Dong Tian

Jiahao Pang, Muhammad Asad Lodhi, Dong Tian

Point cloud compression (PCC) is a key enabler for various 3-D applications, owing to the universality of the point cloud format. Ideally, 3D point clouds endeavor to depict object/scene surfaces that are continuous. Practically, as a set of discrete samples, point clouds are locally disconnected and sparsely distributed. This sparse nature is hindering the discovery of local correlation among points for compression. Motivated by an analysis with fractal dimension, we propose a heterogeneous approach with deep learning for lossy point cloud geometry compression. On top of a base layer compressing a coarse representation of the input, an enhancement layer is designed to cope with the challenging geometric residual/details. Specifically, a point-based network is applied to convert the erratic local details to latent features residing on the coarse point cloud. Then a sparse convolutional neural network operating on the coarse point cloud is launched. It utilizes the continuity/smoothness of the coarse geometry to compress the latent features as an enhancement bit-stream that greatly benefits the reconstruction quality. When this bit-stream is unavailable, e.g., due to packet loss, we support a skip mode with the same architecture which generates geometric details from the coarse point cloud directly. Experimentation on both dense and sparse point clouds demonstrate the state-of-the-art compression performance achieved by our proposal. Our code is available at https://github.com/InterDigitalInc/GRASP-Net.

Eric Lei, Muhammad Asad Lodhi, Jiahao Pang et al.

There have been recent efforts to learn more meaningful representations via fixed length codewords from mesh data, since a mesh serves as a complete model of underlying 3D shape compared to a point cloud. However, the mesh connectivity presents new difficulties when constructing a deep learning pipeline for meshes. Previous mesh unsupervised learning approaches typically assume category-specific templates, e.g., human face/body templates. It restricts the learned latent codes to only be meaningful for objects in a specific category, so the learned latent spaces are unable to be used across different types of objects. In this work, we present WrappingNet, the first mesh autoencoder enabling general mesh unsupervised learning over heterogeneous objects. It introduces a novel base graph in the bottleneck dedicated to representing mesh connectivity, which is shown to facilitate learning a shared latent space representing object shape. The superiority of WrappingNet mesh learning is further demonstrated via improved reconstruction quality and competitive classification compared to point cloud learning, as well as latent interpolation between meshes of different categories.

Yaoqing Yang, Chen Feng, Yiru Shen et al.

Recent deep networks that directly handle points in a point set, e.g., PointNet, have been state-of-the-art for supervised learning tasks on point clouds such as classification and segmentation. In this work, a novel end-to-end deep auto-encoder is proposed to address unsupervised learning challenges on point clouds. On the encoder side, a graph-based enhancement is enforced to promote local structures on top of PointNet. Then, a novel folding-based decoder deforms a canonical 2D grid onto the underlying 3D object surface of a point cloud, achieving low reconstruction errors even for objects with delicate structures. The proposed decoder only uses about 7% parameters of a decoder with fully-connected neural networks, yet leads to a more discriminative representation that achieves higher linear SVM classification accuracy than the benchmark. In addition, the proposed decoder structure is shown, in theory, to be a generic architecture that is able to reconstruct an arbitrary point cloud from a 2D grid. Our code is available at http://www.merl.com/research/license#FoldingNet

Yiru Shen, Chen Feng, Yaoqing Yang et al.

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 http://www.merl.com/research/license#KCNet

Jiahao Pang, Kevin Bui, Dong Tian

The universality of the point cloud format enables many 3D applications, making the compression of point clouds a critical phase in practice. Sampled as discrete 3D points, a point cloud approximates 2D surface(s) embedded in 3D with a finite bit-depth. However, the point distribution of a practical point cloud changes drastically as its bit-depth increases, requiring different methodologies for effective consumption/analysis. In this regard, a heterogeneous point cloud compression (PCC) framework is proposed. We unify typical point cloud representations -- point-based, voxel-based, and tree-based representations -- and their associated backbones under a learning-based framework to compress an input point cloud at different bit-depth levels. Having recognized the importance of voxel-domain processing, we augment the framework with a proposed context-aware upsampling for decoding and an enhanced voxel transformer for feature aggregation. Extensive experimentation demonstrates the state-of-the-art performance of our proposal on a wide range of point clouds.

Jiahao Pang, Muhammad Asad Lodhi, Junghyun Ahn et al.

A deep learning system typically suffers from a lack of reproducibility that is partially rooted in hardware or software implementation details. The irreproducibility leads to skepticism in deep learning technologies and it can hinder them from being deployed in many applications. In this work, the irreproducibility issue is analyzed where deep learning is employed in compression systems while the encoding and decoding may be run on devices from different manufacturers. The decoding process can even crash due to a single bit difference, e.g., in a learning-based entropy coder. For a given deep learning-based module with limited resources for protection, we first suggest that reproducibility can only be assured when the mismatches are bounded. Then a safeguarding mechanism is proposed to tackle the challenges. The proposed method may be applied for different levels of protection either at the reconstruction level or at a selected decoding level. Furthermore, the overhead introduced for the protection can be scaled down accordingly when the error bound is being suppressed. Experiments demonstrate the effectiveness of the proposed approach for learning-based compression systems, e.g., in image compression and point cloud compression.

Haiyan Wang, Jiahao Pang, Muhammad A. Lodhi et al.

Scene flow depicts the dynamics of a 3D scene, which is critical for various applications such as autonomous driving, robot navigation, AR/VR, etc. Conventionally, scene flow is estimated from dense/regular RGB video frames. With the development of depth-sensing technologies, precise 3D measurements are available via point clouds which have sparked new research in 3D scene flow. Nevertheless, it remains challenging to extract scene flow from point clouds due to the sparsity and irregularity in typical point cloud sampling patterns. One major issue related to irregular sampling is identified as the randomness during point set abstraction/feature extraction -- an elementary process in many flow estimation scenarios. A novel Spatial Abstraction with Attention (SA^2) layer is accordingly proposed to alleviate the unstable abstraction problem. Moreover, a Temporal Abstraction with Attention (TA^2) layer is proposed to rectify attention in temporal domain, leading to benefits with motions scaled in a larger range. Extensive analysis and experiments verified the motivation and significant performance gains of our method, dubbed as Flow Estimation via Spatial-Temporal Attention (FESTA), when compared to several state-of-the-art benchmarks of scene flow estimation.

Wei Hu, Jiahao Pang, Xianming Liu et al.

Geometric data acquired from real-world scenes, e.g., 2D depth images, 3D point clouds, and 4D dynamic point clouds, have found a wide range of applications including immersive telepresence, autonomous driving, surveillance, etc. Due to irregular sampling patterns of most geometric data, traditional image/video processing methodologies are limited, while Graph Signal Processing (GSP) -- a fast-developing field in the signal processing community -- enables processing signals that reside on irregular domains and plays a critical role in numerous applications of geometric data from low-level processing to high-level analysis. To further advance the research in this field, we provide the first timely and comprehensive overview of GSP methodologies for geometric data in a unified manner by bridging the connections between geometric data and graphs, among the various geometric data modalities, and with spectral/nodal graph filtering techniques. We also discuss the recently developed Graph Neural Networks (GNNs) and interpret the operation of these networks from the perspective of GSP. We conclude with a brief discussion of open problems and challenges.

Jiahao Pang, Duanshun Li, Dong Tian

Topology matters. Despite the recent success of point cloud processing with geometric deep learning, it remains arduous to capture the complex topologies of point cloud data with a learning model. Given a point cloud dataset containing objects with various genera, or scenes with multiple objects, we propose an autoencoder, TearingNet, which tackles the challenging task of representing the point clouds using a fixed-length descriptor. Unlike existing works directly deforming predefined primitives of genus zero (e.g., a 2D square patch) to an object-level point cloud, our TearingNet is characterized by a proposed Tearing network module and a Folding network module interacting with each other iteratively. Particularly, the Tearing network module learns the point cloud topology explicitly. By breaking the edges of a primitive graph, it tears the graph into patches or with holes to emulate the topology of a target point cloud, leading to faithful reconstructions. Experimentation shows the superiority of our proposal in terms of reconstructing point clouds as well as generating more topology-friendly representations than benchmarks.

Xue Zhang, Gene Cheung, Jiahao Pang et al.

A 3D point cloud is often synthesized from depth measurements collected by sensors at different viewpoints. The acquired measurements are typically both coarse in precision and corrupted by noise. To improve quality, previous works denoise a synthesized 3D point cloud a posteriori after projecting the imperfect depth data onto 3D space. Instead, we enhance depth measurements on the sensed images a priori, exploiting inherent 3D geometric correlation across views, before synthesizing a 3D point cloud from the improved measurements. By enhancing closer to the actual sensing process, we benefit from optimization targeting specifically the depth image formation model, before subsequent processing steps that can further obscure measurement errors. Mathematically, for each pixel row in a pair of rectified viewpoint depth images, we first construct a graph reflecting inter-pixel similarities via metric learning using data in previous enhanced rows. To optimize left and right viewpoint images simultaneously, we write a non-linear mapping function from left pixel row to the right based on 3D geometry relations. We formulate a MAP optimization problem, which, after suitable linear approximations, results in an unconstrained convex and differentiable objective, solvable using fast gradient method (FGM). Experimental results show that our method noticeably outperforms recent denoising algorithms that enhance after 3D point clouds are synthesized.

Andrew Knyazev, Akshay Gadde, Hassan Mansour et al.

An axiomatic approach to signal reconstruction is formulated, involving a sample consistent set and a guiding set, describing desired reconstructions. New frame-less reconstruction methods are proposed, based on a novel concept of a reconstruction set, defined as a shortest pathway between the sample consistent set and the guiding set. Existence and uniqueness of the reconstruction set are investigated in a Hilbert space, where the guiding set is a closed subspace and the sample consistent set is a closed plane, formed by a sampling subspace. Connections to earlier known consistent, generalized, and regularized reconstructions are clarified. New stability and reconstruction error bounds are derived, using the largest nontrivial angle between the sampling and guiding subspaces. Conjugate gradient iterative reconstruction algorithms are proposed and illustrated numerically for image magnification.

Dong Tian, Hassan Mansour, Andrew Knyazev et al.

In 3D image/video acquisition, different views are often captured with varying noise levels across the views. In this paper, we propose a graph-based image enhancement technique that uses a higher quality view to enhance a degraded view. A depth map is utilized as auxiliary information to match the perspectives of the two views. Our method performs graph-based filtering of the noisy image by directly computing a projection of the image to be filtered onto a lower dimensional Krylov subspace of the graph Laplacian. We discuss two graph spectral denoising methods: first using Chebyshev polynomials, and second using iterations of the conjugate gradient algorithm. Our framework generalizes previously known polynomial graph filters, and we demonstrate through numerical simulations that our proposed technique produces subjectively cleaner images with about 1-3 dB improvement in PSNR over existing polynomial graph filters.