Multilayer perceptrons (MLPs) have been successfully used to represent 3D shapes implicitly and compactly, by mapping 3D coordinates to the corresponding signed distance values or occupancy values. In this paper, we propose a novel positional encodin
g scheme, called Spline Positional Encoding, to map the input coordinates to a high dimensional space before passing them to MLPs, for helping to recover 3D signed distance fields with fine-scale geometric details from unorganized 3D point clouds. We verified the superiority of our approach over other positional encoding schemes on tasks of 3D shape reconstruction from input point clouds and shape space learning. The efficacy of our approach extended to image reconstruction is also demonstrated and evaluated.
Point set is a flexible and lightweight representation widely used for 3D deep learning. However, their discrete nature prevents them from representing continuous and fine geometry, posing a major issue for learning-based shape generation. In this wo
rk, we turn the discrete point sets into smooth surfaces by introducing the well-known implicit moving least-squares (IMLS) surface formulation, which naturally defines locally implicit functions on point sets. We incorporate IMLS surface generation into deep neural networks for inheriting both the flexibility of point sets and the high quality of implicit surfaces. Our IMLSNet predicts an octree structure as a scaffold for generating MLS points where needed and characterizes shape geometry with learned local priors. Furthermore, our implicit function evaluation is independent of the neural network once the MLS points are predicted, thus enabling fast runtime evaluation. Our experiments on 3D object reconstruction demonstrate that IMLSNets outperform state-of-the-art learning-based methods in terms of reconstruction quality and computational efficiency. Extensive ablation tests also validate our network design and loss functions.
Although unsupervised feature learning has demonstrated its advantages to reducing the workload of data labeling and network design in many fields, existing unsupervised 3D learning methods still cannot offer a generic network for various shape analy
sis tasks with competitive performance to supervised methods. In this paper, we propose an unsupervised method for learning a generic and efficient shape encoding network for different shape analysis tasks. The key idea of our method is to jointly encode and learn shape and point features from unlabeled 3D point clouds. For this purpose, we adapt HR-Net to octree-based convolutional neural networks for jointly encoding shape and point features with fused multiresolution subnetworks and design a simple-yet-efficient Multiresolution Instance Discrimination (MID) loss for jointly learning the shape and point features. Our network takes a 3D point cloud as input and output both shape and point features. After training, the network is concatenated with simple task-specific back-end layers and fine-tuned for different shape analysis tasks. We evaluate the efficacy and generality of our method and validate our network and loss design with a set of shape analysis tasks, including shape classification, semantic shape segmentation, as well as shape registration tasks. With simple back-ends, our network demonstrates the best performance among all unsupervised methods and achieves competitive performance to supervised methods, especially in tasks with a small labeled dataset. For fine-grained shape segmentation, our method even surpasses existing supervised methods by a large margin.
Acquiring complete and clean 3D shape and scene data is challenging due to geometric occlusion and insufficient views during 3D capturing. We present a simple yet effective deep learning approach for completing the input noisy and incomplete shapes o
r scenes. Our network is built upon the octree-based CNNs (O-CNN) with U-Net like structures, which enjoys high computational and memory efficiency and supports to construct a very deep network structure for 3D CNNs. A novel output-guided skip-connection is introduced to the network structure for better preserving the input geometry and learning geometry prior from data effectively. We show that with these simple adaptions -- output-guided skip-connection and deeper O-CNN (up to 70 layers), our network achieves state-of-the-art results in 3D shape completion and semantic scene computation.
We present an Adaptive Octree-based Convolutional Neural Network (Adaptive O-CNN) for efficient 3D shape encoding and decoding. Different from volumetric-based or octree-based CNN methods that represent a 3D shape with voxels in the same resolution,
our method represents a 3D shape adaptively with octants at different levels and models the 3D shape within each octant with a planar patch. Based on this adaptive patch-based representation, we propose an Adaptive O-CNN encoder and decoder for encoding and decoding 3D shapes. The Adaptive O-CNN encoder takes the planar patch normal and displacement as input and performs 3D convolutions only at the octants at each level, while the Adaptive O-CNN decoder infers the shape occupancy and subdivision status of octants at each level and estimates the best plane normal and displacement for each leaf octant. As a general framework for 3D shape analysis and generation, the Adaptive O-CNN not only reduces the memory and computational cost, but also offers better shape generation capability than the existing 3D-CNN approaches. We validate Adaptive O-CNN in terms of efficiency and effectiveness on different shape analysis and generation tasks, including shape classification, 3D autoencoding, shape prediction from a single image, and shape completion for noisy and incomplete point clouds.
We present O-CNN, an Octree-based Convolutional Neural Network (CNN) for 3D shape analysis. Built upon the octree representation of 3D shapes, our method takes the average normal vectors of a 3D model sampled in the finest leaf octants as input and p
erforms 3D CNN operations on the octants occupied by the 3D shape surface. We design a novel octree data structure to efficiently store the octant information and CNN features into the graphics memory and execute the entire O-CNN training and evaluation on the GPU. O-CNN supports various CNN structures and works for 3D shapes in different representations. By restraining the computations on the octants occupied by 3D surfaces, the memory and computational costs of the O-CNN grow quadratically as the depth of the octree increases, which makes the 3D CNN feasible for high-resolution 3D models. We compare the performance of the O-CNN with other existing 3D CNN solutions and demonstrate the efficiency and efficacy of O-CNN in three shape analysis tasks, including object classification, shape retrieval, and shape segmentation.
