 3D)
editing and can generate novel scenes that are unseen in the input sequence.
Experiments demonstrate that our method achieves high-quality editing on
various dynamic scenes and outperforms the state-of-the-art. Our code and
captured data are available at this https URL

本文提出了可编辑的神经辐射场，使终端用户能够轻松编辑动态场景，甚至支持拓扑变化。我们的方法支持直观的多维度（最多 3D）编辑，并且可以生成在输入序列中未见过的新颖场景。

可编辑的顶点神经辐射场：通过关键点编辑拓扑变化的神经辐射场

EditableNeRF: Editing Topologically Varying Neural Radiance Fields by  Key Points

Triangulated meshes have become ubiquitous discrete-surface representations.
In this paper we address the problem of how to maintain the manifold properties
of a surface while it undergoes strong deformations that may cause topological
changes. We introduce a new self-intersection removal algorithm, TransforMesh,
and we propose a mesh evolution framework based on this algorithm. Numerous
shape modelling applications use surface evolution in order to improve shape
properties, such as appearance or accuracy. Both explicit and implicit
representations can be considered for that purpose. However, explicit mesh
representations, while allowing for accurate surface modelling, suffer from the
inherent difficulty of reliably dealing with self-intersections and topological
changes such as merges and splits. As a consequence, a majority of methods rely
on implicit representations of surfaces, e.g. level-sets, that naturally
overcome these issues. Nevertheless, these methods are based on volumetric
discretizations, which introduce an unwanted precision-complexity trade-off.
The method that we propose handles topological changes in a robust manner and
removes self intersections, thus overcoming the traditional limitations of
mesh-based approaches. To illustrate the effectiveness of TransforMesh, we
describe two challenging applications, namely surface morphing and 3-D
reconstruction.

介绍了一种新的自我交叉消除算法 TransforMesh 和基于此算法的网格演化框架，可以处理高度变形的网格表面同时保持其流形性质，解决了传统方法中自交和拓扑变化等问题。