Local Frequency Interpretation and Non-Local Self-Similarity on Graph for Point Cloud Inpainting

As 3D scanning devices and depth sensors mature, point clouds have attracted increasing attention as a format for 3D object representation, with applications in various fields such as tele-presence, navigation and heritage reconstruction. However, point clouds usually exhibit holes of missing data, mainly due to the limitation of acquisition techniques and complicated structure. Further, point clouds are defined on irregular non-Euclidean domains, which is challenging to address especially with conventional signal processing tools. Hence, leveraging on recent advances in graph signal processing, we propose an efficient point cloud inpainting method, exploiting both the local smoothness and the non-local self-similarity in point clouds. Specifically, we first propose a frequency interpretation in graph nodal domain, based on which we introduce the local graph-signal smoothness prior in order to describe the local smoothness of point clouds. Secondly, we explore the characteristics of non-local self-similarity, by globally searching for the most similar area to the missing region. The similarity metric between two areas is defined based on the direct component and the anisotropic graph total variation of normals in each area. Finally, we formulate the hole-filling step as an optimization problem based on the selected most similar area and regularized by the graph-signal smoothness prior. Besides, we propose voxelization and automatic hole detection methods for the point cloud prior to inpainting. Experimental results show that the proposed approach outperforms four competing methods significantly, both in objective and subjective quality.Comment: 11 pages, 11 figures, submitted to IEEE Transactions on Image Processing at 2018.09.0

ConvPoint: Continuous Convolutions for Point Cloud Processing

Point clouds are unstructured and unordered data, as opposed to images. Thus, most machine learning approach developed for image cannot be directly transferred to point clouds. In this paper, we propose a generalization of discrete convolutional neural networks (CNNs) in order to deal with point clouds by replacing discrete kernels by continuous ones. This formulation is simple, allows arbitrary point cloud sizes and can easily be used for designing neural networks similarly to 2D CNNs. We present experimental results with various architectures, highlighting the flexibility of the proposed approach. We obtain competitive results compared to the state-of-the-art on shape classification, part segmentation and semantic segmentation for large-scale point clouds.Comment: 12 page

Single-view Object Shape Reconstruction Using Deep Shape Prior and Silhouette

3D shape reconstruction from a single image is a highly ill-posed problem. Modern deep learning based systems try to solve this problem by learning an end-to-end mapping from image to shape via a deep network. In this paper, we aim to solve this problem via an online optimization framework inspired by traditional methods. Our framework employs a deep autoencoder to learn a set of latent codes of 3D object shapes, which are fitted by a probabilistic shape prior using Gaussian Mixture Model (GMM). At inference, the shape and pose are jointly optimized guided by both image cues and deep shape prior without relying on an initialization from any trained deep nets. Surprisingly, our method achieves comparable performance to state-of-the-art methods even without training an end-to-end network, which shows a promising step in this direction

NPTC-net: Narrow-Band Parallel Transport Convolutional Neural Network on Point Clouds

Convolution plays a crucial role in various applications in signal and image processing, analysis, and recognition. It is also the main building block of convolution neural networks (CNNs). Designing appropriate convolution neural networks on manifold-structured point clouds can inherit and empower recent advances of CNNs to analyzing and processing point cloud data. However, one of the major challenges is to define a proper way to "sweep" filters through the point cloud as a natural generalization of the planar convolution and to reflect the point cloud's geometry at the same time. In this paper, we consider generalizing convolution by adapting parallel transport on the point cloud. Inspired by a triangulated surface-based method [Stefan C. Schonsheck, Bin Dong, and Rongjie Lai, arXiv:1805.07857.], we propose the Narrow-Band Parallel Transport Convolution (NPTC) using a specifically defined connection on a voxel-based narrow-band approximation of point cloud data. With that, we further propose a deep convolutional neural network based on NPTC (called NPTC-net) for point cloud classification and segmentation. Comprehensive experiments show that the proposed NPTC-net achieves similar or better results than current state-of-the-art methods on point cloud classification and segmentation.Comment: 18 pages, 6 figure

Deep Level Sets: Implicit Surface Representations for 3D Shape Inference

Existing 3D surface representation approaches are unable to accurately classify pixels and their orientation lying on the boundary of an object. Thus resulting in coarse representations which usually require post-processing steps to extract 3D surface meshes. To overcome this limitation, we propose an end-to-end trainable model that directly predicts implicit surface representations of arbitrary topology by optimising a novel geometric loss function. Specifically, we propose to represent the output as an oriented level set of a continuous embedding function, and incorporate this in a deep end-to-end learning framework by introducing a variational shape inference formulation. We investigate the benefits of our approach on the task of 3D surface prediction and demonstrate its ability to produce a more accurate reconstruction compared to voxel-based representations. We further show that our model is flexible and can be applied to a variety of shape inference problems

Dense Object Reconstruction from RGBD Images with Embedded Deep Shape Representations

Most problems involving simultaneous localization and mapping can nowadays be solved using one of two fundamentally different approaches. The traditional approach is given by a least-squares objective, which minimizes many local photometric or geometric residuals over explicitly parametrized structure and camera parameters. Unmodeled effects violating the lambertian surface assumption or geometric invariances of individual residuals are encountered through statistical averaging or the addition of robust kernels and smoothness terms. Aiming at more accurate measurement models and the inclusion of higher-order shape priors, the community more recently shifted its attention to deep end-to-end models for solving geometric localization and mapping problems. However, at test-time, these feed-forward models ignore the more traditional geometric or photometric consistency terms, thus leading to a low ability to recover fine details and potentially complete failure in corner case scenarios. With an application to dense object modeling from RGBD images, our work aims at taking the best of both worlds by embedding modern higher-order object shape priors into classical iterative residual minimization objectives. We demonstrate a general ability to improve mapping accuracy with respect to each modality alone, and present a successful application to real data.Comment: 12 page

Guided Proceduralization: Optimizing Geometry Processing and Grammar Extraction for Architectural Models

We describe a guided proceduralization framework that optimizes geometry processing on architectural input models to extract target grammars. We aim to provide efficient artistic workflows by creating procedural representations from existing 3D models, where the procedural expressiveness is controlled by the user. Architectural reconstruction and modeling tasks have been handled as either time consuming manual processes or procedural generation with difficult control and artistic influence. We bridge the gap between creation and generation by converting existing manually modeled architecture to procedurally editable parametrized models, and carrying the guidance to procedural domain by letting the user define the target procedural representation. Additionally, we propose various applications of such procedural representations, including guided completion of point cloud models, controllable 3D city modeling, and other benefits of procedural modeling

Deep Functional Dictionaries: Learning Consistent Semantic Structures on 3D Models from Functions

Various 3D semantic attributes such as segmentation masks, geometric features, keypoints, and materials can be encoded as per-point probe functions on 3D geometries. Given a collection of related 3D shapes, we consider how to jointly analyze such probe functions over different shapes, and how to discover common latent structures using a neural network --- even in the absence of any correspondence information. Our network is trained on point cloud representations of shape geometry and associated semantic functions on that point cloud. These functions express a shared semantic understanding of the shapes but are not coordinated in any way. For example, in a segmentation task, the functions can be indicator functions of arbitrary sets of shape parts, with the particular combination involved not known to the network. Our network is able to produce a small dictionary of basis functions for each shape, a dictionary whose span includes the semantic functions provided for that shape. Even though our shapes have independent discretizations and no functional correspondences are provided, the network is able to generate latent bases, in a consistent order, that reflect the shared semantic structure among the shapes. We demonstrate the effectiveness of our technique in various segmentation and keypoint selection applications

3D Dynamic Point Cloud Inpainting via Temporal Consistency on Graphs

With the development of 3D laser scanning techniques and depth sensors, 3D dynamic point clouds have attracted increasing attention as a representation of 3D objects in motion, enabling various applications such as 3D immersive tele-presence, gaming and navigation. However, dynamic point clouds usually exhibit holes of missing data, mainly due to the fast motion, the limitation of acquisition and complicated structure. Leveraging on graph signal processing tools, we represent irregular point clouds on graphs and propose a novel inpainting method exploiting both intra-frame self-similarity and inter-frame consistency in 3D dynamic point clouds. Specifically, for each missing region in every frame of the point cloud sequence, we search for its self-similar regions in the current frame and corresponding ones in adjacent frames as references. Then we formulate dynamic point cloud inpainting as an optimization problem based on the two types of references, which is regularized by a graph-signal smoothness prior. Experimental results show the proposed approach outperforms three competing methods significantly, both in objective and subjective quality.Comment: 7 pages, 5 figures, accepted by IEEE ICME 2020 at 2020.04.03. arXiv admin note: text overlap with arXiv:1810.0397

Spherical Conformal Parameterization of Genus-0 Point Clouds for Meshing

Point cloud is the most fundamental representation of 3D geometric objects. Analyzing and processing point cloud surfaces is important in computer graphics and computer vision. However, most of the existing algorithms for surface analysis require connectivity information. Therefore, it is desirable to develop a mesh structure on point clouds. This task can be simplified with the aid of a parameterization. In particular, conformal parameterizations are advantageous in preserving the geometric information of the point cloud data. In this paper, we extend a state-of-the-art spherical conformal parameterization algorithm for genus-0 closed meshes to the case of point clouds, using an improved approximation of the Laplace-Beltrami operator on data points. Then, we propose an iterative scheme called the North-South reiteration for achieving a spherical conformal parameterization. A balancing scheme is introduced to enhance the distribution of the spherical parameterization. High quality triangulations and quadrangulations can then be built on the point clouds with the aid of the parameterizations. Also, the meshes generated are guaranteed to be genus-0 closed meshes. Moreover, using our proposed spherical conformal parameterization, multilevel representations of point clouds can be easily constructed. Experimental results demonstrate the effectiveness of our proposed framework