Signed Distance Field Research Articles

Synchronized Tracing of Primitive-based Implicit Volumes

Implicit volumes are known for their ability to represent smooth shapes of arbitrary topology thanks to hierarchical combinations of primitives using a structure called a blobtree. We present a new tile-based rendering pipeline well suited for modeling scenarios, i.e., no preprocessing is required when primitive parameters are updated. When using approximate signed distance fields (fields with Lipschitz bound close to 1), we rely on compact, smooth CSG operators - extended from standard bounded operators - to compute a tight augmented bounding volume for all primitives of the blobtree. The pipeline relies on a low-resolution A-buffer storing the primitives of interest of a given screen tile. The A-buffer is then used during ray processing to synchronize threads within a subfrustum. This allows coherent field evaluation within workgroups. We use a sparse bottom-up tree traversal to prune the blobtree on-the-fly which allows us to decorrelate field evaluation complexity from the full blobtree size. The ray processing itself is done using the sphere tracing algorithm. The pipeline scales well to volumes consisting of thousands of primitives.

A Neural Network-Based State-Constrained Control Strategy for Underactuated Aerial Transportation Systems Within Narrow Workspace

The aerial transportation system belongs to a symmetrical system and has recently garnered increasing attention from researchers due to its broad application range and convenient operation. The control difficulty of the aerial transportation system lies in the fact that the load is not directly actuated, posing a significant challenge for state-constrained control. Taking the motion of an unmanned aerial vehicle (UAV) suspension transportation system within complex pipelines as an example, this paper employs the the swept volume signed distance field (SVSDF) method to search for state boundaries, which is an aspect not considered or elaborated in many state-constrained control approaches. Furthermore, adaptive state-constrained control based on the radial basis function (RBF) neural network is utilized for the case of experiencing unknown air resistance. The convergence of the proposed method for underactuated and actuated state variables is theoretically demonstrated based on the Lyapunov technique. Compared with existing methods, the error integral index demonstrates that the proposed method displays better convergence capability in the simulation section when considering state constraints under disturbance and air resistance.

Real-Time LiDAR–Inertial Simultaneous Localization and Mesh Reconstruction

In this paper, a novel LiDAR–inertial-based Simultaneous Localization and Mesh Reconstruction (LI-SLAMesh) system is proposed, which can achieve fast and robust pose tracking and online mesh reconstruction in an outdoor environment. The LI-SLAMesh system consists of two components, including LiDAR–inertial odometry and a Truncated Signed Distance Field (TSDF) free online reconstruction module. Firstly, to reduce the odometry drift errors we use scan-to-map matching, and inter-frame inertial information is used to generate prior relative pose estimation for later LiDAR-dominated optimization. Then, based on the motivation that the unevenly distributed residual terms tend to degrade the nonlinear optimizer, a novel residual density-driven Gauss–Newton method is proposed to obtain the optimal pose estimation. Secondly, to achieve fast and accurate 3D reconstruction, compared with TSDF-based mapping mechanism, a more compact map representation is proposed, which only maintains the occupied voxels and computes the vertices’ SDF values of each occupied voxels using an iterative Implicit Moving Least Squares (IMLS) algorithm. Then, marching cube is performed on the voxels and a dense mesh map is generated online. Extensive experiments are conducted on public datasets. The experimental results demonstrate that our method can achieve significant localization and online reconstruction performance improvements. The source code will be made public for the benefit of the robotic community.

Research on wireless channel model based on improved ray tracing algorithm that considers multiple diffuse scattering and employs pyramid-shaped ray tubes as the carrier

This paper extensively utilizes fine three dimensional environmental data obtained from laser point clouds. Based on theories such as geometrical optics and effective roughness theory, a deterministic wireless channel model is established, which integrates higher-order diffuse scattering. This model is referred to as the ray tracing fusion with higher-order diffuse scattering model. To expedite the collision calculation between rays and the scene, this paper introduces a combined approach of voxelization and signed distance field, resulting in a remarkable 16-fold improvement in computational speed. Moreover, aiming to balance accuracy and efficiency, the paper systematically analyzes the optimization computation parameters of the model. Finally, the proposed model is validated using measurement data in the frequency range of 1 GHz to 6 GHz in mountainous terrain. The results indicate that the predicted outcomes of the proposed model have an accuracy within 6 dB compared to the measurement results, and are superior to ITU-R P.1546, which is an international standard recommended by the International Telecommunication Union for modeling electromagnetic wave propagation in undulating terrain. This provides necessary technical support for network planning and optimization.

GS‐Octree: Octree‐based 3D Gaussian Splatting for Robust Object‐level 3D Reconstruction Under Strong Lighting

AbstractThe 3D Gaussian Splatting technique has significantly advanced the construction of radiance fields from multi‐view images, enabling real‐time rendering. While point‐based rasterization effectively reduces computational demands for rendering, it often struggles to accurately reconstruct the geometry of the target object, especially under strong lighting conditions. Strong lighting can cause significant color variations on the object's surface when viewed from different directions, complicating the reconstruction process. To address this challenge, we introduce an approach that combines octree‐based implicit surface representations with Gaussian Splatting. Initially, it reconstructs a signed distance field (SDF) and a radiance field through volume rendering, encoding them in a low‐resolution octree. This initial SDF represents the coarse geometry of the target object. Subsequently, it introduces 3D Gaussians as additional degrees of freedom, which are guided by the initial SDF. In the third stage, the optimized Gaussians enhance the accuracy of the SDF, enabling the recovery of finer geometric details compared to the initial SDF. Finally, the refined SDF is used to further optimize the 3D Gaussians via splatting, eliminating those that contribute little to the visual appearance. Experimental results show that our method, which leverages the distribution of 3D Gaussians with SDFs, reconstructs more accurate geometry, particularly in images with specular highlights caused by strong lighting. The source code can be downloaded from https://github.com/LaoChui999/GS-Octree.

Neural Vector Fields for Implicit Surface Representation and Inference

AbstractNeural implicit fields have recently shown increasing success in representing, learning and analysis of 3D shapes. Signed distance fields and occupancy fields are still the preferred choice of implicit representations with well-studied properties, despite their restriction to closed surfaces. With neural networks, unsigned distance fields as well as several other variations and training principles have been proposed with the goal to represent all classes of shapes. In this paper, we develop a novel and yet a fundamental representation considering unit vectors in 3D space and call it Vector Field (VF). At each point in $$\mathbb {R}^3$$ R 3 , VF is directed to the closest point on the surface. We theoretically demonstrate that VF can be easily transformed to surface density by computing the flux density. Unlike other standard representations, VF directly encodes an important physical property of the surface, its normal. We further show the advantages of VF representation, in learning open, closed, or multi-layered surfaces. We show that, thanks to the continuity property of the neural optimization with VF, a separate distance field becomes unnecessary for extracting surfaces from the implicit field via Marching Cubes. We compare our method on several datasets including ShapeNet where the proposed new neural implicit field shows superior accuracy in representing any type of shape, outperforming other standard methods. Codes are available at https://github.com/edomel/ImplicitVF.

Advances in vision-based deep learning methods for interacting hands reconstruction: A survey

Vision-based hand reconstructions have become noteworthy tools in enhancing interactive experiences in various applications such as virtual reality, augmented reality, and autonomous driving, which enable sophisticated interactions by reconstructing complex motions of human hands. Despite significant progress driven by deep-learning methodologies, the quest for high-fidelity interacting hands reconstruction faces challenges such as limited dataset diversity, lack of detailed hand representation, occlusions, and differentiation between similar hand structures. This survey thoroughly reviews deep learning-based methods, diverse datasets, loss functions, and evaluation metrics addressing the complexities of interacting hands reconstruction. Mainstream algorithms of the past five years are systematically classified into two main categories: algorithms that employ explicit representations, such as parametric meshes and 3D Gaussian splatting, and those that utilize implicit representations, including signed distance fields and neural radiance fields. Novel deep-learning models like graph convolutional networks and transformers are applied to solve the aforementioned challenges in hand reconstruction effectively. Beyond summarizing these interaction-aware algorithms, this survey also briefly discusses hand tracking in virtual reality and augmented reality. To the best of our knowledge, this is the first survey specifically focusing on the reconstruction of both hands and their interactions with objects. The survey contains the various facets of hand modeling, deep learning approaches, and datasets, broadening the horizon of hand reconstruction research and future innovation in natural user interactions.

Improved GAN-based deep learning approach for strain field prediction and failure analysis of precast bridge slab joints

Nonlinear finite element analysis (FEA) is crucial for understanding complex stress-strain behaviors and assessing potential structural failure risks. Building on the recent success of deep learning (DL) methods in physical field predictions, there has been growing interest in forecasting internal force fields of structures beyond the existing data scope. In this study, a data-driven strain field analysis model based on an improved Generative Adversarial Network (GAN) is proposed. To enrich the input data, this novel approach incorporates the Signed Distance Field (SDF) derived from the characteristics of the original Finite Element (FE) models. The generator, based on U-Net, is enhanced with channel attention mechanisms and loss penalty terms, forming the core of the improved GAN. The effectiveness of the proposed method is demonstrated using two parallel datasets comprising 3-Headed bar tension models across two planes. Subsequently, the generated strain field is subjected to feature extraction using the 2D-Principal Component Analysis (2D-PCA) method, followed by structural failure determination through the K-Nearest Neighbor (KNN) algorithm. The results indicate that the proposed improved approach achieves a significant reduction in Root Mean Square Error (RMSE) of 20.71 % and 13.21 % across the two datasets, with the structural failure determination method reaching an F1-score of 0.971. Thus, the intelligent strain field analysis method introduced here effectively predicts strain distributions and promptly identifies failure states, offering valuable insights for further numerical analysis and structural design.

A Toolpath Generator Based on Signed Distance Fields and Clustering Algorithms for Optimized Additive Manufacturing

Additive manufacturing (AM) methods have been gaining momentum because they provide vast design and fabrication possibilities, increasing the accessibility of state-of-the-art hardware through recent developments in user-friendly computer-aided drawing/engineering/manufacturing (CAD/CAE/CAM) tools. However, in comparison to the conventional manufacturing methods, AM processes have some disadvantages, including the machining precision and fabrication process times. The first issue has been mostly resolved through the recent advances in manufacturing hardware, sensors, and controller systems. However, the latter has been widely investigated by researchers with different toolpath planning perspectives. As a contribution to these investigations, the present study proposes a toolpath planning method for AM, which aims to provide highly continuous yet distance-optimized solutions. The approach is based on the utilization of the signed distance field (SDF), clustering, and minimization of toolpath distances among cluster centroids. The method was tested on various geometries with simple closed curves to complex geometries with holes, which provides effective toolpaths, e.g., with relative distance reduction percentages up to 16.5% in comparison to conventional rectilinear infill patterns.

Cone-Traced Supersampling With Subpixel Edge Reconstruction.

While signed distance fields (SDFs) in theory offer infinite level of detail, they are typically rendered using the sphere tracing algorithm at finite resolutions, which causes the common rasterized image synthesis problem of aliasing. Most existing optimized antialiasing solutions rely on polygon mesh representations; SDF-based geometry can only be directly antialiased with the computationally expensive supersampling or with post-processing filters that may produce undesirable blurriness and ghosting. In this work, we present cone-traced supersampling (CTSS), an efficient and robust spatial antialiasing solution that naturally complements the sphere tracing algorithm, does not require casting additional rays per pixel or offline pre-filtering, and can be easily implemented in existing real-time SDF renderers. CTSS performs supersampling along the traced ray near surfaces with partial visibility - object contours - identified by evaluating cone intersections within a pixel's view frustum. We further introduce subpixel edge reconstruction (SER), a technique that extends CTSS to locate and resolve complex pixels with geometric edges in relatively flat regions, which are otherwise undetected by cone intersections. Our combined solution relies on a specialized sampling strategy to minimize the number of shading computations and correlates sample visibility to aggregate the samples. With comparable antialiasing quality at significantly lower computational cost, CTSS is a reliable practical alternative to conventional supersampling.

RGBTSDF: An Efficient and Simple Method for Color Truncated Signed Distance Field (TSDF) Volume Fusion Based on RGB-D Images

RGB-D image mapping is an important tool in applications such as robotics, 3D reconstruction, autonomous navigation, and augmented reality (AR). Efficient and reliable mapping methods can improve the accuracy, real-time performance, and flexibility of sensors in various fields. However, the currently widely used Truncated Signed Distance Field (TSDF) still suffers from the problem of inefficient memory management, making it difficult to directly use it for large-scale 3D reconstruction. In order to address this problem, this paper proposes a highly efficient and accurate TSDF voxel fusion method, RGBTSDF. First, based on the sparse characteristics of the volume, an improved grid octree is used to manage the whole scene, and a hard coding method is proposed for indexing. Second, during the depth map fusion process, the depth map is interpolated to achieve a more accurate voxel fusion effect. Finally, a mesh extraction method with texture constraints is proposed to overcome the effects of noise and holes and improve the smoothness and refinement of the extracted surface. We comprehensively evaluate RGBTSDF and similar methods through experiments on public datasets and the datasets collected by commercial scanning devices. Experimental results show that RGBTSDF requires less memory and can achieve real-time performance experience using only the CPU. It also improves fusion accuracy and achieves finer grid details.

A CAD-oriented parallel-computing design framework for shape and topology optimization of arbitrary structures using parametric level set

Recently, the high-resolution topology optimization to promote engineering applicability has gained much more attentions. However, an accurate and highly-efficient design framework for implementing shape and topology optimization of engineering structures with integration of CAD model is still in demand. In the current work, the critical intention is to develop a CAD-oriented parallel-computing design framework for arbitrary structures, where the Parametric Level Set Method (PLSM) is employed for shape and topology optimization. Firstly, an implicit identification model is constructed for generating a signed distance field using the vertex and normal information from the ‘STL’ file of engineering structures. The signed distance field is combined with the compactly supported radial basis functions (CSRBFs) to solve the initial level set function with a parametrization. This method is applied to present all domains, including design domains, Neumann boundary domains, Dirichlet boundary domains, and non-design domains. Secondly, the CPU parallel strategy is considered for allocating partitions of structural stiffness matrix in finite element analysis to different CPU cores for the parallel-computing to save computation costs. Thirdly, a parallel-computing design formulation is developed for performing shape and topology optimization of arbitrary structures, in which the partitioned terms of all design variables and stiffness matrix are concurrently computed on each CPU core. Finally, several classic benchmarks and the critical engineering structure of Virtual Reality (VR) glass part with extremely complex geometries, are discussed to demonstrate the effectiveness and efficiency of the proposed design framework.

Dynamic Obstacle Avoidance for Mobile Robots Based on 2D Differential Euclidean Signed Distance Field Maps in Park Environment

In this paper, a novel and complete navigation system is proposed for mobile robots in a park environment, which can achieve safe and stable navigation as well as robust dynamic obstacle avoidance. The navigation system includes a global planning layer and a local planning layer. The global planner plans a series of way-points using the A* algorithm based on an offline stored occupancy grid map and sends them to the local planner. The local planner incorporates a dynamic obstacle avoidance mechanism. In contrast to existing dynamic obstacle avoidance algorithms based on trajectory tracking, we innovatively construct a two-dimensional Difference ESDF (Euclidean Signed Distance Field) map to represent obstacle motion information. The local planner outputs control actions by scoring candidate paths. A series of simulation experiments and real-world tests are conducted to verify that the navigation system can safely and robustly accomplish navigation tasks. The safety distance of the simulation experiment group with the dynamic obstacle avoidance scoring item added increased by 1.223 compared to the group without the dynamic obstacle avoidance scoring item.

TensoSDF: Roughness-aware Tensorial Representation for Robust Geometry and Material Reconstruction

Reconstructing objects with realistic materials from multi-view images is problematic, since it is highly ill-posed. Although the neural reconstruction approaches have exhibited impressive reconstruction ability, they are designed for objects with specific materials (e.g., diffuse or specular materials). To this end, we propose a novel framework for robust geometry and material reconstruction, where the geometry is expressed with the implicit signed distance field (SDF) encoded by a tensorial representation, namely TensoSDF. At the core of our method is the roughness-aware incorporation of the radiance and reflectance fields, which enables a robust reconstruction of objects with arbitrary reflective materials. Furthermore, the tensorial representation enhances geometry details in the reconstructed surface and reduces the training time. Finally, we estimate the materials using an explicit mesh for efficient intersection computation and an implicit SDF for accurate representation. Consequently, our method can achieve more robust geometry reconstruction, outperform the previous works in terms of relighting quality, and reduce 50% training times and 70% inference time. Codes and datasets are available at https://github.com/Riga2/TensoSDF.

Spatial and Surface Correspondence Field for Interaction Transfer

In this paper, we introduce a new method for the task of interaction transfer. Given an example interaction between a source object and an agent, our method can automatically infer both surface and spatial relationships for the agent and target objects within the same category, yielding more accurate and valid transfers. Specifically, our method characterizes the example interaction using a combined spatial and surface representation. We correspond the agent points and object points related to the representation to the target object space using a learned spatial and surface correspondence field, which represents objects as deformed and rotated signed distance fields. With the corresponded points, an optimization is performed under the constraints of our spatial and surface interaction representation and additional regularization. Experiments conducted on human-chair and hand-mug interaction transfer tasks show that our approach can handle larger geometry and topology variations between source and target shapes, significantly outperforming state-of-the-art methods.

Implicit Swept Volume SDF: Enabling Continuous Collision-Free Trajectory Generation for Arbitrary Shapes

In the field of trajectory generation for objects, ensuring continuous collision-free motion remains a huge challenge, especially for non-convex geometries and complex environments. Previous methods either oversimplify object shapes, which results in a sacrifice of feasible space or rely on discrete sampling, which suffers from the "tunnel effect". To address these limitations, we propose a novel hierarchical trajectory generation pipeline, which utilizes the Swept Volume Signed Distance Field (SVSDF) to guide trajectory optimization for Continuous Collision Avoidance (CCA). Our interdisciplinary approach, blending techniques from graphics and robotics, exhibits outstanding effectiveness in solving this problem. We formulate the computation of the SVSDF as a Generalized Semi-Infinite Programming model, and we solve for the numerical solutions at query points implicitly, thereby eliminating the need for explicit reconstruction of the surface. Our algorithm has been validated in a variety of complex scenarios and applies to robots of various dynamics, including both rigid and deformable shapes. It demonstrates exceptional universality and superior CCA performance compared to typical algorithms. The code will be released at https://github.com/ZJU-FAST-Lab/Implicit-SVSDF-Planner for the benefit of the community.

Asteroid-NeRF: A deep-learning method for 3D surface reconstruction of asteroids

Context. Asteroids preserve important information about the origin and evolution of the Solar System. Three-dimensional (3D) surface models of asteroids are essential for exploration missions and scientific research. Regular methods for 3D surface reconstruction of asteroids, such as stereo-photogrammetry (SPG), usually struggle to reconstruct textureless areas and can only generate sparse surface models. Stereo-photoclinometry (SPC) can reconstruct pixel-wise topographic details but its performance depends on the availability of images obtained under different illumination conditions and suffers from uncertainties related to surface reflectance and albedo. Aims. This paper presents Asteroid-NeRF, a novel deep-learning method for 3D surface reconstruction of asteroids that is based on the state-of-the-art neural radiance field (NeRF) method. Methods. Asteroid-NeRF uses a signed distance field (SDF) to reconstruct a 3D surface model from multi-view posed images of an asteroid. In addition, Asteroid-NeRF incorporates appearance embedding to adapt to different illumination conditions and to maintain the geometric consistency of a reconstructed surface, allowing it to deal with the different solar angles and exposure conditions commonly seen in asteroid images. Moreover, Asteroid-NeRF incorporates multi-view photometric consistency to constrain the SDF, enabling optimised reconstruction. Results. Experimental evaluations using actual images of asteroids Itokawa and Bennu demonstrate the promising performance of Asteroid-NeRF, complementing traditional methods such as SPG and SPC. Furthermore, due to the global consistency and pixel-wise training of Asteroid-NeRF, it produces highly detailed surface reconstructions. Asteroid-NeRF offers a new and effective solution for high-resolution 3D surface reconstruction of asteroids that will aid future exploratory missions and scientific research on asteroids.

A general particle modeling method for complex geometries

Particle modeling for complex geometries is a challenge for the wide application of particle methods in engineering fields. The traditional modeling method with Cartesian coordinates faces difficulties in accurately representing boundary shapes and would lose flow details near the slender structure. The modeling method with the signed distance field (SDF) and particle shifting technique can obtain a uniform boundary-fitting particle distribution. However, the accuracy and efficiency of SDF construction, as well as the conservation of geometry volume after discretizing the model into particles, need to be further improved. In this paper, a general particle modeling method is proposed for arbitrary geometries. A double search technique is proposed to quickly construct the narrowband signed distance field (NSDF) near the geometry boundary. A scanning method is developed for the NSDF to determine the inner/outer relationship between the non-narrowband grids and the geometry. In addition, a volume compensation technique is proposed to ensure the volume conservation of the particle model. A modeling evaluation system is established, and three evaluation indicators are proposed to evaluate the quality of particle distribution and total volume conservation for particle models. Complex geometries such as the Stanford bunny, the Stanford dragon, and the centrifugal impeller are modeled to validate the accuracy and convergence of the proposed method. The results show that the proposed method can achieve a more uniform and accurate boundary-fitting particle distribution for complex geometries, and it can also effectively model tiny structures while significantly reducing total geometry volume error.

N$^{3}$-Mapping: Normal Guided Neural Non-Projective Signed Distance Fields for Large-Scale 3D Mapping

N$^{3}$-Mapping: Normal Guided Neural Non-Projective Signed Distance Fields for Large-Scale 3D Mapping

Online Learning of Continuous Signed Distance Fields Using Piecewise Polynomials

Online Learning of Continuous Signed Distance Fields Using Piecewise Polynomials