We present a novel compact point cloud representation that is inherently invariant to scale, coordinate change and point permutation. The key idea is to parametrize a distance field around an individual shape into a unique, canonical, and compact vector in an unsupervised manner. We firstly project a distance field to a @math D canonical space using singular value decomposition. We then train a neural network for each instance to non-linearly embed its distance field into network parameters. We employ a bias-free Extreme Learning Machine (ELM) with ReLU activation units, which has scale-factor commutative property between layers. We demonstrate the descriptiveness of the instance-wise, shape-embedded network parameters by using them to classify shapes in @math D datasets. Our learning-based representation requires minimal augmentation and simple neural networks, where previous approaches demand numerous representations to handle coordinate change and point permutation.
Voxel-based methods @cite_16 @cite_18 @cite_10 @cite_0 convert point clouds into voxel data and feeds them to a convolutional neural network to classify them according to the provided labels. Convolution is conducted in a similar manner to CNN-based @math D image classification methods, with @math D filters to convolve local voxels. These methods avoids the issue of point permutation by embedding points into voxels. As the representation cannot handle coordinate change, data augmentation is conducted by rotating the original shape and voxelizing it from another viewpoint. Our method is similar in that we employ a spatial representation of the shapes. However, our representation is invariant to coordinate change, getting rid of the necessity to augment data by random rotations. Our method is also robust to resolution, while the accuracy of voxel-based methods depend heavily on the size of the voxels.
@cite_0 @cite_18 @cite_16 @cite_10
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3D data such as point clouds and meshes are becoming more and more available. The goal of this paper is to obtain 3D object and scene classification and semantic segmentation. Because point clouds have irregular formats, most of the existing methods convert the 3D data into multiple 2D projection images or 3D voxel grids. These representations are suited as input of conventional CNNs but they either ignore the underlying 3D geometrical structure or are constrained by data sparsity and computational complexity. Therefore, recent methods encode the coordinates of each point cloud to certain high dimensional features to cover the 3D space. However, by their design, these models are not able to sufficiently capture the local patterns. In this paper, we propose a method that directly uses point clouds as input and exploits the implicit space partition of k-d tree structure to learn the local contextual information and aggregate features at different scales hierarchically. Extensive experiments on challenging benchmarks show that our proposed model properly captures the local patterns to provide discriminative point set features. For the task of 3D scene semantic segmentation, our method outperforms the state-of-the-art on the challenging Stanford Large-Scale 3D Indoor Spaces Dataset(S3DIS) by a large margin. 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. In this paper, we address semantic segmentation of road-objects from 3D LiDAR point clouds. In particular, we wish to detect and categorize instances of interest, such as cars, pedestrians and cyclists. We formulate this problem as a point- wise classification problem, and propose an end-to-end pipeline called SqueezeSeg based on convolutional neural networks (CNN): the CNN takes a transformed LiDAR point cloud as input and directly outputs a point-wise label map, which is then refined by a conditional random field (CRF) implemented as a recurrent layer. Instance-level labels are then obtained by conventional clustering algorithms. Our CNN model is trained on LiDAR point clouds from the KITTI dataset, and our point-wise segmentation labels are derived from 3D bounding boxes from KITTI. To obtain extra training data, we built a LiDAR simulator into Grand Theft Auto V (GTA-V), a popular video game, to synthesize large amounts of realistic training data. Our experiments show that SqueezeSeg achieves high accuracy with astonishingly fast and stable runtime (8.7 ms per frame), highly desirable for autonomous driving applications. Furthermore, additionally training on synthesized data boosts validation accuracy on real-world data. Our source code and synthesized data will be open-sourced. In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the past few decades. These methods produce excellent results, but can be challenging to deploy in practice due to factors including the high computational cost of the forward and adjoint operators and the difficulty of hyperparameter selection. The starting point of this paper is the observation that unrolled iterative methods have the form of a CNN (filtering followed by pointwise non-linearity) when the normal operator ( @math , where @math is the adjoint of the forward imaging operator, @math ) of the forward model is a convolution. Based on this observation, we propose using direct inversion followed by a CNN to solve normal-convolutional inverse problems. The direct inversion encapsulates the physical model of the system, but leads to artifacts when the problem is ill posed; the CNN combines multiresolution decomposition and residual learning in order to learn to remove these artifacts while preserving image structure. We demonstrate the performance of the proposed network in sparse-view reconstruction (down to 50 views) on parallel beam X-ray computed tomography in synthetic phantoms as well as in real experimental sinograms. The proposed network outperforms total variation-regularized iterative reconstruction for the more realistic phantoms and requires less than a second to reconstruct a @math image on the GPU.