Rotational invariance is a popular inductive bias used by many fields in machine learning, such as computer vision and machine learning for quantum chemistry. Rotation-invariant machine learning methods set the state of the art for many tasks, including molecular property prediction and 3D shape classification. These methods generally either rely on task-specific rotation-invariant features, or they use general-purpose deep neural networks which are complicated to design and train. However, it is unclear whether the success of these methods is primarily due to the rotation invariance or the deep neural networks. To address this question, we suggest a simple and general-purpose method for learning rotation-invariant functions of three-dimensional point cloud data using a random features approach. Specifically, we extend the random features method of Rahimi & Recht 2007 by deriving a version that is invariant to three-dimensional rotations and showing that it is fast to evaluate on point cloud data. We show through experiments that our method matches or outperforms the performance of general-purpose rotation-invariant neural networks on standard molecular property prediction benchmark datasets QM7 and QM9. We also show that our method is general-purpose and provides a rotation-invariant baseline on the ModelNet40 shape classification task. Finally, we show that our method has an order of magnitude smaller prediction latency than competing kernel methods.
Recently, a growing number of work design unsupervised paradigms for point cloud processing to alleviate the limitation of expensive manual annotation and poor transferability of supervised methods. Among them, CrossPoint follows the contrastive learning framework and exploits image and point cloud data for unsupervised point cloud understanding. Although the promising performance is presented, the unbalanced architecture makes it unnecessarily complex and inefficient. For example, the image branch in CrossPoint is $\sim$8.3x heavier than the point cloud branch leading to higher complexity and latency. To address this problem, in this paper, we propose a lightweight Vision-and-Pointcloud Transformer (ViPFormer) to unify image and point cloud processing in a single architecture. ViPFormer learns in an unsupervised manner by optimizing intra-modal and cross-modal contrastive objectives. Then the pretrained model is transferred to various downstream tasks, including 3D shape classification and semantic segmentation. Experiments on different datasets show ViPFormer surpasses previous state-of-the-art unsupervised methods with higher accuracy, lower model complexity and runtime latency. Finally, the effectiveness of each component in ViPFormer is validated by extensive ablation studies. The implementation of the proposed method is available at https://github.com/auniquesun/ViPFormer.
Multi-view projection techniques have shown themselves to be highly effective in achieving top-performing results in the recognition of 3D shapes. These methods involve learning how to combine information from multiple view-points. However, the camera view-points from which these views are obtained are often fixed for all shapes. To overcome the static nature of current multi-view techniques, we propose learning these view-points. Specifically, we introduce the Multi-View Transformation Network (MVTN), which uses differentiable rendering to determine optimal view-points for 3D shape recognition. As a result, MVTN can be trained end-to-end with any multi-view network for 3D shape classification. We integrate MVTN into a novel adaptive multi-view pipeline that is capable of rendering both 3D meshes and point clouds. Our approach demonstrates state-of-the-art performance in 3D classification and shape retrieval on several benchmarks (ModelNet40, ScanObjectNN, ShapeNet Core55). Further analysis indicates that our approach exhibits improved robustness to occlusion compared to other methods. We also investigate additional aspects of MVTN, such as 2D pretraining and its use for segmentation. To support further research in this area, we have released MVTorch, a PyTorch library for 3D understanding and generation using multi-view projections.
Transformer with its underlying attention mechanism and the ability to capture long-range dependencies makes it become a natural choice for unordered point cloud data. However, separated local regions from the general sampling architecture corrupt the structural information of the instances, and the inherent relationships between adjacent local regions lack exploration, while local structural information is crucial in a transformer-based 3D point cloud model. Therefore, in this paper, we propose a novel module named Local Context Propagation (LCP) to exploit the message passing between neighboring local regions and make their representations more informative and discriminative. More specifically, we use the overlap points of adjacent local regions (which statistically show to be prevalent) as intermediaries, then re-weight the features of these shared points from different local regions before passing them to the next layers. Inserting the LCP module between two transformer layers results in a significant improvement in network expressiveness. Finally, we design a flexible LCPFormer architecture equipped with the LCP module. The proposed method is applicable to different tasks and outperforms various transformer-based methods in benchmarks including 3D shape classification and dense prediction tasks such as 3D object detection and semantic segmentation. Code will be released for reproduction.
As two fundamental representation modalities of 3D objects, 3D point clouds and multi-view 2D images record shape information from different domains of geometric structures and visual appearances. In the current deep learning era, remarkable progress in processing such two data modalities has been achieved through respectively customizing compatible 3D and 2D network architectures. However, unlike multi-view image-based 2D visual modeling paradigms, which have shown leading performance in several common 3D shape recognition benchmarks, point cloud-based 3D geometric modeling paradigms are still highly limited by insufficient learning capacity, due to the difficulty of extracting discriminative features from irregular geometric signals. In this paper, we explore the possibility of boosting deep 3D point cloud encoders by transferring visual knowledge extracted from deep 2D image encoders under a standard teacher-student distillation workflow. Generally, we propose PointMCD, a unified multi-view cross-modal distillation architecture, including a pretrained deep image encoder as the teacher and a deep point encoder as the student. To perform heterogeneous feature alignment between 2D visual and 3D geometric domains, we further investigate visibility-aware feature projection (VAFP), by which point-wise embeddings are reasonably aggregated into view-specific geometric descriptors. By pair-wisely aligning multi-view visual and geometric descriptors, we can obtain more powerful deep point encoders without exhausting and complicated network modification. Experiments on 3D shape classification, part segmentation, and unsupervised learning strongly validate the effectiveness of our method. The code and data will be publicly available at https://github.com/keeganhk/PointMCD.
Masked autoencoding has achieved great success for self-supervised learning in the image and language domains. However, mask based pretraining has yet to show benefits for point cloud understanding, likely due to standard backbones like PointNet being unable to properly handle the training versus testing distribution mismatch introduced by masking during training. In this paper, we bridge this gap by proposing a discriminative mask pretraining Transformer framework, MaskPoint}, for point clouds. Our key idea is to represent the point cloud as discrete occupancy values (1 if part of the point cloud; 0 if not), and perform simple binary classification between masked object points and sampled noise points as the proxy task. In this way, our approach is robust to the point sampling variance in point clouds, and facilitates learning rich representations. We evaluate our pretrained models across several downstream tasks, including 3D shape classification, segmentation, and real-word object detection, and demonstrate state-of-the-art results while achieving a significant pretraining speedup (e.g., 4.1x on ScanNet) compared to the prior state-of-the-art Transformer baseline. Code is available at https://github.com/haotian-liu/MaskPoint.
Standard spatial convolutions assume input data with a regular neighborhood structure. Existing methods typically generalize convolution to the irregular point cloud domain by fixing a regular "view" through e.g. a fixed neighborhood size, where the convolution kernel size remains the same for each point. However, since point clouds are not as structured as images, the fixed neighbor number gives an unfortunate inductive bias. We present a novel graph convolution named Difference Graph Convolution (diffConv), which does not rely on a regular view. diffConv operates on spatially-varying and density-dilated neighborhoods, which are further adapted by a learned masked attention mechanism. Experiments show that our model is very robust to the noise, obtaining state-of-the-art performance in 3D shape classification and scene understanding tasks, along with a faster inference speed.
Point cloud processing is a challenging task due to its sparsity and irregularity. Prior works introduce delicate designs on either local feature aggregator or global geometric architecture, but few combine both advantages. We propose Dual-Scale Point Cloud Recognition with High-frequency Fusion (DSPoint) to extract local-global features by concurrently operating on voxels and points. We reverse the conventional design of applying convolution on voxels and attention to points. Specifically, we disentangle point features through channel dimension for dual-scale processing: one by point-wise convolution for fine-grained geometry parsing, the other by voxel-wise global attention for long-range structural exploration. We design a co-attention fusion module for feature alignment to blend local-global modalities, which conducts inter-scale cross-modality interaction by communicating high-frequency coordinates information. Experiments and ablations on widely-adopted ModelNet40, ShapeNet, and S3DIS demonstrate the state-of-the-art performance of our DSPoint.
3D shape representation and its processing have substantial effects on 3D shape recognition. The polygon mesh as a 3D shape representation has many advantages in computer graphics and geometry processing. However, there are still some challenges for the existing deep neural network (DNN)-based methods on polygon mesh representation, such as handling the variations in the degree and permutations of the vertices and their pairwise distances. To overcome these challenges, we propose a DNN-based method (PolyNet) and a specific polygon mesh representation (PolyShape) with a multi-resolution structure. PolyNet contains two operations; (1) a polynomial convolution (PolyConv) operation with learnable coefficients, which learns continuous distributions as the convolutional filters to share the weights across different vertices, and (2) a polygonal pooling (PolyPool) procedure by utilizing the multi-resolution structure of PolyShape to aggregate the features in a much lower dimension. Our experiments demonstrate the strength and the advantages of PolyNet on both 3D shape classification and retrieval tasks compared to existing polygon mesh-based methods and its superiority in classifying graph representations of images. The code is publicly available from https://myavartanoo.github.io/polynet/.
Point cloud is one of the widely used techniques for representing and storing 3D geometric data. In the past several methods have been proposed for processing point clouds. Methods such as PointNet and FoldingNet have shown promising results for tasks like 3D shape classification and segmentation. This work proposes a tree-structured autoencoder framework to generate robust embeddings of point clouds by utilizing hierarchical information using graph convolution. We perform multiple experiments to assess the quality of embeddings generated by the proposed encoder architecture and visualize the t-SNE map to highlight its ability to distinguish between different object classes. We further demonstrate the applicability of the proposed framework in applications like: 3D point cloud completion and Single image-based 3D reconstruction.
To date, various 3D scene understanding tasks still lack practical and generalizable pre-trained models, primarily due to the intricate nature of 3D scene understanding tasks and their immense variations introduced by camera views, lighting, occlusions, etc. In this paper, we tackle this challenge by introducing a spatio-temporal representation learning (STRL) framework, capable of learning from unlabeled 3D point clouds in a self-supervised fashion. Inspired by how infants learn from visual data in the wild, we explore the rich spatio-temporal cues derived from the 3D data. Specifically, STRL takes two temporally-correlated frames from a 3D point cloud sequence as the input, transforms it with the spatial data augmentation, and learns the invariant representation self-supervisedly. To corroborate the efficacy of STRL, we conduct extensive experiments on three types (synthetic, indoor, and outdoor) of datasets. Experimental results demonstrate that, compared with supervised learning methods, the learned self-supervised representation facilitates various models to attain comparable or even better performances while capable of generalizing pre-trained models to downstream tasks, including 3D shape classification, 3D object detection, and 3D semantic segmentation. Moreover, the spatio-temporal contextual cues embedded in 3D point clouds significantly improve the learned representations.
State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of this principle, their defining characteristic being the shift-equivariance. By sliding a filter over the input, when the input shifts, the response shifts by the same amount, exploiting the structure of natural images where semantic content is independent of absolute pixel positions. This property is essential to the success of CNNs in audio, image and video recognition tasks. In this thesis, we extend equivariance to other kinds of transformations, such as rotation and scaling. We propose equivariant models for different transformations defined by groups of symmetries. The main contributions are (i) polar transformer networks, achieving equivariance to the group of similarities on the plane, (ii) equivariant multi-view networks, achieving equivariance to the group of symmetries of the icosahedron, (iii) spherical CNNs, achieving equivariance to the continuous 3D rotation group, (iv) cross-domain image embeddings, achieving equivariance to 3D rotations for 2D inputs, and (v) spin-weighted spherical CNNs, generalizing the spherical CNNs and achieving equivariance to 3D rotations for spherical vector fields. Applications include image classification, 3D shape classification and retrieval, panoramic image classification and segmentation, shape alignment and pose estimation. What these models have in common is that they leverage symmetries in the data to reduce sample and model complexity and improve generalization performance. The advantages are more significant on (but not limited to) challenging tasks where data is limited or input perturbations such as arbitrary rotations are present.
Multi-view projection methods have demonstrated their ability to reach state-of-the-art performance on 3D shape recognition. Those methods learn different ways to aggregate information from multiple views. However, the camera view-points for those views tend to be heuristically set and fixed for all shapes. To circumvent the lack of dynamism of current multi-view methods, we propose to learn those view-points. In particular, we introduce the Multi-View Transformation Network (MVTN) that regresses optimal view-points for 3D shape recognition, building upon advances in differentiable rendering. As a result, MVTN can be trained end-to-end along with any multi-view network for 3D shape classification. We integrate MVTN in a novel adaptive multi-view pipeline that can render either 3D meshes or point clouds. MVTN exhibits clear performance gains in the tasks of 3D shape classification and 3D shape retrieval without the need for extra training supervision. In these tasks, MVTN achieves state-of-the-art performance on ModelNet40, ShapeNet Core55, and the most recent and realistic ScanObjectNN dataset (up to 6% improvement). Interestingly, we also show that MVTN can provide network robustness against rotation and occlusion in the 3D domain. The code is available at https://github.com/ajhamdi/MVTN .
Fine-grained 3D shape classification is important for shape understanding and analysis, which poses a challenging research problem. However, the studies on the fine-grained 3D shape classification have rarely been explored, due to the lack of fine-grained 3D shape benchmarks. To address this issue, we first introduce a new 3D shape dataset (named FG3D dataset) with fine-grained class labels, which consists of three categories including airplane, car and chair. Each category consists of several subcategories at a fine-grained level. According to our experiments under this fine-grained dataset, we find that state-of-the-art methods are significantly limited by the small variance among subcategories in the same category. To resolve this problem, we further propose a novel fine-grained 3D shape classification method named FG3D-Net to capture the fine-grained local details of 3D shapes from multiple rendered views. Specifically, we first train a Region Proposal Network (RPN) to detect the generally semantic parts inside multiple views under the benchmark of generally semantic part detection. Then, we design a hierarchical part-view attention aggregation module to learn a global shape representation by aggregating generally semantic part features, which preserves the local details of 3D shapes. The part-view attention module hierarchically leverages part-level and view-level attention to increase the discriminability of our features. The part-level attention highlights the important parts in each view while the view-level attention highlights the discriminative views among all the views of the same object. In addition, we integrate a Recurrent Neural Network (RNN) to capture the spatial relationships among sequential views from different viewpoints. Our results under the fine-grained 3D shape dataset show that our method outperforms other state-of-the-art methods.
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.
One of the essential tasks in connectomics is the morphology analysis of neurons and organelles like mitochondria to shed light on their biological properties. However, these biological objects often have tangled parts or complex branching patterns, which make it hard to abstract, categorize, and manipulate their morphology. In this paper, we develop a novel topological nomenclature system to name these objects like the appellation for chemical compounds to promote neuroscience analysis based on their skeletal structures. We first convert the volumetric representation into the topology-preserving reduced graph to untangle the objects. Next, we develop nomenclature rules for pyramidal neurons and mitochondria from the reduced graph and finally learn the feature embedding for shape manipulation. In ablation studies, we quantitatively show that graphs generated by our proposed method align with the perception of experts. On 3D shape retrieval and decomposition tasks, we qualitatively demonstrate that the encoded topological nomenclature features achieve better results than state-of-the-art shape descriptors. To advance neuroscience, we will release a 3D segmentation dataset of mitochondria and pyramidal neurons reconstructed from a 100um cube electron microscopy volume with their reduced graph and topological nomenclature annotations. Code is publicly available at https://github.com/donglaiw/ibexHelper.
Several popular approaches to 3D vision tasks process multiple views of the input independently with deep neural networks pre-trained on natural images, achieving view permutation invariance through a single round of pooling over all views. We argue that this operation discards important information and leads to subpar global descriptors. In this paper, we propose a group convolutional approach to multiple view aggregation where convolutions are performed over a discrete subgroup of the rotation group, enabling, thus, joint reasoning over all views in an equivariant (instead of invariant) fashion, up to the very last layer. We further develop this idea to operate on smaller discrete homogeneous spaces of the rotation group, where a polar view representation is used to maintain equivariance with only a fraction of the number of input views. We set the new state of the art in several large scale 3D shape retrieval tasks, and show additional applications to panoramic scene classification.
Deep neural networks are known to be vulnerable to adversarial examples which are carefully crafted instances to cause the models to make wrong predictions. While adversarial examples for 2D images and CNNs have been extensively studied, less attention has been paid to 3D data such as point clouds. Given many safety-critical 3D applications such as autonomous driving, it is important to study how adversarial point clouds could affect current deep 3D models. In this work, we propose several novel algorithms to craft adversarial point clouds against PointNet, a widely used deep neural network for point cloud processing. Our algorithms work in two ways: adversarial point perturbation and adversarial point generation. For point perturbation, we shift existing points negligibly. For point generation, we generate either a set of independent and scattered points or a small number (1-3) of point clusters with meaningful shapes such as balls and airplanes which could be hidden in the human psyche. In addition, we formulate six perturbation measurement metrics tailored to the attacks in point clouds and conduct extensive experiments to evaluate the proposed algorithms on the ModelNet40 3D shape classification dataset. Overall, our attack algorithms achieve a success rate higher than 99% for all targeted attacks
Current best local descriptors are learned on a large dataset of matching and non-matching keypoint pairs. However, data of this kind is not always available since detailed keypoint correspondences can be hard to establish. On the other hand, we can often obtain labels for pairs of keypoint bags. For example, keypoint bags extracted from two images of the same object under different views form a matching pair, and keypoint bags extracted from images of different objects form a non-matching pair. On average, matching pairs should contain more corresponding keypoints than non-matching pairs. We describe an end-to-end differentiable architecture that enables the learning of local keypoint descriptors from such weakly-labeled data. Additionally, we discuss how to improve the method by incorporating the procedure of mining hard negatives. We also show how can our approach be used to learn convolutional features from unlabeled video signals and 3D models. Our implementation is available at https://github.com/nenadmarkus/wlrn