You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Generative models for 3D geometric data arise in many important applications in 3D computer vision and graphics. In this paper, we focus on 3D deformable shapes that share a common topological structure, such as human faces and bodies. Morphable Models and their variants, despite their linear formulation, have been widely used for shape representation, while most of the recently proposed nonlinear approaches resort to intermediate representations, such as 3D voxel grids or 2D views. In this work, we introduce a novel graph convolutional operator, acting directly on the 3D mesh, that explicitly models the inductive bias of the fixed underlying graph. This is achieved by enforcing consistent local orderings of the vertices of the graph, through the spiral operator, thus breaking the permutation invariance property that is adopted by all the prior work on Graph Neural Networks. Our operator comes by construction with desirable properties (anisotropic, topology-aware, lightweight, easy-to-optimise), and by using it as a building block for traditional deep generative architectures, we demonstrate state-of-the-art results on a variety of 3D shape datasets compared to the linear Morphable Model and other graph convolutional operators.

Cited Abstract(s):
[1]: Robust object recognition is a crucial skill for robots operating autonomously in real world environments. Range sensors such as LiDAR and RGBD cameras are increasingly found in modern robotic systems, providing a rich source of 3D information that can aid in this task. However, many current systems do not fully utilize this information and have trouble efficiently dealing with large amounts of point cloud data. In this paper, we propose VoxNet, an architecture to tackle this problem by integrating a volumetric Occupancy Grid representation with a supervised 3D Convolutional Neural Network (3D CNN). We evaluate our approach on publicly available benchmarks using LiDAR, RGBD, and CAD data. VoxNet achieves accuracy beyond the state of the art while labeling hundreds of instances per second.

[2]: Recent deep networks that directly handle points in a point set, e.g., PointNet, have been state-of-the-art for supervised learning tasks on point clouds such as classification and segmentation. In this work, a novel end-to-end deep auto-encoder is proposed to address unsupervised learning challenges on point clouds. On the encoder side, a graph-based enhancement is enforced to promote local structures on top of PointNet. Then, a novel folding-based decoder deforms a canonical 2D grid onto the underlying 3D object surface of a point cloud, achieving low reconstruction errors even for objects with delicate structures. The proposed decoder only uses about 7 parameters of a decoder with fully-connected neural networks, yet leads to a more discriminative representation that achieves higher linear SVM classification accuracy than the benchmark. In addition, the proposed decoder structure is shown, in theory, to be a generic architecture that is able to reconstruct an arbitrary point cloud from a 2D grid. Our code is available at http: www.merl.com research license#FoldingNet

[3]: 3D shape is a crucial but heavily underutilized cue in today's computer vision systems, mostly due to the lack of a good generic shape representation. With the recent availability of inexpensive 2.5D depth sensors (e.g. Microsoft Kinect), it is becoming increasingly important to have a powerful 3D shape representation in the loop. Apart from category recognition, recovering full 3D shapes from view-based 2.5D depth maps is also a critical part of visual understanding. To this end, we propose to represent a geometric 3D shape as a probability distribution of binary variables on a 3D voxel grid, using a Convolutional Deep Belief Network. Our model, 3D ShapeNets, learns the distribution of complex 3D shapes across different object categories and arbitrary poses from raw CAD data, and discovers hierarchical compositional part representation automatically. It naturally supports joint object recognition and shape completion from 2.5D depth maps, and it enables active object recognition through view planning. To train our 3D deep learning model, we construct ModelNet - a large-scale 3D CAD model dataset. Extensive experiments show that our 3D deep representation enables significant performance improvement over the-state-of-the-arts in a variety of tasks.

[4]: 3D shape models are becoming widely available and easier to capture, making available 3D information crucial for progress in object classification. Current state-of-theart methods rely on CNNs to address this problem. Recently, we witness two types of CNNs being developed: CNNs based upon volumetric representations versus CNNs based upon multi-view representations. Empirical results from these two types of CNNs exhibit a large gap, indicating that existing volumetric CNN architectures and approaches are unable to fully exploit the power of 3D representations. In this paper, we aim to improve both volumetric CNNs and multi-view CNNs according to extensive analysis of existing approaches. To this end, we introduce two distinct network architectures of volumetric CNNs. In addition, we examine multi-view CNNs, where we introduce multiresolution filtering in 3D. Overall, we are able to outperform current state-of-the-art methods for both volumetric CNNs and multi-view CNNs. We provide extensive experiments designed to evaluate underlying design choices, thus providing a better understanding of the space of methods available for object classification on 3D data.

[5]: 3D reconstruction from single view images is an ill-posed problem. Inferring the hidden regions from self-occluded images is both challenging and ambiguous. We propose a two-pronged approach to address these issues. To better incorporate the data prior and generate meaningful reconstructions, we propose 3D-LMNet, a latent embedding matching approach for 3D reconstruction. We first train a 3D point cloud auto-encoder and then learn a mapping from the 2D image to the corresponding learnt embedding. To tackle the issue of uncertainty in the reconstruction, we predict multiple reconstructions that are consistent with the input view. This is achieved by learning a probablistic latent space with a novel view-specific diversity loss. Thorough quantitative and qualitative analysis is performed to highlight the significance of the proposed approach. We outperform state-of-the-art approaches on the task of single-view 3D reconstruction on both real and synthetic datasets while generating multiple plausible reconstructions, demonstrating the generalizability and utility of our approach.

[6]: 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.

[7]: What is a good vector representation of an object? We believe that it should be generative in 3D, in the sense that it can produce new 3D objects; as well as be predictable from 2D, in the sense that it can be perceived from 2D images. We propose a novel architecture, called the TL-embedding network, to learn an embedding space with these properties. The network consists of two components: (a) an autoencoder that ensures the representation is generative; and (b) a convolutional network that ensures the representation is predictable. This enables tackling a number of tasks including voxel prediction from 2D images and 3D model retrieval. Extensive experimental analysis demonstrates the usefulness and versatility of this embedding.

[8]: Generation of 3D data by deep neural network has been attracting increasing attention in the research community. The majority of extant works resort to regular representations such as volumetric grids or collection of images, however, these representations obscure the natural invariance of 3D shapes under geometric transformations, and also suffer from a number of other issues. In this paper we address the problem of 3D reconstruction from a single image, generating a straight-forward form of output &#x2013; point cloud coordinates. Along with this problem arises a unique and interesting issue, that the groundtruth shape for an input image may be ambiguous. Driven by this unorthordox output form and the inherent ambiguity in groundtruth, we design architecture, loss function and learning paradigm that are novel and effective. Our final solution is a conditional shape sampler, capable of predicting multiple plausible 3D point clouds from an input image. In experiments not only can our system outperform state-of-the-art methods on single image based 3D reconstruction benchmarks, but it also shows strong performance for 3D shape completion and promising ability in making multiple plausible predictions.

[9]: Three-dimensional geometric data offer an excellent domain for studying representation learning and generative modeling. In this paper, we look at geometric data represented as point clouds. We introduce a deep autoencoder (AE) network with excellent reconstruction quality and generalization ability. The learned representations outperform the state of the art in 3D recognition tasks and enable basic shape editing applications via simple algebraic manipulations, such as semantic part editing, shape analogies and shape interpolation. We also perform a thorough study of different generative models including GANs operating on the raw point clouds, significantly improved GANs trained in the fixed latent space our AEs and, Gaussian mixture models (GMM). Interestingly, GMMs trained in the latent space of our AEs produce samples of the best fidelity and diversity. To perform our quantitative evaluation of generative models, we propose simple measures of fidelity and diversity based on optimally matching between sets point clouds.

[10]: We study the problem of 3D object generation. We propose a novel framework, namely 3D Generative Adversarial Network (3D-GAN), which generates 3D objects from a probabilistic space by leveraging recent advances in volumetric convolutional networks and generative adversarial nets. The benefits of our model are three-fold: first, the use of an adversarial criterion, instead of traditional heuristic criteria, enables the generator to capture object structure implicitly and to synthesize high-quality 3D objects; second, the generator establishes a mapping from a low-dimensional probabilistic space to the space of 3D objects, so that we can sample objects without a reference image or CAD models, and explore the 3D object manifold; third, the adversarial discriminator provides a powerful 3D shape descriptor which, learned without supervision, has wide applications in 3D object recognition. Experiments demonstrate that our method generates high-quality 3D objects, and our unsupervisedly learned features achieve impressive performance on 3D object recognition, comparable with those of supervised learning methods.

[11]: With the advent of affordable depth sensors, 3D capture becomes more and more ubiquitous and already has made its way into commercial products. Yet, capturing the geometry or complete shapes of everyday objects using scanning devices (e.g. Kinect) still comes with several challenges that result in noise or even incomplete shapes.
Perhaps the most common approaches for generating arbitrary shapes are [3] [4] [1] acting on 3D voxels. In [7] , the authors propose to jointly learn to autoencode 3D voxel occupancy grids and regress to them from images. [6]7 introduced a voxel denoising autoencoder. [6]0 proposed a voxel-GAN to generate novel shapes. Among the key drawbacks of volumetric methods are their inherent high computational complexity and coarse representation that can alter the topological structure of the shapes. are a simple and lightweight alternative to volumetric representation recently gaining popularity. Several methods have been proposed for representation learning of fixed-size point clouds [9] using the Pointnet [6] architecture. In [2] , point clouds of arbitrary size were addressed. In [8] and [5] , point cloud reconstruction from single images was performed. Despite their compactness, point clouds are not popular for realistic and high-quality 3D geometry generation due to the absence of neighborhood connectivity and lack of an underlying smooth structure.