This study proposes a high-precision fast approximation method for the ℓ2-norm evaluation of 2-tuple data arrays using a rotated ℓi-norm evaluation with fixed-point arithmetic. In several signal processing applications, such as image restoration with isotropic total variation (TV) and one with complex ℓ1-norm regularization, a large number of calculations for the 2-tuple ℓ2-norm are frequently required. To achieve a hardware (HW)-friendly calculation, the square and square root operations involved in the ℓ2-norm calculation should be adequately approximated. However, several existing techniques have been challenged with respect to approximations. Thus, in this paper, a HW-friendly approximation algorithm is proposed. The proposed method uses the fact that the upper bound of the surface of a first-order rotational cone traces a second-order cone, that is, the ℓ2-cone. As a result, less variable multiplication is required, and parallel implementation is easily achieved using fixed-point arithmetic. To demonstrate the effectiveness of the proposed method, it was applied to image restoration, and then its performance on field programmable gate arrays (FPGA) is evaluated in terms of the quality, circuit area, latency, and throughput. The effectiveness of the proposed method is verified by comparing it with typical implementations using commercial circuits.

The rapid development of three-dimensional (3D) sensing technologies has led to an exponential growth in the availability of 3D point cloud data, consisting of a set of 3D coordinates indicating the spatial locations of points to explicitly represent the geometric structures of objects/scenes, associated with additional attribute information, e.g., color and normal. 3D point clouds are widely used in various fields, such as immersive telepresence, virtual/augmented reality, geographic mapping, and autonomous driving. This special issue focuses on all aspects of 3D point cloud data modeling, processing, and analysis. This special issue has collected 8 excellent articles reviewed and highly recommended by the editors and reviewers.

Region adaptive hierarchical transform (RAHT) is employed in G-PCC to make attribute compression more efficient. The performance of RAHT is closely related to the quantization parameter (QP), where applying different QPs to different transform depths is beneficial for coding efficiency. In this paper, QP cascading (QPC) is designed based on rate-distortion modelling. Firstly, the single-layer rate-quantization and distortion-quantization models are built by investigating the distribution of residuals. Later, the dependency of adjacent layers is studied to establish the rate-distortion model with dependency. Based on the proposed model, a ratedistortion optimization (RDO) guided QPC (O-QPC) and a fast implementation (F-QPC) are proposed. The experimental results verify the efficiency of the proposed methods. Compared with the G-PCC anchor, under the lossless geometry compression, O-QPC achieves an average of 1.5% performance gain in luma and nearly 13% gain in chroma, and F-QPC achieved an average performance gain of 1.0% in luma and almost 11% in chroma; Under the lossy geometry compression, O-QPC obtained an average of 3.9% gain in luma, and 13% gain in chroma, and F-QPC achieved an average of 3.4% gain in luma and nearly 12% gain in chroma. In particular, F-QPC achieves gains with almost no increase in complexity.

The autoregressive entropy model facilitates high compression efficiency by capturing intricate dependencies but suffers from slow decoding due to its serial context dependencies. To address this, we propose ParaPCAC, a lossy Parallel Point Cloud Attribute Compression scheme, designed to optimize the efficiency of the autoregressive entropy model. Our approach focuses on two main components: a parallel decoding strategy and a multi-stage context-based entropy model. In the parallel decoding strategy, we partition the voxels of the quantized latent features into non-overlapping groups for independent context entropy modeling, enabling parallel processing. The multi-stage context based entropy model is employed to decode neighboring features concurrently, utilizing previously decoded features at each stage. Global hyperprior is incorporated after the first stage to improve the estimation of attribute probability. Through these two techniques, ParaPCAC achieves significant decoding speed enhancements, with an acceleration of up to 160 × and a 24.15% BD-Rate reduction compared to serial autoregressive entropy models. Furthermore, experimental results demonstrate that ParaPCAC outperforms existing learning-based methods in rate-distortion performance and decoding latency.

Point cloud compression can effectively save the amount of data required for transmission and storage of point clouds. However, the commonly used methods of point cloud compression have serious impacts on the performance of downstream visual tasks due to the ignorance of the semantic information represented by point cloud. Towards this end, this paper proposes an object semantic-aware compression network for 3D point cloud, namely OSC-Net. Firstly, a ground points removal module based on the elevation difference is designed, enabling the network to pay more attention to the semantic information of objects. Secondly, a 3D voxel attention module is proposed to extract multiple priors in deep entropy model that can predict the probability distribution of occupied symbols in voxel space. Finally, experimental results show that our proposed network gains a notable bitrate saving of 16.71% compared to the baseline on the KITTI 3D object detection dataset, while maintaining a comparable detection accuracy.

Surface reconstruction from point cloud scans is crucial in 3D vision and graphics. Recent approaches focus on training deep-learning (DL) models to generate representations through learned priors. These models use neural networks to map point clouds into compact representations and then decode these latent representations into signed distance functions (SDFs). Such methods rely on heavy supervision and incur high computational costs. Moreover, they lack interpretability regarding how the encoded representations influence the resulting surfaces. This work proposes a computationally efficient and mathematically transparent Green Learning (GL) solution. We name it the lightweight point-cloud surface reconstruction (LPSR) method. LPSR reconstructs surfaces in two steps. First, it progressively generates a sparse voxel representation using a feedforward approach. Second, it decodes the representation into unsigned distance functions (UDFs) based on anisotropic heat diffusion. Experimental results show that LPSR offers competitive performance against state-of-the-art surface reconstruction methods on the FAMOUS, ABC, and Thingi10K datasets at modest model complexity.

Human point cloud completion is a challenging yet indispensable task, devoted to filling missing parts in the collected incomplete point clouds. Existing methods overly rely on features extracted from surface points, neglecting the intrinsic joints information point clouds possess. To address this problem, we propose a new network with an encoder-decoder framework, named JointFormer. Firstly, we design a joint-enhanced encoder that provides more prior guidance on the overall structure of the partial input. Then, a generator is employed to generate sparse but complete point clouds. Finally, a decoder refines the rough point clouds into complete and dense human body point clouds in a coarse-to-fine manner. Moreover, combining transformer with the Convolutional Block Attention Module (CBAM), we design the Channel-Spatial Attention Transformer (CSAT) to better capture point cloud spatial relationships. Quantitative and qualitative evaluations demon strate that JointFormer outperforms the state-of-the-art completion method on our two human body point cloud datasets.

The Moving Picture Experts Group (MPEG) has published the geometry-based point cloud compression (G-PCC) standard. It converts the compression of irregular point coordinates to the coding of structured binary octree node occupancy, where the Context-based Adaptive Binary Arithmetic Coding (CABAC) can be applied. The context model, constructed by intra and inter-octree layer information, drives the probability update of the arithmetic coder with a so-called Optimal Binarization with Update On-the-Fly (OBUF) scheme. The original OBUF design, while effective, lacks a probability range limitation for each binary coder, leading to issues in probability estimation accuracy and convergence speed. Moreover, when coding dynamic point clouds, the inter-frame information is not efficiently considered in OBUF, leading to excessive memory consumption for storing and tracking context states. To address these challenges, we propose an initialization strategy for both fine-grained context states (Fine-CtxS) and coarse-grained context states (Coarse-CtxS) in OBUF, alongside an adaptive probability bound determination method for each Coarse-CtxS to confine probability estimation. Furthermore, the paper delves into improvements for inter-frame geometry coding, including the construction of Fine-CtxS, and reducing memory consumption of Fine-CtxS in OBUF. The proposed methods have been adopted in recent G-PCC Edition 2 standardization activities, demonstrating enhanced performance.

Point cloud is a prevalent 3D data representation format with significant application values in immersive media, autonomous driving, digital heritage protection, etc. However, the large data size of point clouds poses challenges to transmission and storage, which influences the wide deployments. Therefore, point cloud compression plays a crucial role in practical applications for both human and machine perception optimization. To this end, the Moving Picture Experts Group (MPEG) has established two standards for point cloud compression, including Geometry-based Point Cloud Compression (G-PCC) and Video-based Point Cloud Compression (V-PCC). In the meantime, the Audio Video coding Standard (AVS) Workgroup of China also have launched and completed the development for its first generation point cloud compression standard, namely AVS PCC. This new standardization effort has adopted many new coding tools and techniques, which are different from the other counterpart standards. This paper reviews the AVS PCC standard from two perspectives, i.e., the related technologies and performance comparisons.