Signed Distance Functions

Also known as SDF

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3 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

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Latest papers 25

Sep 28, 2026cs.RO

QuadHand: A Compact Quadrotor Aerial Manipulator with MRC-SDF-Based Whole-Body Motion Planning

Uncrewed aerial manipulators (UAMs) integrate robotic arms with aerial platforms for three-dimensional physical interaction. However, enlarging the workspace increases arm-induced disturbances, while existing geometric representations face a trade-off between geometric fidelity and computational efficiency in close-proximity interaction. This paper presents QuadHand, a compact quadrotor aerial manipulator with a 3-DoF arm, gripper, and battery-assisted passive CoG compensation module to reduce dominant arm-induced disturbances. We further propose MRC-SDF, a Multi-articulated Robot-Centric Signed Distance Field that preserves fine geometric detail with tractable computation, and a spatiotemporal whole-body trajectory optimization framework that jointly optimizes the quadrotor and manipulator for safe and executable trajectory generation. Simulations and real-world experiments demonstrate safe and executable aerial manipulation in complex environments.

Rui Jin, Ruiyang Liu, Xinhang Xu +4

School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 · NTU–VinUni Joint Research Laboratory for Embodied AI and Robotics, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, and VinUniversity, Hanoi, Vietnam

Signed Distance Functions Whole-Body Robotic Manipulation Robot Motion Planning Aerial Manipulation

Sep 21, 2026cs.RO

Feasibility Distance Fields for Heterogeneous Constraints in Robot Configuration Space

Robot manipulators are monitored by constraint-specific indicators whose units and gradient scales are not comparable, so they do not provide a common measure of the configuration-space motion remaining before violation. We define the feasibility distance field (FDF) as the distance, under a fixed positive-definite joint-space metric, to the union of infeasible configuration sets. Classical distance-to-set theory gives 1-Lipschitz continuity, almost-everywhere differentiability, and unit dual-gradient norm wherever the nearest projection is unique. The robotics contribution is an admissibility analysis showing when practical constraints define non-empty closed sets. We derive admissible formulations for external and self-collision, joint limits, dexterity, Cartesian and task-projected compliance, joint torque under payload, and dynamic manipulability. Since every field uses the same metric, heterogeneous constraints compose by a pointwise minimum, conditioned constraints retain a fixed distance space, and multi-robot constraints produce block-sparse gradients that identify which robots must react. We generate projection-based labels and train neural approximations with a distance loss and an Eikonal penalty. Simulations on a UR5e and a dual-arm cell evaluate seven fields using value, projection, sign, gradient, composition, and moving-obstacle diagnostics. Across 8,000 configurations, the largest feasible-side secant ratio is 0.920, mean learned gradient norms range from 0.994 to 0.998, and projection residuals range from 0.011 to 0.034 rad. Across 24 random obstacle paths, the external and composed collision fields achieve 90.4% and 91.6% success within 3 cm, with sign-error rates below 2%. The results support a common configuration-space margin and identify approximation errors near medial axes and sparsely sampled boundaries.

Xijing Cui, Huayan Pu, Jun Luo +1

First and third authors' affiliation · Second author's affiliation

Constrained Motion Planning Signed Distance Functions Safe Motion Planning

Sep 8, 2026cs.CV

MRI-Guided Reslice-Refined Cross-Slice SDF Reconstruction of the Left Ventricle from Cardiac MRI with Sparse Axial Supervision

Reconstructing a three-dimensional left-ventricular (LV) endocardial surface from cardiac magnetic resonance (CMR) data is challenging when supervision is available on only a small number of axial slices. Through-plane geometry is weakly constrained, and automatically generated two-dimensional masks can propagate segmentation errors into the recovered shape. We present MR-RS-SDFR, a per-case implicit signed distance field (SDF) framework that reconstructs a continuous LV surface from a CMR volume and sparse axial weak masks. The method first builds a cross-slice SDF initialization from axial and longitudinal geometric cues and then refines the field using two complementary signals: MRI edge-field normal alignment, which provides an image-derived boundary cue independent of the weak masks, and differentiable reslice Dice and contour consistency, which preserve agreement with the observed planes. We evaluate three weak-mask generators -- LOO TransUNet, LOO nnU-Net, and an off-the-shelf Medical SAM3 model used without MM-WHS-specific training or fine-tuning -- and five sparsity levels from 4 to 64 axial planes. In the sparse-16 setting, final MR-RS-SDFR reconstruction reaches 0.928 Dice and 3.80mm HD95 with Medical SAM3 masks. The upstream generators do not exhibit a single common ranking across 2D and dense 3D segmentation, and nnU-Net- and Medical-SAM3-driven sparse reconstruction achieve the same mean final Dice despite different upstream error profiles. Across all three sparse-16 mask sources, MR-RS-SDFR is numerically better than protocol-matched full GHD+DVS in both Dice and HD95. Final Dice improves markedly from sparse-4 to sparse-16 and then saturates at the reported precision through sparse-64. These results support MRI-guided per-case SDF refinement as a reconstruction strategy that remains effective across weak-mask generators and supervision densities.

Quanxin Zheng, Shuai Zhao

1China Electronics (Beijing) Information Technology Research Institute Co., Ltd.

Implicit Neural Representations Signed Distance Functions Sparse-View 3D Reconstruction Cardiac MRI

Aug 13, 2026cs.CV

Predicting Signed Distance Functions for Visual Instance Segmentation

Visual instance segmentation is a challenging problem and becomes even more difficult if objects of interest varies unconstrained in shape. Some objects are well described by a rectangle, however, this is hardly always the case. Consider for instance long, slender objects such as ropes. Anchor-based approaches classify predefined bounding boxes as either negative or positive and thus provide a limited set of shapes that can be handled. Defining anchor-boxes that fit well to all possible shapes leads to an infeasible number of prior boxes. We explore a different approach and propose to train a neural network to compute distance maps along different directions. The network is trained at each pixel to predict the distance to the closest object contour in a given direction. By pooling the distance maps we obtain an approximation to the signed distance function (SDF). The SDF may then be thresholded in order to obtain a foreground-background segmentation. We compare this segmentation to foreground segmentations obtained from the state-of-the-art instance segmentation method YOLACT. On the COCO dataset, our segmentation yields a higher performance in terms of foreground intersection over union (IoU). However, while the distance maps contain information on the individual instances, it is not straightforward to map them to the full instance segmentation. We still believe that this idea is a promising research direction for instance segmentation, as it better captures the different shapes found in the real world.

Emil Brissman, Joakim Johnander, Michael Felsberg

1Computer Vision Laboratory, Dept. of Electrical Engineering, Linköping University · 2Saab, Sweden · 3Zenseact, Sweden

Signed Distance Functions Instance Segmentation

Aug 7, 2026cs.RO

Hölder Signed Distance: A Differentiable, Signed, Parallelizable Metric for Robotics

Computing distances between sets is essential in robotic motion planning and control, where differentiable gradients enable real-time optimization. The Euclidean Signed Distance Function (SDF), however, is not differentiable everywhere, and existing alternatives often sacrifice differentiability, sign information, or computational efficiency. In this letter, we introduce a novel differentiable signed distance between convex polyhedra. To this end, we first propose differentiable versions of the minimum and maximum operators, termed the Hölder minimum and Hölder maximum. We then replace the original min-max operators in the classical SDF formulation, yielding the Hölder signed distance. Unlike prior differentiable distance formulations that rely on iterative algorithms, our approach is computed in closed form, eliminating convergence issues while remaining naturally amenable to GPU parallelization. We validate the practical advantages and computational performance of the proposed distance through runtime comparisons with existing approaches. We also present a robotic manipulator experiment, demonstrating its suitability for applications in control.

Felipe Bartelt, Ali Umut Kaypak, Anthony Tzes +3

Signed Distance Functions Differentiable Optimization Robot Motion Planning

Aug 7, 2026cs.RO

Real-time Whole-Body Motion Planning for Mobile Manipulators Carrying Arbitrarily Shaped Payloads via Kinematically-Coupled SVSDF

Mobile manipulators are increasingly tasked with transporting large, non-convex payloads through cluttered environments, yet existing planners either oversimplify the payload geometry or fail to handle the kinematic coupling between manipulator links, leading to lost feasible space or stalled optimization. This letter presents a real-time whole-body motion planning framework for mobile manipulators carrying arbitrarily shaped payloads. The front-end employs a chain-decomposed kernel-based collision check that preserves the true geometry of the robot and payload, with compact storage and fast bit-level queries. A mid-end preprocessing stage converts the front-end path into a continuous trajectory enforcing smoothness and feasibility, and executes it directly when collision-free to bypass the costly back-end. When refinement is required, the back-end performs trajectory optimization built on a Kinematically-Coupled SVSDF (KC-SVSDF), which propagates collision-avoidance gradients along the kinematic chain to produce coherent whole-body escape directions. Ablation studies, comparative benchmarks against state-of-the-art baselines, and real-world experiments on a differential-drive mobile manipulator demonstrate that the proposed framework reliably transports large, non-convex payloads through tight passages and cluttered environments.

Yisheng Li, Longji Yin, Tingrui Zhang +6

Department of Mechanical Engineering, University of Hong Kong · Institute for Interdisciplinary Information Sciences, Tsinghua University

Signed Distance Functions Mobile Manipulation Robotic Manipulation Robot Motion Planning Robot Collision Avoidance

Aug 3, 2026cs.RO

Control Barrier Functions via Minkowski Operations for Safe Navigation among Polytopes

Safely navigating polytopic environments while respecting the dynamics, control, and exact geometry of the underlying system is a challenge in robotics. Control barrier functions (CBFs) synthesize safe control policies by rendering the safe set forward invariant, but many existing CBF-based methods approximate polytopes using conservative smooth shapes, such as spheres or ellipsoids, to obtain explicit differentiable distance functions. In this article, we propose an exact Signed Distance Function (SDF) formulation for a {\it polytopic} robot and {\it polytopic} obstacles and integrate it with nonsmooth CBFs. Leveraging Minkowski operations, the proposed method computes the exact SDF via companion convex programs in both the collision-free (positive-sign) and in-collision (negative-sign) cases. Furthermore, by exploiting the convenient geometric properties of 2D Minkowski operations and the optimality conditions of the two companion convex programs, we derive a unified analytical expression for the gradient of the exact SDF via sensitivity analysis. The exact rotational gradient further reveals a previously masked class of local minima induced by the coupling between geometry and nonholonomic kinematics. We demonstrate the effectiveness of the proposed framework through a pure-translation case and three scenarios with unicycle models involving recovery from an unsafe initialization and single- and multiple-obstacle avoidance. Comparisons with baseline methods highlight how the proposed framework enables non-conservative maneuvers and safety recovery.

Yi-Hsuan Chen, Shuo Liu, Wei Xiao +2

Department of Aerospace Engineering, University of Maryland, College Park, MD 20742, USA · Department of Mechanical Engineering, Boston University, Boston, MA 02215, USA · School of Electrical and Electronic Engineering, Nanyang Technological University, and with M3S, SMART, Singapore +1

Signed Distance Functions Control Barrier Functions Safe Robot Navigation Robot Collision Avoidance

Aug 1, 2026cs.RO

Grasp Execution Without a Planner: Configuration-Space Grasp Distance Fields with Certified Safety & Guaranteed Quality

Mainstream plan-then-track approaches to multifingered grasp execution entail selecting a grasp, planning a collision-free trajectory, and tracking the resulting trajectory via a feedback controller. Pose-estimation error during execution or scene motion can invalidate this open-loop commitment and trigger replanning. We thus present Grasp Distance Fields (GDFs), smooth softmin distances to finite sets of arm-hand grasp configurations. Using their negative gradients as feedback, we jointly select and execute grasps without planning a trajectory. A CBF-CLF quadratic program (QP) enforces self-collision, workspace, object, and obstacle-clearance constraints, while its CLF slack quantifies obstruction of task progress. We bound the softmin approximation error by

\log N/ρ

and prove forward invariance of the filtered safe set. To handle changes in contact topology, we combine a hysteretic contact-mode transition with a wrench-quality CBF that limits degradation of the realized force-closure margin relative to hold onset. Using our method, a fixed-base manipulator and a Unitree G1 equipped with the same underactuated hand grasp and lift 46 of 50 test objects amid clutter and moving obstacles. The realized grasps also retain a median 94% of their synthesized quality margin, and each QP solve requires 0.09 ms within a 20 ms control interval. Project page: www.clintonenwerem.com/gdf.

Clinton Enwerem, John S. Baras, Calin Belta

Department of Electrical and Computer Engineering and the Institute for Systems Research (ISR), University of Maryland, College Park, MD, USA

Robotic Control Robotic Grasping Signed Distance Functions Contact-Rich Robotic Manipulation

Jul 21, 2026cs.RO

From Distances to Trajectories: Real-Time Signed Distance Function Mapping and Distance-Accelerated Motion Planning for UAVs

Autonomous flight in cluttered environments requires a robot to build a geometric map of its surroundings and plan safe, dynamically feasible trajectories, all onboard and in real time. Conventional approaches treat mapping and planning as separate stages and often rely on binary occupancy for collision checking. We argue that these two stages should be co-designed around a single representation: a signed distance function (SDF). By encoding distance to the nearest obstacle, an SDF provides richer information for planning and trajectory optimization than occupancy alone. We develop an Octree REsidual Network (OREN) that pairs an explicit octree prior with an implicit neural residual to reconstruct SDFs online from point cloud observations with the efficiency of volumetric methods and the accuracy and differentiability of neural methods. In tandem, we develop Bubble

^\star

, a search-based planner that exploits the distance information to grow maximal collision-free balls, which we call bubbles, with formal guarantees of termination, completeness, and failure detection. Planning over a graph of bubbles significantly reduces collision checks compared to a grid-based A

^\star

search and returns a bubble sequence that forms a safe corridor for trajectory optimization. We demonstrate the integrated OREN-Bubble

^\star

approach onboard a quadrotor, navigating unseen indoor environments in real time under tight compute constraints. OREN improves SDF estimation by

22

% compared to baselines, while Bubble

^\star

finds trajectories spanning

\approx 90

m through a cluttered environment in

1

-

3

sec., whereas baselines take up to

10

sec. in the same environment.

Jason Stanley, Zhirui Dai, Qihao Qian +6

UC San Diego, La Jolla, USA · Electrical and Computer Engineering Department, UC San Diego, 9500 Gilman Dr, La Jolla, 92093, CA, USA. · Shield AI, San Diego, USA +1

Trajectory Generation Signed Distance Functions UAV Navigation UAV Trajectory Optimization Safe Motion Planning Motion Planning+1

Jul 18, 2026cs.GR

Points as Tori: Fast Pointwise Signed Distance for Point Clouds

We describe a method for computing signed distance to point clouds that allows fast pointwise evaluation at arbitrary spatial resolution. As input, our method takes a point cloud with normals; as output, it provides an analytical parameterization that allows queries of signed distance to the approximate underlying surface at arbitrary points - simultaneously providing reconstruction and distance. Our key idea is to reconstruct shapes by locally fitting point clouds with tori, which have closed-form signed distance functions. Tori are fitted in a feed-forward manner, using a pre-trained network to output per-point curvature and shift parameters. Importantly, our method does not require costly global optimization or spatial discretization, and is easily parallelizable. Underlying our method is a new theory that unifies signed distance with the classic reconstruction methods of winding numbers and Poisson surface reconstruction. We use our method to compute signed distance to point clouds arising from photogrammetry, meshes, 3D Gaussians, and neural implicits. Our method allows point clouds to be used directly in applications, without explicit surface reconstruction: as examples, we take offsets of point clouds, apply morphological and Boolean operations, and directly visualize offset surfaces using sphere tracing.

Nicole Feng, Ioannis Gkioulekas, Keenan Crane

Carnegie Mellon University, USA · Roblox, USA

Signed Distance Functions 3D Reconstruction Point Cloud Surface Reconstruction Feed-Forward 3D Reconstruction

Jul 15, 2026cs.CV

CASA-SDF: Curriculum-Aware Spatial Adaptation with Curvature-Guided Density for Neural Implicit Surface Reconstruction

Neural implicit representations have emerged as a powerful paradigm for 3D reconstruction. However, high-fidelity indoor surface reconstruction remains a significant challenge, primarily due to the pronounced \emph{geometric heterogeneity} of indoor scenes. Large texture-less planar regions typically require stronger regularization to suppress high-frequency artifacts, while thin structures demand sharper, more adaptive representations to mitigate the spectral bias of multi-layer perceptrons (MLPs) and prevent over-smoothing. Existing approaches often rely on spatially indiscriminate prior supervision and a scene-global SDF-to-density transformation, which constrains their ability to balance planar smoothness and detail preservation. In this paper, we propose CASA-SDF (Curriculum-Aware Spatial Adaptation for SDF), a unified framework that addresses this challenge via complementary adaptations of supervision and representation capacity. Specifically, Hybrid Spatially-Adaptive Uncertainty Annealing (SAUA) fuses semantic and photometric uncertainties to construct a pixel-wise curriculum for monocular prior supervision. This strategy maintains regularization in reliable regions while attenuating unreliable supervision early in training to enable data-driven photometric refinement. Meanwhile, Curvature-Aware Locally Adaptive Density Transformation (CALADT) progressively modulates the sharpness of the SDF-to-density mapping via a curvature proxy to enhance the representation of thin structures. Extensive experiments on benchmark indoor datasets demonstrate that CASA-SDF improves surface completeness and detail recovery on high-frequency structures, without compromising the stability of planar surfaces.

Lei Yang, Weiqing Li, Zhiyong Su +1

School of Computer Science and Engineering, Nanjing University of Science and Technology, 200 Xiaolingwei, Nanjing, Jiangsu, China210094 · School of Automation, Nanjing University of Science and Technology, 200 Xiaolingwei, Nanjing, Jiangsu, China210094

Signed Distance Functions 3D Reconstruction Curriculum Learning Indoor Scene Reconstruction

Jul 5, 2026cs.RO

GPU-Accelerated Polygonal Signed Distance Functions for Real-Time Collision Avoidance

Optimization-based local planning and control require high-rate evaluation of collision-avoidance constraints over a prediction horizon. Accurately accounting for robot and obstacle geometry in these evaluations can be computationally expensive. The resulting bottleneck motivates collision-avoidance constraints that combine computational efficiency with geometric fidelity. The proposed polygonal signed distance function (PSDF) returns the minimum of exact signed distances between a convex polygonal robot footprint and convex obstacle components represented by their boundary edges. It is implemented as a training-free, branch-free tensorized geometric pipeline enabling batched GPU execution and automatic differentiation. The PSDF is embedded in model predictive control by locally linearizing the PSDF-based safety constraint within a sequential quadratic programming--based real-time iteration scheme, yielding the PSDF-embedded model predictive controller (PSDF-MPC). The design separates CPU/GPU computation so that the GPU evaluates batched PSDF values and gradients while the CPU solves a sparse quadratic program whose size and sparsity are determined by system dimensions and horizon length rather than obstacle and edge counts. Microbenchmarks show that PSDF scales favorably relative to geometric and learned collision-field baselines. Closed-loop comparisons in simulation, together with real-world navigation experiments, demonstrate that PSDF-MPC operates in real time and achieves collision-free navigation in dense polygonal environments.

Taekwon Ga, Jongeun Choi

School of Mechanical Engineering, Yonsei University, Seoul 03722, South Korea

Signed Distance Functions GPU Acceleration Model Predictive Control Robot Collision Avoidance

Jun 30, 2026cs.CV

HSDF-Lane: Height-Aligned Signed Distance Field with Semantic Lane Prior for 3D Lane Detection

Monocular 3D lane detection plays a critical role in autonomous driving, yet recovering reliable 3D geometry from a single image remains challenging due to inherent depth ambiguity. Prior methods project image features into Bird's-Eye-View (BEV) space under a flat-ground assumption, causing geometric distortion on real-world roads. Recent methods instead predict explicit height maps to capture non-planar surfaces, but still rely on sparse anchor-based regression and exploit the recovered geometry merely for spatial transformation rather than semantic understanding. To overcome these limitations, we propose HSDF-Lane, which implicitly models the road surface as a Height-aligned Signed Distance Field (HSDF) over a densely sampled 3D feature volume. Through differentiable rendering, the HSDF jointly produces an accurate height map and surface-aligned features. We further introduce Lane-aware Semantic Positional Encoding (LSPE), which injects a lane-existence prior derived from the surface-aligned features into the transformer queries, coupling geometric structure with semantic guidance. Extensive experiments on the OpenLane benchmark show that HSDF-Lane achieves state-of-the-art performance in both 3D lane detection and height map estimation.

Jiyong Boo, Byeongin Joung, Hyemin Yang +1

KAIST, Republic of Korea

Signed Distance Functions Autonomous Driving Perception

Jun 1, 2026cs.RO

Embedding Semantic Risk into Distance Fields and CBFs for Online Monocular Safe Control

We propose an online monocular perception-to-control framework that embeds semantic risk into the distance field used by Control Barrier Function (CBF)-based safe navigation and teleoperation. Many perception-based safety filters assign the same distance-based safety margin to all mapped obstacles or use semantics only as a downstream controller adjustment, rather than encoding semantic risk in the spatial representation. Our framework instead reasons online about obstacle geometry and class-dependent risk by embedding semantic information directly into the Euclidean Signed Distance Field (ESDF). This design encodes semantic risk before control optimization, so high-risk objects exert a larger spatial influence in the safety field while retaining efficient ESDF queries at runtime. Specifically, a foundation-model-based SLAM front end reconstructs dense 3-D geometry from monocular RGB video, while per-frame semantic segmentation provides pixel-level class labels that are fused into the reconstructed geometry. The resulting geometric-semantic representation is then converted into an ESDF, where semantic labels identify safety-relevant regions and impose class-dependent inflation before field computation. The semantic-aware ESDF provides the local distance values and spatial derivatives required by the CBF controller, while class-dependent gains further regulate the controller response. Extensive simulation and hardware experiments demonstrate online operation at 10--20 Hz and semantic-aware safe behavior in both teleoperation and autonomous navigation.

Dawei Zhang, Nuo Chen, Shuo Liu +2

Division of Systems Engineering, Boston University, United States · Department of Electrical and Computer Engineering at Texas A&M University, United States · Department of Mechanical Engineering, Boston University, United States

Signed Distance Functions Control Barrier Functions Safe Robot Navigation

May 30, 2026cs.GR

Directed Distance Fields for Constant-Time Ray Queries on Gaussian Splatting

3D Gaussian Splatting (3DGS) renders new views of a scene in real time. Like every rasterizer, it answers only primary rays, the rays from the camera through the image. It cannot trace the secondary rays that shadows, ambient occlusion, and global illumination need. We turn a trained 3DGS scene into a ray oracle by distilling a Directed Distance Function (DDF). The DDF is a small neural field. It takes a ray, given by an origin and a direction, and returns the distance to the first surface and whether the ray hits anything. Each query is one forward pass. The field is 52MB, and its size does not depend on the number of Gaussians, so its cost and memory stay flat as the scene grows. We make three points. First, we study what supervision a DDF needs. Depth rendered from the Gaussians is too blurry to teach thin parts, while clean distance supervision recovers them. Second, we measure speed. The DDF is 26 to 72 times faster than sphere tracing an equivalent signed distance field, and unlike a bounding volume hierarchy built over the Gaussians, even on dedicated RT-core hardware, its query time and memory do not grow with the scene. Third, we show a pipeline that needs no mesh: images give a 3DGS scene, a neural surface gives clean distances, and the DDF learns from them. We use the DDF as a secondary-ray oracle for global illumination. It reproduces reference ray-traced shadows at 30.3dB and ambient occlusion at 21.3~dB across 142 objects, and on real captured scenes. Our codes are available at https://github.com/smlab-niser/ddf-gs.

Subhankar MIshra

School of Computer Sciences, National Institute of Science Education and Research (NISER), 752050, India

3D Gaussian Splatting Signed Distance Functions

May 29, 2026cs.RO

Geometry-Aware Control Barrier Functions for Collision Avoidance via Bernstein Polynomial Approximations

Safe navigation often relies on well-defined conditions based on the shape of robots and obstacles, and can be challenging when they have irregular geometries. While Control Barrier Functions (CBFs) offer an efficient mechanism to enforce safe set forward invariance, common shape surrogates (e.g., spheres or super-ellipsoids) either are overly conservative in unstructured scenes or require many local primitives, which inflates constraint counts and degrades real-time performance. In this paper, we introduce a novel geometry-aware Control Barrier Function (CBF) based on Bernstein-Polynomial Signed Distance Fields (BP-SDFs). It provides a unified way to represent the obstacles and robots, so as to represent the barrier function with a unified minimum distance. Benefiting from the differentiability of the Bernstein polynomials, one can easily enforce the control constraints in a closed loop. We validate the method's efficiency and performance to guarantee safety in single-robot navigation and heterogeneous multi-robot collision avoidance via simulations under different environments.

Siwon Jo, Yanze Zhang, Yupeng Yang +1

GRASP Laboratory, University of Pennsylvania, Philadelphia, PA, USA · Department of Computer Science, University of Illinois Chicago, Chicago, IL, USA · Department of Computer Science, University of North Carolina at Charlotte, Charlotte, NC, USA

Multi-Robot Motion Planning Signed Distance Functions Control Barrier Functions Safe Robot Navigation Robot Safety Robot Collision Avoidance

May 28, 2026cs.CV

S2MDF: A Plug-And-Play Layer for Intersection-Free Multi-Object Signed Distance Fields

Compositional implicit surface representations model scenes as collections of objects, each encoded by a Signed Distance Field (SDF). A fundamental limitation of this approach is that multiple SDFs can produce geometries that interpenetrate, violating physical plausibility. Existing mitigation strategies rely on soft penalty terms that reduce but do not eliminate intersections, and require careful loss weighting. To truly prevent interpenetration, we propose a hard constraint on vector-valued SDFs and introduce S2MDF, a lightweight plug-and-play module that enforces the constraint on any object-compositional SDF representation without architectural modifications. It introduces negligible computational overhead and is compatible with linearly-interpolated standard meshing algorithms such as Marching Cubes. It can be applied during training or as a post-processing step. Experiments on multiple state-of-the-art compositional methods show that S2MDF reduces intersections to numerical precision while preserving reconstruction quality, outperforming existing mitigation strategies.

Deniz Sayin Mercadier, Federico Stella, Aurel Bizeau +2

CVLab, Ecole Polytechnique Fédérale de Lausanne (EPFL) Lausanne, Switzerland

Signed Distance Functions 3D Reconstruction 3D Scene Representation

May 25, 2026cs.CV

Metric--Phase Fields: Decoupling Distance and Sign for Thin-Structure Reconstruction from Unoriented Point Clouds

Neural Signed Distance Functions (SDFs) excel at reconstructing watertight manifolds but fail on thin structures and open boundaries due to strict inside--outside constraints. Conversely, Unsigned Distance Fields (UDFs) accommodate general geometries but suffer from gradient singularities at the zero-level set, hindering optimization and extraction. We introduce Metric--Phase Fields (MPFs), a decoupled implicit representation that separates metric proximity from topological phase. Given an unoriented point cloud, MPFs learn (i) an unsigned metric field

r

and (ii) a smooth phase field

θ

, for which we derive a bounded phase indicator

P=\tanh(βθ)

that provides soft inside--outside cues where they are meaningful. We couple the two fields via a gated-metric formulation with a residual phase injection to obtain a signed implicit function with stable near-surface gradients. The phase coefficient

β

is learnable, allowing MPFs to adaptively control the sharpness of the phase transition and the degree of saturation of the soft sign indicator. Experiments on both synthetic and scanned thin-shell and thin-plate shapes demonstrate that MPFs preserve thin and layered structures more faithfully than recent SDF-based methods, while also enabling more robust training and more reliable surface extraction than UDF-based approaches. Check out MPFs-GitHub for source code and test models.

Jiayi Kong, Xuhui Chen, Chen Zong +4

S-Lab, Nanyang Technological University, Singapore · Key Laboratory of System Software (CAS), Institute of Software, Chinese Academy of Sciences, China · University of Chinese Academy of Sciences, China +3

Signed Distance Functions 3D Reconstruction Point Cloud Surface Reconstruction

May 11, 2026cs.CV

DySurface: Consistent 4D Surface Reconstruction via Bridging Explicit Gaussians and Implicit Functions

While novel view synthesis (NVS) for dynamic scenes has seen significant progress, reconstructing temporally consistent geometric surfaces remains a challenge. Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS) offer powerful dynamic scene rendering capabilities; however, relying solely on photometric optimization often leads to geometric ambiguities. This results in discontinuous surfaces, severe artifacts, and broken surfaces over time. To address these limitations, we present DySurface, a novel framework that bridges the effectiveness of explicit Gaussians with the geometric fidelity of implicit Signed Distance Functions (SDFs) in dynamic scenes. Our approach tackles the structural discrepancy between the forward deformation of 3DGS (

canonical \rightarrow dynamic

) and the backward deformation required for volumetric SDF rendering (

dynamic \rightarrow canonical

). Specifically, we propose the VoxGS-DSDF branch that leverages deformed Gaussians to construct a dynamic sparse voxel grid, providing explicit geometric guidance to the implicit SDF field. This explicit anchoring effectively regularizes the volumetric rendering process, significantly improving surface reconstruction quality, with watertight boundaries and detailed representations. Quantitative and qualitative experiments demonstrate that DySurface significantly outperforms state-of-the-art baselines in geometric accuracy while maintaining competitive rendering performance.

Minje Kim, Younghyun Noh, Jaesoon Kim +1

KAIST · KT · Sungkyunkwan University

3D Gaussian Splatting Signed Distance Functions Dynamic Scene Reconstruction

May 5, 2026cs.CV

First Shape, Then Meaning: Efficient Geometry and Semantics Learning for Indoor Reconstruction

Neural Surface Reconstruction has become a standard methodology for indoor 3D reconstruction, with Signed Distance Functions (SDFs) proving particularly effective for representing scene geometry. A variety of applications require a detailed understanding of the scene context, driving the need for object-level semantic signals. While recent methods successfully integrate semantic labels, they often inherit the slow training time and limited scalability of multi-SDF learning. In this paper, we introduce FSTM, a unified approach for learning geometry and semantics through a two-step process: a geometry warm-up using RGB inputs and geometric cues, followed by semantic field estimation. By first optimising geometry without semantic supervision, we observe substantial improvements compared to the standard joint optimisation. Rather than relying on specialised modules or complex multi-SDF designs, FSTM shows that a streamlined formulation is sufficient to achieve strong geometric and semantic reconstructions. Experiments on both synthetic and real-world indoor datasets show that our method outperforms multi-SDF approaches. It trains 2.3x faster on Replica, improves robustness to real-world imperfections on ScanNet++, and achieves higher recall by recovering the surfaces of more objects in the scene. The code will be made available at https://remichierchia.github.io/FSTM.

Remi Chierchia, Léo Lebrat, David Ahmedt-Aristizabal +3

School of Electrical Engineering & Robotics, Queensland University of Technology, Australia · Imaging and Computer Vision Group, CSIRO Data61, Australia

Signed Distance Functions 3D Reconstruction 3D Semantic Segmentation Indoor Scene Reconstruction

May 5, 2026cs.CV

Learning Discriminative Signed Distance Functions from Multi-scale Level-of-detail Features for 3D Anomaly Detection

Detecting anomalies from 3D point clouds has received increasing attention in the field of computer vision, with some group-based or point-based methods achieving impressive results in recent years. However, learning accurate point-wise representations for 3D anomaly detection faces great challenges due to the large scale and sparsity of point clouds. In this study, a surface-based method is proposed for 3D anomaly detection, which learns a discriminative signed distance function using multi-scale level-of-detail features. We first present a Noisy Points Generation (NPG) module to generate different types of noise, thereby facilitating the learning of discriminative features by exposing abnormal points. Then, we introduce a Multi-scale Level-of-detail Feature (MLF) module to capture multi-scale information from a point cloud, which provides both fine-grained local and coarse-grained global feature information. Finally, we design an Implicit Surface Discrimination (ISD) module that leverages the extracted multi-scale features to learn an implicit surface representation of point clouds, which effectively trains a signed distance function to distinguish between abnormal and normal points. Experimental results demonstrate that the proposed method achieves an average object-level AUROC of 92.1% and 85.9% on the Anomaly-ShapeNet and Real3D-AD datasets, outperforming the current best approach by 2.1% and 3.6%, respectively. Codes are available at https://anonymous.4open.science/r/DLF-3AD-DA61.

Haibo Xiao, Hanzhe Liang, Jie Zhou +2

College of Computer Science and Software Engineering, Shenzhen University · Biological and Life Sciences Division, Mohamed bin Zayed University of Artificial Intelligence, UAE · Shenzhen Audencia Financial Technology Institute, Shenzhen University, China +1

Point Cloud Anomaly Detection Signed Distance Functions Point Cloud Learning Anomaly Detection

Apr 19, 2026cs.RO

Novel Algorithms for Smoothly Differentiable and Efficiently Vectorizable Contact Manifold Construction

Generating intelligent robot behavior in contact-rich settings is a research problem where zeroth-order methods currently prevail. Developing methods that make use of first/second order information about rigid-body dynamics in the presence of contact holds great promise in terms of increasing the solution speed and computational efficiency. The main bottleneck in this research direction is the difficulty in obtaining gradients and Hessians that are actually useful for numerical optimization, due to pathologies in all three steps of a common simulation pipeline: i) collision detection, ii) contact dynamics, iii) time integration. This abstract proposes a method that aims to address the collision detection part of the puzzle, via a novel pipeline designed from scratch with smooth (i.e. twice) differentiability and massive vectorizability on GPUs as the main priorities. This is in contrast to standard collision detection routines that are instead optimized for runtime on CPUs and minimal memory footprint, but do employ logic and control flow that hinder differentiability and vectorization. The proposed pipeline consists of the following contributions: i) highly expressive and compute efficient SDF representations, ii) differentiable broad-phase and narrow-phase routines that use these representations to generate vertex-SDF and edge-SDF contacts, iii) a differentiable routine for convex decomposition based contact blending.

Onur Beker, Andreas René Geist, Anselm Paulus +1

University of Tübingen

Signed Distance Functions Contact-Rich Robotic Manipulation Differentiable Programming Differentiable Physics

Nov 20, 2025cs.CV

TetraSDF: Analytic Isosurface Extraction with Multi-resolution Tetrahedral Grid

Extracting an explicit surface that exactly matches the zero-level set of a neural signed distance function (SDF) remains challenging. Sampling-based isosurfacing methods such as Marching Cubes introduce discretization error. In contrast, continuous piecewise affine (CPWA) analytic approaches typically require plain ReLU MLPs, which limits the ability to learn high-frequency SDFs in practice. We present TetraSDF, an analytic isosurface extraction framework for SDFs that retains the expressiveness of grid-based encoders while enabling exact zero-level set extraction, by representing the SDF with a ReLU MLP composed with a multi-resolution tetrahedral positional encoder. Our positional encoder's barycentric interpolation preserves a global CPWA structure, allowing us to track ReLU linear regions within an encoder-induced polyhedral complex. We further introduce a fixed analytic input preconditioner derived from the encoder's metric to reduce directional bias, thereby stabilizing training. Across multiple benchmarks, TetraSDF matches or surpasses existing grid-based encoders in SDF reconstruction accuracy, while faithfully recovering the network's zero-level set as a triangle mesh.

Seonghun Oh, Youngjung Uh, Jin-Hwa Kim

Yonsei University, Republic of Korea · NAVER AI Lab, Republic of Korea · Seoul National University, Republic of Korea

3D Mesh Generation Neural Representation Geometry Signed Distance Functions 3D Reconstruction

Oct 21, 2025cs.RO

OREN: Octree Residual Network for Real-Time Euclidean Signed Distance Mapping

Reconstructing signed distance functions (SDFs) from point cloud data benefits many robot autonomy capabilities, including localization, mapping, motion planning, and control. Methods that support online and large-scale SDF reconstruction often rely on discrete volumetric data structures, which affects the continuity and differentiability of the SDF estimates. Neural network methods have demonstrated high-fidelity differentiable SDF reconstruction but they tend to be less efficient, experience catastrophic forgetting and memory limitations in large environments, and are often restricted to truncated SDF. This work proposes OREN, a hybrid method that combines an explicit prior from octree interpolation with an implicit residual from neural network regression. Our method achieves non-truncated (Euclidean) SDF reconstruction with computational and memory efficiency comparable to volumetric methods and differentiability and accuracy comparable to neural network methods. Extensive experiments demonstrate that OREN outperforms the state of the art in terms of accuracy and efficiency, providing a scalable solution for downstream tasks in robotics and computer vision.

Zhirui Dai, Qihao Qian, Tianxing Fan +1

Department of Electrical and Computer Engineering, University of California San Diego, La Jolla, CA 92093, USA

Implicit Neural Representations Signed Distance Functions 3D Reconstruction

Nov 24, 2024cs.CV

GSurf: Learning Signed Distance Fields from Splatting Opaque Gaussians for High-quality 3D Reconstruction

High-fidelity surface reconstruction from multi-view images is a core problem in 3D computer vision. While neural implicit surfaces like SDFs offer smooth geometry, they are often bottlenecked by the computational intensity of volume rendering. Conversely, 3D Gaussian Splatting (3DGS) provides rapid training but lacks geometry continuity, often leading to fragmented surfaces. This paper presents a novel framework that integrates Signed Distance Fields directly into the splatting pipeline. By leveraging the continuous nature of SDFs to regularize Gaussian primitives, our method effectively fills geometric holes and suppresses noise inherent in sparse point clouds. Unlike hybrid approaches that rely on heavy volumetric sampling, our approach utilizes the efficiency of splatting to achieve faster convergence. Extensive evaluations demonstrate that our method produces high-quality surfaces with significantly fewer primitives, offering a more compact and efficient representation for both indoor and outdoor environments.

Baixin Xu, Jiangbei Hu, Jiaze Li +1

College of Computing and Data Science, Nanyang Technological University · School of Software, Dalian University of Technology

3D Gaussian Splatting Signed Distance Functions 3D Reconstruction Multi-View 3D Reconstruction