Sparse Set Of Points Research Articles

Robust and Accurate Recognition of Carriage Linear Array Images for Train Fault Detection

Train fault detection often relies on comparing collected images with reference images, making accurate image type recognition crucial. Current systems use Automatic Equipment Identification (AEI) devices to recognize carriage numbers while capturing images, but damaged Radio Frequency (RF) tags or blurred characters can hinder this process. Carriage linear array images, with their high resolution, extreme aspect ratios, and local nonlinear distortions, present challenges for recognition algorithms. This paper proposes a method tailored for recognizing such images. We apply an object detection algorithm to locate key components, simplifying image recognition into a sparse point set alignment task. To handle local distortions, we introduce a weighted radial basis function (RBF) and maximize the similarity between Gaussian mixtures of point sets to determine RBF weights. Experiments show 100% recognition accuracy under nonlinear distortions up to 15%. The algorithm also performs robustly with detection errors and identifies categories from 79 image classes in 24 ms on an i7 CPU without GPU support. This method significantly reduces system costs and advances automatic exterior fault detection for trains.

Reward shaping via expectation maximization method

Reinforcement Learning (RL) has found widespread applications in various decision making tasks. However, it still faces challenges such as the deadly triad, slow convergence, and rewards drop, which limit its practical scope. This paper primarily addresses the issues of slow convergence and rewards drop observed during RL training. Our proposed solution involves a reward shaping method composed of two distinct components, each serving a specific purpose: speeding up training and enhancing stability. These two components are interconnected through hyper-parameters, and it has been observed that the choice of hyper-parameters plays a critical role in determining the final performance of the RL algorithm. To optimize these hyper-parameters effectively, we employ a discrete sampling technique to cover the value ranges of these parameters. This discrete sampling creates a sparse set of data points within the reward matrix. Subsequently, we introduce a fitting approach based on the Expectation Maximization (EM) algorithm to estimate the global maximum of the reward matrix along with the corresponding hyper-parameters combination. This EM method significantly reduces computational complexity. Our extensive experimental results across various RL environments have demonstrated the effectiveness of our proposed method. It successfully mitigates the issue of rewards drop while simultaneously accelerating the convergence speed of the RL algorithm.

Reconstructing Curves from Sparse Samples on Riemannian Manifolds

AbstractReconstructing 2D curves from sample points has long been a critical challenge in computer graphics, finding essential applications in vector graphics. The design and editing of curves on surfaces has only recently begun to receive attention, primarily relying on human assistance, and where not, limited by very strict sampling conditions. In this work, we formally improve on the state‐of‐the‐art requirements and introduce an innovative algorithm capable of reconstructing closed curves directly on surfaces from a given sparse set of sample points. We extend and adapt a state‐of‐the‐art planar curve reconstruction method to the realm of surfaces while dealing with the challenges arising from working on non‐Euclidean domains. We demonstrate the robustness of our method by reconstructing multiple curves on various surface meshes. We explore novel potential applications of our approach, allowing for automated reconstruction of curves on Riemannian manifolds.

A point mapping strategy-based sparse grid integration method for statistical moments estimation and structural reliability analysis

The high-order moment-based method is an attractive non-intrusive approach for structural reliability analysis, while it remains a challenge to strike a balance between accuracy, efficiency, and versatility in estimating statistical moments of performance functions. In this paper, a point mapping strategy-based sparse grid integration (SGI) method is proposed for statistical moment estimation and structural reliability analysis, with improved efficiency while ensuring the accuracy. Firstly, a point mapping strategy (PMS) is developed based on the adaptive high dimensional model representation (HDMR), by which the traditional SGI is reconstructed as a sum of multiple integrations over the sparse grid point sets with different effective dimensions. With this new form of SGI, the estimation of statistical moments only requires the evaluation of the performance function at a small number of necessary reference points, once the effects of some interaction terms are negligible. The validity and feasibility of the proposed PMS-based SGI method for statistical moments estimation are verified by several numerical examples. Then, the proposed method is applied to structural reliability analysis with the aid of an improved maximum entropy method. Two engineering examples are investigated, including the strength failure problem of tubular tower K-shape connection joints and the fatigue failure problem of a marine riser resulting from the vortex-induced vibration (VIV). The results indicate that the proposed method provides a better trade-off between accuracy and efficiency in evaluating the first four order statistical moments and structural failure probability compared to conventional methods.

Multi‐Spacecraft Magnetic Field Reconstructions: A Cross‐Scale Comparison of Methods

AbstractSpace plasma studies frequently use in situ magnetic field measurements taken from many spacecraft simultaneously. A useful data product of these measurements is the reconstructed magnetic field in a volume near the spacecraft observatory. We compare a standard Linear method of computing the magnetic field at arbitrary spatial points to two novel approaches: a Radial Basis Function interpolation and a time‐dependent 2D inverse distance weighted interpolation scheme called Timesync. These three methods, which only require in situ measurements of the magnetic fields and bulk plasma velocities at a sparse set of spatial points, are implemented on synthetic data drawn from a time‐evolving numerical simulation of plasma turbulence. We compare both the topology of the reconstructed field to the ground truth of the simulation and the statistics of the fluctuations found in the reconstructed field to those from the simulated turbulence. We conclude that the Radial Basis Function and Timesync methods outperform the Linear method in both topological and statistical comparisons.

OptCtrlPoints: Finding the Optimal Control Points for Biharmonic 3D Shape Deformation

AbstractWe propose OptCtrlPoints, a data‐driven framework designed to identify the optimal sparse set of control points for reproducing target shapes using biharmonic 3D shape deformation. Control‐point‐based 3D deformation methods are widely utilized for interactive shape editing, and their usability is enhanced when the control points are sparse yet strategically distributed across the shape. With this objective in mind, we introduce a data‐driven approach that can determine the most suitable set of control points, assuming that we have a given set of possible shape variations. The challenges associated with this task primarily stem from the computationally demanding nature of the problem. Two main factors contribute to this complexity: solving a large linear system for the biharmonic weight computation and addressing the combinatorial problem of finding the optimal subset of mesh vertices. To overcome these challenges, we propose a reformulation of the biharmonic computation that reduces the matrix size, making it dependent on the number of control points rather than the number of vertices. Additionally, we present an efficient search algorithm that significantly reduces the time complexity while still delivering a nearly optimal solution. Experiments on SMPL, SMAL, and DeformingThings4D datasets demonstrate the efficacy of our method. Our control points achieve better template‐to‐target fit than FPS, random search, and neural‐network‐based prediction. We also highlight the significant reduction in computation time from days to approximately 3 minutes.

Sparse-to-Dense Matching Network for Large-scale LiDAR Point Cloud Registration.

Point cloud registration is a fundamental problem in 3D computer vision. Previous learning-based methods for LiDAR point cloud registration can be categorized into two schemes: dense-to-dense matching methods and sparse-to-sparse matching methods. However, for large-scale outdoor LiDAR point clouds, solving dense point correspondences is time-consuming, whereas sparse keypoint matching easily suffers from keypoint detection error. In this paper, we propose SDMNet, a novel Sparse-to-Dense Matching Network for large-scale outdoor LiDAR point cloud registration. Specifically, SDMNet performs registration in two sequential stages: sparse matching stage and local-dense matching stage. In the sparse matching stage, we sample a set of sparse points from the source point cloud and then match them to the dense target point cloud using a spatial consistency enhanced soft matching network and a robust outlier rejection module. Furthermore, a novel neighborhood matching module is developed to incorporate local neighborhood consensus, significantly improving performance. The local-dense matching stage is followed for fine-grained performance, where dense correspondences are efficiently obtained by performing point matching in local spatial neighborhoods of high-confidence sparse correspondences. Extensive experiments on three large-scale outdoor LiDAR point cloud datasets demonstrate that the proposed SDMNet achieves state-of-the-art performance with high efficiency.

Point Set Self-Embedding.

This work presents an innovative method for point set self-embedding, that encodes the structural information of a dense point set into its sparser version in a visual but imperceptible form. The self-embedded point set can function as the ordinary downsampled one and be visualized efficiently on mobile devices. Particularly, we can leverage the self-embedded information to fully restore the original point set for detailed analysis on remote servers. This new task is challenging, cause both the self-embedded point set and restored point set should resemble the original one. To achieve a learnable self-embedding scheme, we design a novel framework with two jointly-trained networks: one to encode the input point set into its self-embedded sparse point set and the other to leverage the embedded information for inverting the original point set back. Further, we develop a pair of up-shuffle and down-shuffle units in the two networks, and formulate loss terms to encourage the shape similarity and point distribution in the results. Extensive qualitative and quantitative results demonstrate the effectiveness of our method on both synthetic and real-scanned datasets. The source code and trained models will be publicly available at https://github.com/liruihui/Self-Embedding.

Density-Imbalance-Eased LiDAR Point Cloud Upsampling via Feature Consistency Learning

3D point-cloud upsampling, a crucial perceptual module to help us understand the complex scene and object, aims to generate a high-resolution point cloud given a sparse point set. While considerable attention has been paid to single object point-cloud upsampling, literature on upsampling complex scenes has emerged slowly. Remarkably, few related works target LiDAR-based point clouds, which inherently have a density imbalance problem over distance. This paper proposed LiUpNet, a LiDAR-based point cloud upsampling network. Given a sparse and imbalanced point cloud of a natural and complex scene, LiUpNet extracts robust regional features and generates a uniformly distributed dense point cloud that preserves the fine-grained structural architecture. Specifically, in LiUpNet, an attentive and transformer-based feature extractor is applied to learn the detailed regional representation to model the underlying complex local structure. Also, a novel densityinvariant feature consistency loss is introduced to improve the robustness of the learned features against the sparsity changes. Finally, given the regional representations, we append a manifold-based upsampler to super-resolve the regional point clouds up to different scales according to the sparsity and implicitly regresses non-linear 3D scene surfaces. A more uniformly distributed and denser scene point cloud is then achieved with the scheme of dynamic regional upsampling rates. The experimental results on single-object and scene point-cloud upsampling show that LiUpNet outperforms related works qualitatively and quantitatively. Additionally, we demonstrate that the enhanced scene point clouds can efficiently improve the performance of downstream tasks such as point-cloud-based 3D object detection and depth completion.

Neural Parameterization for Dynamic Human Head Editing

Implicit radiance functions emerged as a powerful scene representation for reconstructing and rendering photo-realistic views of a 3D scene. These representations, however, suffer from poor editability. On the other hand, explicit representations such as polygonal meshes allow easy editing but are not as suitable for reconstructing accurate details in dynamic human heads, such as fine facial features, hair, teeth, and eyes. In this work, we present Neural Parameterization (NeP), a hybrid representation that provides the advantages of both implicit and explicit methods. NeP is capable of photo-realistic rendering while allowing fine-grained editing of the scene geometry and appearance. We first disentangle the geometry and appearance by parameterizing the 3D geometry into 2D texture space. We enable geometric editability by introducing an explicit linear deformation blending layer. The deformation is controlled by a set of sparse key points, which can be explicitly and intuitively displaced to edit the geometry. For appearance, we develop a hybrid 2D texture consisting of an explicit texture map for easy editing and implicit view and time-dependent residuals to model temporal and view variations. We compare our method to several reconstruction and editing baselines. The results show that the NeP achieves almost the same level of rendering accuracy while maintaining high editability.

Deposition path-dependent lightweight support design and its implication to self-support topology optimization

Abstract This paper presents a lightweight support design method for material extrusion-type three-dimensional printed panel structures that innovatively involves the deposition path curvature information for support point determination. Specifically, this support design method provides a robust segmentation algorithm to divide the filament deposition paths into segments based on the curvature sign alternating condition, and then searches for the fewest support points for the filaments counting on the experimentally calibrated relationship between the maximum allowable self-support distance and the local mean curvature. The proposed method features in generating thin-walled skeleton-ray styled support structures that are lightweight while providing firm support for the panels. More importantly, the support design method provides a new type of self-support criterion for structural topology optimization involving non-designable planar panels, i.e., only a sparse point set would be sufficient to support the panel. Consequently, more materials could be spent on enhancing the load-bearing capacity instead of being wasted on oversupporting. The achievable structural performances from self-support topology optimization with this new self-support criterion can improve significantly. Support design and printing tests were conducted on a few panel structures that validated the improved support effect compared with equal-volume supports generated by commercial software. Equidistant and gap-free deposited filaments, no filament collapse due to insufficient support, and no isolated voids reflect the improved support effect. The improved self-support topological design was also validated through a comparative numerical case study, and a compliance reduction of 7.76% was achieved.

Piecewise-smooth surface fitting onto unstructured 3D sketches

We propose a method to transform unstructured 3D sketches into piecewise smooth surfaces that preserve sketched geometric features. Immersive 3D drawing and sketch-based 3D modeling applications increasingly produce imperfect and unstructured collections of 3D strokes as design output. These 3D sketches are readily perceived as piecewise smooth surfaces by viewers, but are poorly handled by existing 3D surface techniques tailored to well-connected curve networks or sparse point sets. Our algorithm is aligned with human tendency to imagine the strokes as a small set of simple smooth surfaces joined along stroke boundaries. Starting with an initial proxy surface, we iteratively segment the surface into smooth patches joined sharply along some strokes, and optimize these patches to fit surrounding strokes. Our evaluation is fourfold: we demonstrate the impact of various algorithmic parameters, we evaluate our method on synthetic sketches with known ground truth surfaces, we compare to prior art, and we show compelling results on more than 50 designs from a diverse set of 3D sketch sources.

Satellite Pose Estimation via Only a Single Spatial Circle

To estimate the pose of satellites in space, the docking ring component has strong rigid body characteristics and can provide a fixed circular feature, which is an important object. However, due to the need for additional constraints to estimate a single spatial circle pose on the docking ring, practical applications are greatly limited. In response to the above problems, this paper proposes a pose solution method based on a single spatial circle. First, the spatial circle is discretized into a set of 3D asymmetric specific sparse points, eliminating the strict central symmetry of the circle. Then, a two-stage pose estimation network, Hvnet, based on Hough voting is proposed to locate the 2D sparse points on the image. Finally, the position and orientation of the spatial circle are obtained by the Perspective-n-Point (PnP) algorithm. The effectiveness of the proposed method was verified through experiments, and the method was found to achieve good solution accuracy under a complex lighting environment.

Towards real-time 3D visualization with multiview RGB camera array.

A real-time 3D visualization (RT3DV) system using a multiview RGB camera array is presented. RT3DV can process multiple synchronized video streams to produce a stereo video of a dynamic scene from a chosen view angle. Its design objective is to facilitate 3D visualization at the video frame rate with good viewing quality. To facilitate 3D vision, RT3DV estimates and updates a surface mesh model formed directly from a set of sparse key points. The 3D coordinates of these key points are estimated from matching 2D key points across multiview video streams with the aid of epipolar geometry and trifocal tensor. To capture the scene dynamics, 2D key points in individual video streams are tracked between successive frames. We implemented a proof of concept RT3DV system tasked to process five synchronous video streams acquired by an RGB camera array. It achieves a processing speed of 44 milliseconds per frame and a peak signal to noise ratio (PSNR) of 15.9 dB from a viewpoint coinciding with a reference view. As a comparison, an image-based MVS algorithm utilizing a dense point cloud model and frame by frame feature detection and matching will require 7 seconds to render a frame and yield a reference view PSNR of 16.3 dB.

VPU: A Video-Based Point Cloud Upsampling Framework

In this work, we propose a new patch-based framework called VPU for the video-based point cloud upsampling task by effectively exploiting temporal dependency among multiple consecutive point cloud frames, in which each frame consists of a set of unordered, sparse and irregular 3D points. Rather than adopting the sophisticated motion estimation strategy in video analysis, we propose a new spatio-temporal aggregation (STA) module to effectively extract, align and aggregate rich local geometric clues from consecutive frames at the feature level. By more reliably summarizing spatio-temporally consistent and complementary knowledge from multiple frames in the resultant local structural features, our method better infers the local geometry distributions at the current frame. In addition, our STA module can be readily incorporated with various existing single frame-based point upsampling methods (e.g., PU-Net, MPU, PU-GAN and PU-GCN). Comprehensive experiments on multiple point cloud sequence datasets demonstrate our video-based point cloud upsampling framework achieves substantial performance improvement over its single frame-based counterparts.

SPU-Net: Self-Supervised Point Cloud Upsampling by Coarse-to-Fine Reconstruction With Self-Projection Optimization.

The task of point cloud upsampling aims to acquire dense and uniform point sets from sparse and irregular point sets. Although significant progress has been made with deep learning models, state-of-the-art methods require ground-truth dense point sets as the supervision, which makes them limited to be trained under synthetic paired training data and not suitable to be under real-scanned sparse data. However, it is expensive and tedious to obtain large numbers of paired sparse-dense point sets as supervision from real-scanned sparse data. To address this problem, we propose a self-supervised point cloud upsampling network, named SPU-Net, to capture the inherent upsampling patterns of points lying on the underlying object surface. Specifically, we propose a coarse-to-fine reconstruction framework, which contains two main components: point feature extraction and point feature expansion, respectively. In the point feature extraction, we integrate the self-attention module with the graph convolution network (GCN) to capture context information inside and among local regions simultaneously. In the point feature expansion, we introduce a hierarchically learnable folding strategy to generate upsampled point sets with learnable 2D grids. Moreover, to further optimize the noisy points in the generated point sets, we propose a novel self-projection optimization associated with uniform and reconstruction terms as a joint loss to facilitate the self-supervised point cloud upsampling. We conduct various experiments on both synthetic and real-scanned datasets, and the results demonstrate that we achieve comparable performances to state-of-the-art supervised methods.

Near-field photometric stereo using a ring-light imaging device

Traditional photometric stereo reconstructs the 3D surface shape of the target in fine details but assumes distant/directional lighting and orthogonal imaging. Yet, systematic errors occur in practical applications where the lights are divergent and near to the object. In this paper, we present a new post-processing method to correct the bias using a ring-light imaging device. We demonstrate and put forward a bias regulation process in ring-light equipment using traditional photometric stereo, where an approximate linear deviation exists in the surface gradient and a related quadratic deviation exists in the estimated surface height. Based on this low-frequency bias regulation, the proposed method corrects the systematic errors in traditional photometric stereo by using a set of sparse known real 3D points of the object surface, in order to fit the quadratic height error model and obtain more accurate 3D heights estimation. The proposed method has been evaluated using both simulated and real data to verify its accuracy and effectiveness, and has achieved significant performance. In addition, we integrated ring-light sources in homemade equipment to conduct real-world experiments, which demonstrates significant bias reduction and higher reconstruction quality compared to the existing methods. The source code of our method is available at https://github.com/fanhao/ring-light-photometric-stereo.

GeometryMotion-Net: A Strong Two-Stream Baseline for 3D Action Recognition

In this work, we propose a strong two-stream baseline method referred to as GeometryMotion-Net for 3D action recognition. For efficient 3D action recognition, we first represent each point cloud sequence as a limited number of randomly sampled frames with each frame consisting of a sparse set of points. After that, we propose a new two-stream framework for effective 3D action recognition. For the geometry stream, we propose a new module to produce a virtual overall geometry point cloud by first merging all 3D points from these selected frames, and then we exploit local neighborhood information of each point in the feature space. In the motion stream, for any two neighboring point cloud frames, we also propose a new module to generate one virtual forward motion point cloud and one virtual backward motion point cloud. Specifically, for each point in the current frame, we first produce a set of 3D offset features relative to the neighboring points in the reference frame ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> , the previous/subsequent frame) and then exploit local neighborhood information of this point in the offset feature space. Based on the newly generated virtual overall geometry point cloud and multiple virtual forward/backward motion point clouds, any existing point cloud analysis methods ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e.g.</i> , PointNet) can be readily adopted for extracting discriminant geometry and bidirectional motion features in the geometry and motion streams, respectively, which are further aggregated to make our two-stream network trainable in an end-to-end fashion. Comprehensive experiments on both large-scale datasets ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> NTU RGB+D 60 and NTU RGB+D 120) and small-scale datasets ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> , N-UCLA and UWA3DII) demonstrate the effectiveness and efficiency of our two-stream network for 3D action recognition.

Combinational spectral band activation complexity: Uncovering hidden neuromuscular firing dynamics in EMG

A new approach, Combinational Spectral Band Activation Complexity (CSB-AC), that extracts the neuromuscular firing dynamics of surface electromyography (sEMG) signals by applying entropic methods in a multi-dimensional fashion by analyzing the signals temporally, spectrally, and intensity dynamics simultaneously is presented. The CSB-AC signal processing approach introduces a methodology that highlights that a small amount of key fiducial points embedded within the sEMG, 1000x reduction in EMG data, are only needed to show statistically significant changes of the neuromuscular firing dynamics.CSB-AC was compared to the more generalized sample entropy method to demonstrate physiological differences between cohorts and baseline mapping between the two measurements. Results indicated significant differences between CSB-AC and sample entropy regardless of age groups for tibialis anterior and plantar flexion muscles (gastrocnemius medialis, gastrocnemius lateralis, and soleus). Significant differences were found between older and younger subject groups for the gastrocnemius medialis and soleus with the older adults having higher complexity values. CSB-AC produces greater complexity than sample entropy, where this sparser set of data holds paramount information for describing neuromuscular firing and should not be ignored. CSB-AC, accomplishes this by simultaneously assessing the complexity of sEMG’s time, intensity, and spectral content, where latent properties of neuromuscular dynamics within this unique set of sparse sEMG data points are critical to characterizing neuromuscular firing.

Building High-Fidelity Human Body Models From User-Generated Data

We propose a key point-based approach, refers to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">KPhub-PC</i> , to estimate high-fidelity human body models from low-quality point clouds acquired with an affordable 3D scanner and a variation <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">KPhub-I</i> that can achieve the same purpose based on low-resolution single images taken by smartphones. In KPhub-PC, a sparse set of key points is annotated to guide the deformation of a parametric 3D human body model SMPL and then a high-fidelity human body model that can explain the target point clouds is built. Besides building 3D human body models from point clouds, KPhub-I is designed to estimate accurate 3D human body models from single 2D images. The SMPL model is fitted to 2D joints and the boundary of the human body which are detected using CNN based methods automatically. Considering that people are in stable poses most of the time, a stable pose prior is defined from CMU motion capture dataset for further improving accuracy. Extensive experiments demonstrate that in both types of user-generated data, the proposed approaches can build believable and animatable human body models robustly. Our approach outperforms the state-of-the-arts in the accuracy of both human body shape and pose estimation.