3D网格的几何特征学习是计算机图形的核心，对于许多视觉应用非常重要。然而，由于缺乏所需的操作和/或其有效的实现，深度学习目前滞后于异构3D网格的层次建模。在本文中，我们提出了一系列模块化操作，以实现异构3D网格的有效几何深度学习。这些操作包括网格卷曲，（UN）池和高效的网格抽取。我们提供这些操作的开源实施，统称为\ Texit {Picasso}。 Picasso的网格抽取模块是GPU加速的模块，可以在飞行中加工一批用于深度学习的网格。我们（联合国）汇集操作在不同分辨率的网络层跨网络层计算新创建的神经元的功能。我们的网格卷曲包括FaceT2Vertex，Vertex2Facet和FaceT2Facet卷积，用于利用VMF混合物和重心插值来包含模糊建模。利用Picasso的模块化操作，我们贡献了一个新型的分层神经网络Picassonet-II，以了解3D网格的高度辨别特征。 Picassonet-II接受原始地理学和Mesh Facet的精细纹理作为输入功能，同时处理完整场景网格。我们的网络达到了各种基准的形状分析和场景的竞争性能。我们在github https://github.com/enyahermite/picasso发布Picasso和Picassonet-II。

3D点云的卷积经过广泛研究，但在几何深度学习中却远非完美。卷积的传统智慧在3D点之间表现出特征对应关系，这是对差的独特特征学习的内在限制。在本文中，我们提出了自适应图卷积（AGCONV），以供点云分析的广泛应用。 AGCONV根据其动态学习的功能生成自适应核。与使用固定/各向同性核的解决方案相比，AGCONV提高了点云卷积的灵活性，有效，精确地捕获了不同语义部位的点之间的不同关系。与流行的注意力体重方案不同，AGCONV实现了卷积操作内部的适应性，而不是简单地将不同的权重分配给相邻点。广泛的评估清楚地表明，我们的方法优于各种基准数据集中的点云分类和分割的最新方法。同时，AGCONV可以灵活地采用更多的点云分析方法来提高其性能。为了验证其灵活性和有效性，我们探索了基于AGCONV的完成，DeNoing，Upsmpling，注册和圆圈提取的范式，它们与竞争对手相当甚至优越。我们的代码可在https://github.com/hrzhou2/adaptconv-master上找到。

卷积神经网络（CNNS）在2D计算机视觉中取得了很大的突破。然而，它们的不规则结构使得难以在网格上直接利用CNNS的潜力。细分表面提供分层多分辨率结构，其中闭合的2 - 歧管三角网格中的每个面正恰好邻近三个面。本文推出了这两种观察，介绍了具有环形细分序列连接的3D三角形网格的创新和多功能CNN框架。在2D图像中的网格面和像素之间进行类比允许我们呈现网状卷积操作者以聚合附近面的局部特征。通过利用面部街区，这种卷积可以支持标准的2D卷积网络概念，例如，可变内核大小，步幅和扩张。基于多分辨率层次结构，我们利用汇集层，将四个面均匀地合并成一个和上采样方法，该方法将一个面分为四个。因此，许多流行的2D CNN架构可以容易地适应处理3D网格。可以通过自我参数化来回收具有任意连接的网格，以使循环细分序列连接，使子变量是一般的方法。广泛的评估和各种应用展示了SubDIVNet的有效性和效率。

近年来，由于强大的3D CNN，基于体素的方法已成为室内场景3D语义分割的最新方法。然而，基于体素的方法忽略了基础的几何形状，由于缺乏地理位置信息而在空间上闭合物体上的模棱两可的特征遭受了含糊的特征，并努力处理复杂和不规则的几何形状。鉴于此，我们提出了Voxel-Mesh网络（VMNET），这是一种新颖的3D深度体系结构，该架构在Voxel和网格表示上运行，并利用了欧几里得和地球信息。从直觉上讲，从体素中提取的欧几里得信息可以提供代表附近对象之间交互的上下文提示，而从网格中提取的地理信息可以帮助空间上接近但断开表面的分离对象。为了合并两个域中的此类信息，我们设计了一个内域的专注模块，以进行有效的特征聚集和一个用于自适应特征融合的专注于域间的模块。实验结果验证了VMNET的有效性：具体而言，在具有挑战性的扫描仪数据集上，用于大规模的室内场景分割，它的表现优于最先进的Sparseconvnet和Minkowskownet（74.6％vs 72.5％和73.6％）更简单的网络结构（17m vs 30m和38m参数）。代码发布：https：//github.com/hzykent/vmnet

基于简单的扩散层对空间通信非常有效的洞察力，我们对3D表面进行深度学习的新的通用方法。由此产生的网络是自动稳健的，以改变表面的分辨率和样品 - 一种对实际应用至关重要的基本属性。我们的网络可以在各种几何表示上离散化，例如三角网格或点云，甚至可以在一个表示上培训然后应用于另一个表示。我们优化扩散的空间支持，作为连续网络参数，从纯粹的本地到完全全球范围，从而消除手动选择邻域大小的负担。该方法中唯一的其他成分是在每个点处独立地施加的多层的Perceptron，以及用于支持方向滤波器的空间梯度特征。由此产生的网络简单，坚固，高效。这里，我们主要专注于三角网格表面，并且展示了各种任务的最先进的结果，包括表面分类，分割和非刚性对应。

Point clouds are characterized by irregularity and unstructuredness, which pose challenges in efficient data exploitation and discriminative feature extraction. In this paper, we present an unsupervised deep neural architecture called Flattening-Net to represent irregular 3D point clouds of arbitrary geometry and topology as a completely regular 2D point geometry image (PGI) structure, in which coordinates of spatial points are captured in colors of image pixels. \mr{Intuitively, Flattening-Net implicitly approximates a locally smooth 3D-to-2D surface flattening process while effectively preserving neighborhood consistency.} \mr{As a generic representation modality, PGI inherently encodes the intrinsic property of the underlying manifold structure and facilitates surface-style point feature aggregation.} To demonstrate its potential, we construct a unified learning framework directly operating on PGIs to achieve \mr{diverse types of high-level and low-level} downstream applications driven by specific task networks, including classification, segmentation, reconstruction, and upsampling. Extensive experiments demonstrate that our methods perform favorably against the current state-of-the-art competitors. We will make the code and data publicly available at https://github.com/keeganhk/Flattening-Net.

Point cloud learning has lately attracted increasing attention due to its wide applications in many areas, such as computer vision, autonomous driving, and robotics. As a dominating technique in AI, deep learning has been successfully used to solve various 2D vision problems. However, deep learning on point clouds is still in its infancy due to the unique challenges faced by the processing of point clouds with deep neural networks. Recently, deep learning on point clouds has become even thriving, with numerous methods being proposed to address different problems in this area. To stimulate future research, this paper presents a comprehensive review of recent progress in deep learning methods for point clouds. It covers three major tasks, including 3D shape classification, 3D object detection and tracking, and 3D point cloud segmentation. It also presents comparative results on several publicly available datasets, together with insightful observations and inspiring future research directions.

We present a network architecture for processing point clouds that directly operates on a collection of points represented as a sparse set of samples in a high-dimensional lattice. Naïvely applying convolutions on this lattice scales poorly, both in terms of memory and computational cost, as the size of the lattice increases. Instead, our network uses sparse bilateral convolutional layers as building blocks. These layers maintain efficiency by using indexing structures to apply convolutions only on occupied parts of the lattice, and allow flexible specifications of the lattice structure enabling hierarchical and spatially-aware feature learning, as well as joint 2D-3D reasoning. Both point-based and image-based representations can be easily incorporated in a network with such layers and the resulting model can be trained in an end-to-end manner. We present results on 3D segmentation tasks where our approach outperforms existing state-of-the-art techniques.

Unlike images which are represented in regular dense grids, 3D point clouds are irregular and unordered, hence applying convolution on them can be difficult. In this paper, we extend the dynamic filter to a new convolution operation, named PointConv. PointConv can be applied on point clouds to build deep convolutional networks. We treat convolution kernels as nonlinear functions of the local coordinates of 3D points comprised of weight and density functions. With respect to a given point, the weight functions are learned with multi-layer perceptron networks and density functions through kernel density estimation. The most important contribution of this work is a novel reformulation proposed for efficiently computing the weight functions, which allowed us to dramatically scale up the network and significantly improve its performance. The learned convolution kernel can be used to compute translation-invariant and permutation-invariant convolution on any point set in the 3D space. Besides, PointConv can also be used as deconvolution operators to propagate features from a subsampled point cloud back to its original resolution. Experiments on ModelNet40, ShapeNet, and ScanNet show that deep convolutional neural networks built on PointConv are able to achieve state-of-the-art on challenging semantic segmentation benchmarks on 3D point clouds. Besides, our experiments converting CIFAR-10 into a point cloud showed that networks built on PointConv can match the performance of convolutional networks in 2D images of a similar structure.

Point cloud is an important type of geometric data structure. Due to its irregular format, most researchers transform such data to regular 3D voxel grids or collections of images. This, however, renders data unnecessarily voluminous and causes issues. In this paper, we design a novel type of neural network that directly consumes point clouds, which well respects the permutation invariance of points in the input. Our network, named PointNet, provides a unified architecture for applications ranging from object classification, part segmentation, to scene semantic parsing. Though simple, PointNet is highly efficient and effective. Empirically, it shows strong performance on par or even better than state of the art. Theoretically, we provide analysis towards understanding of what the network has learnt and why the network is robust with respect to input perturbation and corruption.

A number of problems can be formulated as prediction on graph-structured data. In this work, we generalize the convolution operator from regular grids to arbitrary graphs while avoiding the spectral domain, which allows us to handle graphs of varying size and connectivity. To move beyond a simple diffusion, filter weights are conditioned on the specific edge labels in the neighborhood of a vertex. Together with the proper choice of graph coarsening, we explore constructing deep neural networks for graph classification. In particular, we demonstrate the generality of our formulation in point cloud classification, where we set the new state of the art, and on a graph classification dataset, where we outperform other deep learning approaches. The source code is available at https://github.com/mys007/ecc.

Intelligent mesh generation (IMG) refers to a technique to generate mesh by machine learning, which is a relatively new and promising research field. Within its short life span, IMG has greatly expanded the generalizability and practicality of mesh generation techniques and brought many breakthroughs and potential possibilities for mesh generation. However, there is a lack of surveys focusing on IMG methods covering recent works. In this paper, we are committed to a systematic and comprehensive survey describing the contemporary IMG landscape. Focusing on 110 preliminary IMG methods, we conducted an in-depth analysis and evaluation from multiple perspectives, including the core technique and application scope of the algorithm, agent learning goals, data types, targeting challenges, advantages and limitations. With the aim of literature collection and classification based on content extraction, we propose three different taxonomies from three views of key technique, output mesh unit element, and applicable input data types. Finally, we highlight some promising future research directions and challenges in IMG. To maximize the convenience of readers, a project page of IMG is provided at \url{https://github.com/xzb030/IMG_Survey}.

We present an approach to semantic scene analysis using deep convolutional networks. Our approach is based on tangent convolutions -a new construction for convolutional networks on 3D data. In contrast to volumetric approaches, our method operates directly on surface geometry. Crucially, the construction is applicable to unstructured point clouds and other noisy real-world data. We show that tangent convolutions can be evaluated efficiently on large-scale point clouds with millions of points. Using tangent convolutions, we design a deep fully-convolutional network for semantic segmentation of 3D point clouds, and apply it to challenging real-world datasets of indoor and outdoor 3D environments. Experimental results show that the presented approach outperforms other recent deep network constructions in detailed analysis of large 3D scenes.

Recently, implicit neural representations have gained popularity for learning-based 3D reconstruction. While demonstrating promising results, most implicit approaches are limited to comparably simple geometry of single objects and do not scale to more complicated or large-scale scenes. The key limiting factor of implicit methods is their simple fullyconnected network architecture which does not allow for integrating local information in the observations or incorporating inductive biases such as translational equivariance. In this paper, we propose Convolutional Occupancy Networks, a more flexible implicit representation for detailed reconstruction of objects and 3D scenes. By combining convolutional encoders with implicit occupancy decoders, our model incorporates inductive biases, enabling structured reasoning in 3D space. We investigate the effectiveness of the proposed representation by reconstructing complex geometry from noisy point clouds and low-resolution voxel representations. We empirically find that our method enables the fine-grained implicit 3D reconstruction of single objects, scales to large indoor scenes, and generalizes well from synthetic to real data.

We present Kernel Point Convolution 1 (KPConv), a new design of point convolution, i.e. that operates on point clouds without any intermediate representation. The convolution weights of KPConv are located in Euclidean space by kernel points, and applied to the input points close to them. Its capacity to use any number of kernel points gives KP-Conv more flexibility than fixed grid convolutions. Furthermore, these locations are continuous in space and can be learned by the network. Therefore, KPConv can be extended to deformable convolutions that learn to adapt kernel points to local geometry. Thanks to a regular subsampling strategy, KPConv is also efficient and robust to varying densities. Whether they use deformable KPConv for complex tasks, or rigid KPconv for simpler tasks, our networks outperform state-of-the-art classification and segmentation approaches on several datasets. We also offer ablation studies and visualizations to provide understanding of what has been learned by KPConv and to validate the descriptive power of deformable KPConv.

Point cloud completion is a generation and estimation issue derived from the partial point clouds, which plays a vital role in the applications in 3D computer vision. The progress of deep learning (DL) has impressively improved the capability and robustness of point cloud completion. However, the quality of completed point clouds is still needed to be further enhanced to meet the practical utilization. Therefore, this work aims to conduct a comprehensive survey on various methods, including point-based, convolution-based, graph-based, and generative model-based approaches, etc. And this survey summarizes the comparisons among these methods to provoke further research insights. Besides, this review sums up the commonly used datasets and illustrates the applications of point cloud completion. Eventually, we also discussed possible research trends in this promptly expanding field.

We present OctNet, a representation for deep learning with sparse 3D data. In contrast to existing models, our representation enables 3D convolutional networks which are both deep and high resolution. Towards this goal, we exploit the sparsity in the input data to hierarchically partition the space using a set of unbalanced octrees where each leaf node stores a pooled feature representation. This allows to focus memory allocation and computation to the relevant dense regions and enables deeper networks without compromising resolution. We demonstrate the utility of our OctNet representation by analyzing the impact of resolution on several 3D tasks including 3D object classification, orientation estimation and point cloud labeling.

Computational fluid dynamics (CFD) is a valuable asset for patient-specific cardiovascular-disease diagnosis and prognosis, but its high computational demands hamper its adoption in practice. Machine-learning methods that estimate blood flow in individual patients could accelerate or replace CFD simulation to overcome these limitations. In this work, we consider the estimation of vector-valued quantities on the wall of three-dimensional geometric artery models. We employ group-equivariant graph convolution in an end-to-end SE(3)-equivariant neural network that operates directly on triangular surface meshes and makes efficient use of training data. We run experiments on a large dataset of synthetic coronary arteries and find that our method estimates directional wall shear stress (WSS) with an approximation error of 7.6% and normalised mean absolute error (NMAE) of 0.4% while up to two orders of magnitude faster than CFD. Furthermore, we show that our method is powerful enough to accurately predict transient, vector-valued WSS over the cardiac cycle while conditioned on a range of different inflow boundary conditions. These results demonstrate the potential of our proposed method as a plugin replacement for CFD in the personalised prediction of hemodynamic vector and scalar fields.

由于其高质量的对象表示和有效的获取方法，3D点云吸引了越来越多的架构，工程和构建的关注。因此，文献中已经提出了许多点云特征检测方法来自动化一些工作流，例如它们的分类或部分分割。然而，点云自动化系统的性能显着落后于图像对应物。尽管这种故障的一部分源于云云的不规则性，非结构性和混乱，这使得云特征检测的任务比图像一项更具挑战性，但我们认为，图像域缺乏灵感可能是主要的。这种差距的原因。确实，鉴于图像特征检测中卷积神经网络（CNN）的压倒性成功，设计其点云对应物似乎是合理的，但是所提出的方法都不类似于它们。具体而言，即使许多方法概括了点云中的卷积操作，但它们也无法模仿CNN的多种功能检测和汇总操作。因此，我们提出了一个基于图卷积的单元，称为收缩单元，可以垂直和水平堆叠，以设计类似CNN的3D点云提取器。鉴于点云中点之间的自我，局部和全局相关性传达了至关重要的空间几何信息，因此我们在特征提取过程中还利用它们。我们通过为ModelNet-10基准数据集设计功能提取器模型来评估我们的建议，并达到90.64％的分类精度，表明我们的创新想法是有效的。我们的代码可在github.com/albertotamajo/shrinking-unit上获得。