Point cloud upsampling aims to generate dense and uniformly distributed point
sets from a sparse point cloud, which plays a critical role in 3D computer
vision. Previous methods typically split a sparse point cloud into several
local patches, upsample patch points, and merge all upsampled patches. However,
these methods often produce holes, outliers or nonuniformity due to the
splitting and merging process which does not maintain consistency among local
patches. To address these issues, we propose a novel approach that learns an
unsigned distance field guided by local priors for point cloud upsampling.
Specifically, we train a local distance indicator (LDI) that predicts the
unsigned distance from a query point to a local implicit surface. Utilizing the
learned LDI, we learn an unsigned distance field to represent the sparse point
cloud with patch consistency. At inference time, we randomly sample queries
around the sparse point cloud, and project these query points onto the
zero-level set of the learned implicit field to generate a dense point cloud.
We justify that the implicit field is naturally continuous, which inherently
enables the application of arbitrary-scale upsampling without necessarily
retraining for various scales. We conduct comprehensive experiments on both
synthetic data and real scans, and report state-of-the-art results under widely
used benchmarks.

提出了一种学习局部先验引导的无符号距离场的点云上采样方法，稀疏点云通过局部一致性表示，通过在学习的隐式场的零级集上生成稠密点云，实验结果在综合数据和真实扫描中显示出最先进的效果。

使用本地距离指示器学习任意尺度点云上采样的连续隐式场

Learning Continuous Implicit Field with Local Distance Indicator for  Arbitrary-Scale Point Cloud Upsampling

In this paper, we present Surf-D, a novel method for generating high-quality
3D shapes as Surfaces with arbitrary topologies using Diffusion models.
Specifically, we adopt Unsigned Distance Field (UDF) as the surface
representation, as it excels in handling arbitrary topologies, enabling the
generation of complex shapes. While the prior methods explored shape generation
with different representations, they suffer from limited topologies and
geometry details. Moreover, it's non-trivial to directly extend prior diffusion
models to UDF because they lack spatial continuity due to the discrete volume
structure. However, UDF requires accurate gradients for mesh extraction and
learning. To tackle the issues, we first leverage a point-based auto-encoder to
learn a compact latent space, which supports gradient querying for any input
point through differentiation to effectively capture intricate geometry at a
high resolution. Since the learning difficulty for various shapes can differ, a
curriculum learning strategy is employed to efficiently embed various surfaces,
enhancing the whole embedding process. With pretrained shape latent space, we
employ a latent diffusion model to acquire the distribution of various shapes.
Our approach demonstrates superior performance in shape generation across
multiple modalities and conducts extensive experiments in unconditional
generation, category conditional generation, 3D reconstruction from images, and
text-to-shape tasks.

本文介绍了 Surf-D 方法，一种使用扩散模型在任意拓扑结构上生成高质量三维形状表面的新方法。通过采用无符号距离场（UDF）作为表面表示，能够处理任意拓扑结构并生成复杂形状，解决了先前方法在拓扑结构和几何细节方面的限制。通过点云自编码器学习紧凑的潜在空间，并使用梯度查询来捕捉详细几何信息，结合课程学习策略提高嵌入过程的效率。使用预训练的形状潜变空间，采用潜变扩散模型获取各种形状的分布，并在多种模式下展示出出色的形状生成性能，并对无条件生成、类别条件生成、图像三维重建和文本到形状任务进行了广泛实验。