Distance Field Research Articles

Safe motion planning and formation control of quadruped robots

This paper introduces a motion planning and cooperative formation control approach for quadruped robots and multi-agent systems. First, in order to improve the efficiency and safety of quadruped robots navigating in complex environments, this paper proposes a new planning method that combines the dynamic model of quadruped robots and a gradient-optimized obstacle avoidance strategy without Euclidean Signed Distance Field. The framework is suitable for both static and slow dynamic obstacle environments, aiming to achieve multiple goals of obstacle avoidance, minimizing energy consumption, reducing impact, satisfying dynamic constraints, and ensuring trajectory smoothness. This approach differs in that it reduces energy consumption throughout the movement from a new perspective. Meanwhile, this method effectively reduces the impact of the ground on the robot, thus mitigating the damage to its structure. Second, we combine the dynamic control barrier function and the virtual leader-follower model to achieve efficient and safe formation control through model predictive control. Finally, the proposed algorithm is validated through both simulations and real-world scenarios testing.

Implicit conformal design for gradient architected materials

This paper develops a conformal architected materials design method based on implicit modeling, which enables functional gradient modulation. This method utilizes the mapping relationship between conformal hexahedral element and the cubic bounding box of architected material to construct the signed distance field. To enhance strength and stiffness of the structure, this study integrates the relative density distribution obtained from topology optimization to regulate the density of conformal architected materials through density mapping. Compared to traditional methods, the proposed method not only reduces the damage of the boundary structure caused by cutting, achieving a mutual match between the architected materials and curved geometry, but also retains the ability to control the distribution of relative density. The numerical analysis and experimental results demonstrate that conformal gradient architected materials exhibit better structural strength and stiffness compared to array-generated gradient architected materials, which indicates that the proposed method has potential applications in lightweight design.

CAP-UDF: Learning Unsigned Distance Functions Progressively From Raw Point Clouds With Consistency-Aware Field Optimization.

Surface reconstruction for point clouds is an important task in 3D computer vision. Most of the latest methods resolve this problem by learning signed distance functions from point clouds, which are limited to reconstructing closed surfaces. Some other methods tried to represent open surfaces using unsigned distance functions (UDF) which are learned from ground truth distances. However, the learned UDF is hard to provide smooth distance fields due to the discontinuous character of point clouds. In this paper, we propose CAP-UDF, a novel method to learn consistency-aware UDF from raw point clouds. We achieve this by learning to move queries onto the surface with a field consistency constraint, where we also enable to progressively estimate a more accurate surface. Specifically, we train a neural network to gradually infer the relationship between queries and the approximated surface by searching for the moving target of queries in a dynamic way. Meanwhile, we introduce a polygonization algorithm to extract surfaces using the gradients of the learned UDF. We conduct comprehensive experiments in surface reconstruction for point clouds, real scans or depth maps, and further explore our performance in unsupervised point normal estimation, which demonstrate non-trivial improvements of CAP-UDF over the state-of-the-art methods.

Interactive Distance Field Mapping and Planning to Enable Human-Robot Collaboration

Interactive Distance Field Mapping and Planning to Enable Human-Robot Collaboration

High-throughput 3D shape completion of potato tubers on a harvester

Potato yield is an important metric for farmers to further optimize their cultivation practices. Potato yield can be estimated on a harvester using an RGB-D camera that can estimate the three-dimensional (3D) volume of individual potato tubers. A challenge, however, is that the 3D shape derived from RGB-D images is only partially completed, underestimating the actual volume. To address this issue, we developed a 3D shape completion network, called CoRe++, which can complete the 3D shape from RGB-D images. CoRe++ is a deep learning network that consists of a convolutional encoder and a decoder. The encoder compresses RGB-D images into latent vectors that are used by the decoder to complete the 3D shape using the deep signed distance field network (DeepSDF). To evaluate our CoRe++ network, we collected partial and complete 3D point clouds of 339 potato tubers on an operational harvester in Japan. On the 1425 RGB-D images in the test set (representing 51 unique potato tubers), our network achieved a completion accuracy of 2.8 mm on average. For volumetric estimation, the root mean squared error (RMSE) was 22.6 ml, and this was better than the RMSE of the linear regression (31.1 ml) and the base model (36.9 ml). We found that the RMSE can be further reduced to 18.2 ml when performing the 3D shape completion in the center of the RGB-D image. With an average 3D shape completion time of 10 ms per tuber, we can conclude that CoRe++ is both fast and accurate enough to be implemented on an operational harvester for high-throughput potato yield estimation. CoRe++’s high-throughput and accurate processing allows it to be applied to other tuber, fruit and vegetable crops, thereby enabling versatile, accurate and real-time yield monitoring in precision agriculture. Our code, network weights and dataset are publicly available at https://github.com/UTokyo-FieldPhenomics-Lab/corepp.git.

Enhanced block-structured quadrilateral mesh generation: integrating cross-field and distance field for optimal domain decomposition

Enhanced block-structured quadrilateral mesh generation: integrating cross-field and distance field for optimal domain decomposition

Generative 3D Cardiac Shape Modelling for in-silico Trials.

We propose a deep learning method to model and generate synthetic aortic shapes based on representing shapes as the zero-level set of a neural signed distance field, conditioned by a family of trainable embedding vectors with encode the geometric features of each shape. The network is trained on a dataset of aortic root meshes reconstructed from CT images by making the neural field vanish on sampled surface points and enforcing its spatial gradient to have unit norm. Empirical results show that our model can represent aortic shapes with high fidelity. Moreover, by sampling from the learned embedding vectors, we can generate novel shapes that resemble real patient anatomies, which can be used for in-silico trials.

PCO: Precision-Controllable Offset Surfaces with Sharp Features

Surface offsetting is a crucial operation in digital geometry processing and computer-aided design, where an offset is defined as an iso-value surface of the distance field. A challenge emerges as even smooth surfaces can exhibit sharp features in their offsets due to the non-differentiable characteristics of the underlying distance field. Prevailing approaches to the offsetting problem involve approximating the distance field and then extracting the iso-surface. However, even with dual contouring (DC), there is a risk of degrading sharp feature points/lines due to the inaccurate discretization of the distance field. This issue is exacerbated when the input is a piecewise-linear triangle mesh. This study is inspired by the observation that a triangle-based distance field, unlike the complex distance field rooted at the entire surface, remains smooth across the entire 3D space except at the triangle itself. With a polygonal surface comprising n triangles, the final distance field for accommodating the offset surface is determined by minimizing these n triangle-based distance fields. In implementation, our approach starts by tetrahedralizing the space around the offset surface, enabling a tetrahedron-wise linear approximation for each triangle-based distance field. The final offset surface within a tetrahedral range can be traced by slicing the tetrahedron with planes. As illustrated in the teaser figure, a key advantage of our algorithm is its ability to precisely preserve sharp features. Furthermore, this paper addresses the problem of simplifying the offset surface's complexity while preserving sharp features, formulating it as a maximal-clique problem.

Real-time Large-scale Deformation of Gaussian Splatting

Neural implicit representations, including Neural Distance Fields and Neural Radiance Fields, have demonstrated significant capabilities for reconstructing surfaces with complicated geometry and topology, and generating novel views of a scene. Nevertheless, it is challenging for users to directly deform or manipulate these implicit representations with large deformations in a real-time fashion. Gaussian Splatting (GS) has recently become a promising method with explicit geometry for representing static scenes and facilitating high-quality and real-time synthesis of novel views. However, it cannot be easily deformed due to the use of discrete Gaussians and the lack of explicit topology. To address this, we develop a novel GS-based method (GaussianMesh) that enables interactive deformation. Our key idea is to design an innovative mesh-based GS representation, which is integrated into Gaussian learning and manipulation. 3D Gaussians are defined over an explicit mesh, and they are bound with each other: the rendering of 3D Gaussians guides the mesh face split for adaptive refinement, and the mesh face split directs the splitting of 3D Gaussians. Moreover, the explicit mesh constraints help regularize the Gaussian distribution, suppressing poor-quality Gaussians ( e.g. , misaligned Gaussians, long-narrow shaped Gaussians), thus enhancing visual quality and reducing artifacts during deformation. Based on this representation, we further introduce a large-scale Gaussian deformation technique to enable deformable GS, which alters the parameters of 3D Gaussians according to the manipulation of the associated mesh. Our method benefits from existing mesh deformation datasets for more realistic data-driven Gaussian deformation. Extensive experiments show that our approach achieves high-quality reconstruction and effective deformation, while maintaining the promising rendering results at a high frame rate (65 FPS on average on a single commodity GPU).

3DGSR: Implicit Surface Reconstruction with 3D Gaussian Splatting

In this paper, we present an implicit surface reconstruction method with 3D Gaussian Splatting (3DGS), namely 3DGSR, that allows for accurate 3D reconstruction with intricate details while inheriting the high efficiency and rendering quality of 3DGS. The key insight is to incorporate an implicit signed distance field (SDF) within 3D Gaussians for surface modeling, and to enable the alignment and joint optimization of both SDF and 3D Gaussians. To achieve this, we design coupling strategies that align and associate the SDF with 3D Gaussians, allowing for unified optimization and enforcing surface constraints on the 3D Gaussians. With alignment, optimizing the 3D Gaussians provides supervisory signals for SDF learning, enabling the reconstruction of intricate details. However, this only offers sparse supervisory signals to the SDF at locations occupied by Gaussians, which is insufficient for learning a continuous SDF. Then, to address this limitation, we incorporate volumetric rendering and align the rendered geometric attributes (depth, normal) with that derived from 3DGS. In sum, these two designs allow SDF and 3DGS to be aligned, jointly optimized, and mutually boosted. Our extensive experimental results demonstrate that our 3DGSR enables high-quality 3D surface reconstruction while preserving the efficiency and rendering quality of 3DGS. Besides, our method competes favorably with leading surface reconstruction techniques while offering a more efficient learning process and much better rendering qualities.

NU-NeRF: Neural Reconstruction of Nested Transparent Objects with Uncontrolled Capture Environment

The geometry reconstruction of transparent objects is a challenging problem due to the highly noncontinuous and rapidly changing surface color caused by refraction. Existing methods rely on special capture devices, dedicated backgrounds, or ground-truth object masks to provide more priors and reduce the ambiguity of the problem. However, it is hard to apply methods with these special requirements to real-life reconstruction tasks, like scenes captured in the wild using mobile devices. Moreover, these methods can only cope with solid and homogeneous materials, greatly limiting the scope of the application. To solve the problems above, we propose NU-NeRF to reconstruct nested transparent objects without requiring a dedicated capture environment or additional input. NU-NeRF is built upon a neural signed distance field formulation and leverages neural rendering techniques. It consists of two main stages. In Stage I, the surface color is separated into reflection and refraction. The reflection is decomposed using physically based material and rendering. The refraction is modeled using a single MLP given the refraction and view directions, which is a simple yet effective solution of refraction modeling. This step produces high-fidelity geometry of the outer surface. In stage II, we use explicit ray tracing on the reconstructed outer surface for accurate light transport simulation. The surface reconstruction is executed again inside the outer geometry to obtain any inner surface geometry. In this process, a novel transparent interface formulation is used to cope with different types of transparent surfaces. Experiments conducted on synthetic scenes and real captured scenes show that NU-NeRF is capable of producing better reconstruction results than previous methods and achieves accurate nested surface reconstruction under an uncontrolled capture environment.

DreamUDF: Generating Unsigned Distance Fields from A Single Image

Recent advances in diffusion models and neural implicit surfaces have shown promising progress in generating 3D models. However, existing generative frameworks are limited to closed surfaces, failing to cope with a wide range of commonly seen shapes that have open boundaries. In this work, we present DreamUDF, a novel framework for generating high-quality 3D objects with arbitrary topologies from a single image. To address the challenge of generating proper topology given sparse and ambiguous observations, we propose to incorporate both the data priors from a multi-view diffusion model and the geometry priors brought by an unsigned distance field (UDF) reconstructor. In particular, we leverage a joint framework that consists of 1) a generation module that produces a neural radiance field for photorealistic renderings from arbitrary views; and 2) a reconstruction module that distills the learnable radiance field into surfaces with arbitrary topologies. We further introduce a field coupler that bridges the radiance field and UDF under a novel optimization scheme. This allows the two modules to mutually boost each other during training. Extensive experiments and evaluations demonstrate that DreamUDF achieves high-quality reconstruction and robust 3D generation on both closed and open surfaces with arbitrary topologies, compared to the previous works.

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.

TriMe++: Multi-threaded triangular meshing in two dimensions

We present TriMe++, a multi-threaded software library designed for generating two-dimensional meshes for intricate geometric shapes using the Delaunay triangulation. Multi-threaded parallel computing is implemented throughout the meshing procedure, making it suitable for fast generation of large-scale meshes. Three iterative meshing algorithms are implemented: the DistMesh algorithm, the centroidal Voronoi diagram meshing, and a hybrid of the two. We compare the performance of the three meshing methods in TriMe++, and show that the hybrid method retains the advantages of the other two. The software library achieves significant parallel speedup when generating a large mesh with 106 points. TriMe++ can handle complicated geometries and generates adaptive meshes of high quality. Program summaryProgram title:TriMe++CPC Library link to program files:https://doi.org/10.17632/jxcsxtywtw.1Developer's repository link:https://github.com/jiayinlu19960224/TriMeLicensing provisions: BSD 3-clauseProgramming language: C++External routines/libraries: OpenMP, multi-threaded Voro++Nature of problem: Multi-threaded geometry meshing in two dimension using the Delaunay triangulationSolution method: The TriMe++ library is built around several C++ classes that follows a structured meshing pipeline. During initialization, the shape_2d class reads the geometry input and generates a signed distance field using a grid-based data structure to represent the shape. The sizing_2d class subsequently produces adaptive element sizing and density fields for the mesh. It uses an adaptive quad-tree data structure, enabling efficient refinement of sizing and density values in areas with complex geometries. In the meshing procedure, the parallel_meshing_2d class iteratively improves point positions in the mesh. In each meshing iteration, the multi-threaded Voro++ library generates the Delaunay triangulation of the points. Users can select from three meshing algorithms, the DistMesh algorithm in the mesh_alg_2d_dm class, the centroidal Voronoi diagram meshing algorithm in the mesh_alg_2d_cvd class, and a hybrid method of the two in the mesh_alg_2d_hybrid class Throughout this meshing workflow, we use OpenMP for multi-threaded parallel computations.

Citation classics on distance and online learning: a bibliometric analysis

Purpose The purpose of this study is to identify seminal research works on distance and online learning that have had significant impact on the domain. Design/methodology/approach The authors used the SCOPUS database for this study as the data source, and a well-defined search strategy retrieved the items for analysis. First, the authors identified the h-index (n = 207) of the discipline to determine the threshold for listing the top works. The authors critically analysed these classic publications using several bibliometric parameters to present the analysis. To understand the primary focus of the classic research works, the authors also carried out a keyword cluster analysis using VOSviewer. Findings While the USA produced maximum classic research, authors from Canada have maximum research visibility in terms of citations (n = 474.06). Canada also received the highest value of RCI (1.30), followed by Taiwan and Australia. The majority of the classics are published in 67 scientific journals. Of these, Computers and Education published the highest number with a quarter of the total citations (n = 19,403). Although e-learning was the nucleus of the research theme, the authors observed that students, learning systems, online learning, blended learning, learning management systems and computer-aided instructions dominated their influence in the research cluster. Originality/value To the best of the authors’ knowledge, this is the first of its kind work in the field of distance and online learning. Findings of this study would be useful to faculty, researchers and students in the discipline to focus on the seminal works and understand their implications better in the context of the growing significance of the discipline.

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.

Assessing the lightning performance of sustainable GTL type dielectric liquids versus mineral oils and synthetic ester in a non-uniform electric field

This paper presents for the first time the results of complex comparative tests on the lightning performance of a wide range of sustainable electrical insulating liquids made in GTL (Gas-to-Liquids) technology. Three different GTLs are compared with conventional mineral oils (inhibited and uninhibited) as well as biodegradable synthetic ester. Tests are aimed to determine Lightning Impulse Breakdown Voltage (LIBV) and Acceleration Voltage (Va) at standard lightning impulse voltage of both polarities. Those are performed at 25 mm gap distance of point-sphere electrode setup representing non-uniform electric field distribution. In addition, light emission is studied as well. Results show that for the conditions of experiment LIBV values tend to be similar for all tested dielectric liquids with a slight advantage of mineral oils at negative polarity and GTL-I oil at positive polarity. In turn, in terms of Va, it was found that at negative polarity the GTL oils are, in general, fully comparable with a high grade inhibited mineral oil. The Va of GTLs is in the range 260–275 kV versus 255–260 kV that characterizes mineral oils. When considering positive polarity the GTL-I is slightly inferior to other hydrocarbons with Va equal to 195 kV versus 230–255 kV characterizing other GTLs and mineral oils. For both polarities tested synthetic ester has much lower acceleration voltage in relation to hydrocarbon liquids including GTLs, which constitutes a huge disadvantage of the ester. Although the studies are limited to only one gap distance and non-uniform electric field distribution, it can be stated that the GTLs are worth to be examined as alternative to mineral oil when considering LIBV and Va as the analysed quantities. In addition, a special added value of the performed measurements should be mentioned that the measurements confirmed that Va parameter may be a good dielectric indicator of a dielectric liquid performance, especially when examining new product introduced to the market.

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.