In this paper, we propose a novel generative adversarial network (GAN) for 3D point clouds generation, which is called tree-GAN. To achieve state-of-the-art performance for multi-class 3D point cloud generation, a tree-structured graph convolution network (TreeGCN) is introduced as a generator for tree-GAN. Because TreeGCN performs graph convolutions within a tree, it can use ancestor information to boost the representation power for features. To evaluate GANs for 3D point clouds accurately, we develop a novel evaluation metric called Frechet point cloud distance (FPD). Experimental results demonstrate that the proposed tree-GAN outperforms state-of-the-art GANs in terms of both conventional metrics and FPD, and can generate point clouds for different semantic parts without prior knowledge.
There have been several attempts to represent convolutional neural networks or long short-term memory using tree structures @cite_43 @cite_27 @cite_31 @cite_30 @cite_37 . However, to the best of our knowledge, no previous methods have used tree structures for either graph convolutions or GANs. For example, Gadelha @cite_17 used tree-structured networks to generate 3D point clouds via variational autoencoder (VAE). However, this method needed the assumption that inputs are the 1D-ordered lists of points obtained by space-partitioning algorithms such as K-dimensional tree and random projection tree @cite_28 . Thus, it required additional preprocessing steps for valid implementations. Because its network only comprised 1D convolution layers, the method could not extract the meaningful information from unordered 3D point clouds. In contrast, the proposed tree-GAN can not only deal with unordered points, but also extract semantic parts of objects.
@cite_30 @cite_37 @cite_28 @cite_43 @cite_27 @cite_31 @cite_17
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We present multiresolution tree-structured networks to process point clouds for 3D shape understanding and generation tasks. Our network represents a 3D shape as a set of locality-preserving 1D ordered list of points at multiple resolutions. This allows efficient feed-forward processing through 1D convolutions, coarse-to-fine analysis through a multi-grid architecture, and it leads to faster convergence and small memory footprint during training. The proposed tree-structured encoders can be used to classify shapes and outperform existing point-based architectures on shape classification benchmarks, while tree-structured decoders can be used for generating point clouds directly and they outperform existing approaches for image-to-shape inference tasks learned using the ShapeNet dataset. Our model also allows unsupervised learning of point-cloud based shapes by using a variational autoencoder, leading to higher-quality generated shapes. 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. Recent advances in convolutional neural networks have shown promising results in 3D shape completion. But due to GPU memory limitations, these methods can only produce low-resolution outputs. To inpaint 3D models with semantic plausibility and contextual details, we introduce a hybrid framework that combines a 3D Encoder-Decoder Generative Adversarial Network (3D-ED-GAN) and a Long-term Recurrent Convolutional Network (LRCN). The 3D-ED-GAN is a 3D convolutional neural network trained with a generative adversarial paradigm to fill missing 3D data in low-resolution. LRCN adopts a recurrent neural network architecture to minimize GPU memory usage and incorporates an Encoder-Decoder pair into a Long Short-term Memory Network. By handling the 3D model as a sequence of 2D slices, LRCN transforms a coarse 3D shape into a more complete and higher resolution volume. While 3D-ED-GAN captures global contextual structure of the 3D shape, LRCN localizes the fine-grained details. Experimental results on both real-world and synthetic data show reconstructions from corrupted models result in complete and high-resolution 3D objects. Deep neural networks have enjoyed remarkable success for various vision tasks, however it remains challenging to apply CNNs to domains lacking a regular underlying structures such as 3D point clouds. Towards this we propose a novel convolutional architecture, termed SpiderCNN, to efficiently extract geometric features from point clouds. SpiderCNN is comprised of units called SpiderConv, which extend convolutional operations from regular grids to irregular point sets that can be embedded in ( R ^n ), by parametrizing a family of convolutional filters. We design the filter as a product of a simple step function that captures local geodesic information and a Taylor polynomial that ensures the expressiveness. SpiderCNN inherits the multi-scale hierarchical architecture from classical CNNs, which allows it to extract semantic deep features. Experiments on ModelNet40 demonstrate that SpiderCNN achieves state-of-the-art accuracy (92.4 ) on standard benchmarks, and shows competitive performance on segmentation task.