How to obtain the desirable representation of a 3D shape, which is discriminative across categories and polymerized within classes, is a significant challenge in 3D shape retrieval. Most existing 3D shape retrieval methods focus on capturing strong discriminative shape representation with softmax loss for the classification task, while the shape feature learning with metric loss is neglected for 3D shape retrieval. In this paper, we address this problem based on the intuition that the cosine distance of shape embeddings should be close enough within the same class and far away across categories. Since most of 3D shape retrieval tasks use cosine distance of shape features for measuring shape similarity, we propose a novel metric loss named angular triplet-center loss, which directly optimizes the cosine distances between the features. It inherits the triplet-center loss property to achieve larger inter-class distance and smaller intra-class distance simultaneously. Unlike previous metric loss utilized in 3D shape retrieval methods, where Euclidean distance is adopted and the margin design is difficult, the proposed method is more convenient to train feature embeddings and more suitable for 3D shape retrieval. Moreover, the angle margin is adopted to replace the cosine margin in order to provide more explicit discriminative constraints on an embedding space. Extensive experimental results on two popular 3D object retrieval benchmarks, ModelNet40 and ShapeNetCore 55, demonstrate the effectiveness of our proposed loss, and our method has achieved state-of-the-art results on various 3D shape datasets.
 Establishing correspondence between shapes is a fundamental problem in geometry processing, arising in a wide variety of applications. The problem is especially difficult in the setting of non-isometric deformations, as well as in the presence of topological noise and missing parts, mainly due to the limited capability to model such deformations axiomatically. Several recent works showed that invariance to complex shape transformations can be learned from examples. In this paper, we introduce an intrinsic convolutional neural network architecture based on anisotropic diffusion kernels, which we term Anisotropic Convolutional Neural Network (ACNN). In our construction, we generalize convolutions to non-Euclidean domains by constructing a set of oriented anisotropic diffusion kernels, creating in this way a local intrinsic polar representation of the data ( patch'), which is then correlated with a filter. Several cascades of such filters, linear, and non-linear operators are stacked to form a deep neural network whose parameters are learned by minimizing a task-specific cost. We use ACNNs to effectively learn intrinsic dense correspondences between deformable shapes in very challenging settings, achieving state-of-the-art results on some of the most difficult recent correspondence benchmarks. Unlike on images, semantic learning on 3D point clouds using a deep network is challenging due to the naturally unordered data structure. Among existing works, PointNet has achieved promising results by directly learning on point sets. However, it does not take full advantage of a point's local neighborhood that contains fine-grained structural information which turns out to be helpful towards better semantic learning. In this regard, we present two new operations to improve PointNet with a more efficient exploitation of local structures. The first one focuses on local 3D geometric structures. In analogy to a convolution kernel for images, we define a point-set kernel as a set of learnable 3D points that jointly respond to a set of neighboring data points according to their geometric affinities measured by kernel correlation, adapted from a similar technique for point cloud registration. The second one exploits local high-dimensional feature structures by recursive feature aggregation on a nearest-neighbor-graph computed from 3D positions. Experiments show that our network can efficiently capture local information and robustly achieve better performances on major datasets. Our code is available at this http URL To address the high computational and memory cost in 3-D volumetric convolutional neural networks (CNNs), we propose an approach to train binary volumetric CNNs for 3-D object recognition. Our method is specifically designed for 3-D data, in which it transforms the inputs and weights in convolutional fully connected layers to binary values, which can potentially accelerate the networks by efficient bitwise operations. Two loss calculation methods are designed to solve the accuracy decrease problem when the weights in the last layer are binarized. Four binary volumetric CNNs are obtained from their corresponding floating-point networks using our approach. Evaluations on three public datasets from different domains (Computer Aided Design (CAD), light detection and ranging (LiDAR), and RGB-D) show that our binary volumetric CNNs can achieve a comparable recognition performance as their floating-point counterparts but consume less computational and memory resources. 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. Building discriminative representations for 3D data has been an important task in computer graphics and computer vision research. Convolutional Neural Networks (CNNs) have shown to operate on 2D images with great success for a variety of tasks. Lifting convolution operators to 3D (3DCNNs) seems like a plausible and promising next step. Unfortunately, the computational complexity of 3D CNNs grows cubically with respect to voxel resolution. Moreover, since most 3D geometry representations are boundary based, occupied regions do not increase proportionately with the size of the discretization, resulting in wasted computation. In this work, we represent 3D spaces as volumetric fields, and propose a novel design that employs field probing filters to efficiently extract features from them. Each field probing filter is a set of probing points --- sensors that perceive the space. Our learning algorithm optimizes not only the weights associated with the probing points, but also their locations, which deforms the shape of the probing filters and adaptively distributes them in 3D space. The optimized probing points sense the 3D space "intelligently", rather than operating blindly over the entire domain. We show that field probing is significantly more efficient than 3DCNNs, while providing state-of-the-art performance, on classification tasks for 3D object recognition benchmark datasets.  Few prior works study deep learning on point sets. PointNet by is a pioneer in this direction. However, by design PointNet does not capture local structures induced by the metric space points live in, limiting its ability to recognize fine-grained patterns and generalizability to complex scenes. In this work, we introduce a hierarchical neural network that applies PointNet recursively on a nested partitioning of the input point set. By exploiting metric space distances, our network is able to learn local features with increasing contextual scales. With further observation that point sets are usually sampled with varying densities, which results in greatly decreased performance for networks trained on uniform densities, we propose novel set learning layers to adaptively combine features from multiple scales. Experiments show that our network called PointNet++ is able to learn deep point set features efficiently and robustly. In particular, results significantly better than state-of-the-art have been obtained on challenging benchmarks of 3D point clouds. A longstanding question in computer vision concerns the representation of 3D shapes for recognition: should 3D shapes be represented with descriptors operating on their native 3D formats, such as voxel grid or polygon mesh, or can they be effectively represented with view-based descriptors? We address this question in the context of learning to recognize 3D shapes from a collection of their rendered views on 2D images. We first present a standard CNN architecture trained to recognize the shapes' rendered views independently of each other, and show that a 3D shape can be recognized even from a single view at an accuracy far higher than using state-of-the-art 3D shape descriptors. Recognition rates further increase when multiple views of the shapes are provided. In addition, we present a novel CNN architecture that combines information from multiple views of a 3D shape into a single and compact shape descriptor offering even better recognition performance. The same architecture can be applied to accurately recognize human hand-drawn sketches of shapes. We conclude that a collection of 2D views can be highly informative for 3D shape recognition and is amenable to emerging CNN architectures and their derivatives.