Source-linked AI summary
Neural Unsigned Distance Fields for Implicit Function Learning
Julian Chibane, Aymen Mir, Gerard Pons-Moll
TL;DR
Existing implicit representations generally require closed surfaces, limiting reconstruction of open or internally structured real-world objects. The paper introduces Neural Distance Fields, which regress unsigned distances from sparse point clouds and provide procedures for extraction and rendering. NDF achieves state-of-the-art ShapeNet reconstruction while representing inner structures and broader classes such as curves, manifolds, and functions.
Problem
Existing implicit function methods are limited to closed surfaces, requiring artificial closure that can introduce artifacts and lose detail while preventing open-surface representation.
Method
NDF learns an unsigned distance field from sparse point clouds, using its gradients and modified sphere tracing to extract or render the implicit surface.
Results
NDF obtains state-of-the-art ShapeNet point-cloud reconstruction and represents shapes with inner structures, open surfaces, manifolds, curves, and functions.
Takeaways & Limitations
NDF broadens implicit shape learning beyond closed 3D surfaces and supports dense point-cloud, mesh, and image outputs.
Takeaways & Limitations
NDF relies on off-the-shelf methods for meshing dense point clouds, which can be slow, and the method is not yet real time.
Abstract
from arXiv · showhide
In this work we target a learnable output representation that allows continuous, high resolution outputs of arbitrary shape. Recent works represent 3D surfaces implicitly with a Neural Network, thereby breaking previous barriers in resolution, and ability to represent diverse topologies. However, neural implicit representations are limited to closed surfaces, which divide the space into inside and outside. Many real world objects such as walls of a scene scanned by a sensor, clothing, or a car with inner structures are not closed. This constitutes a significant barrier, in terms of data pre-processing (objects need to be artificially closed creating artifacts), and the ability to output open surfaces. In this work, we propose Neural Distance Fields (NDF), a neural network based model which predicts the unsigned distance field for arbitrary 3D shapes given sparse point clouds. NDF represent surfaces at high resolutions as prior implicit models, but do not require closed surface data, and significantly broaden the class of representable shapes in the output. NDF allow to extract the surface as very dense point clouds and as meshes. We also show that NDF allow for surface normal calculation and can be rendered using a slight modification of sphere tracing. We find NDF can be used for multi-target regression (multiple outputs for one input) with techniques that have been exclusively used for rendering in graphics. Experiments on ShapeNet show that NDF, while simple, is the state-of-the art, and allows to reconstruct shapes with inner structures, such as the chairs inside a bus. Notably, we show that NDF are not restricted to 3D shapes, and can approximate more general open surfaces such as curves, manifolds, and functions. Code is available for research at https://virtualhumans.mpi-inf.mpg.de/ndf/.
1 Introduction
Existing implicit function methods provide continuous, arbitrary-resolution shape representations but generally require closed surfaces. Neural Distance Fields instead regress unsigned distances, enabling open and internally structured shapes alongside dense reconstruction and rendering operations.
- Implicit function learning represents continuous 3D points with occupancies or signed distance fields, supporting arbitrary-resolution surfaces and varied topologies.
- Existing methods require closed surfaces that divide space into inside and outside, causing preprocessing artifacts and preventing open-surface output.
- Neural Distance Fields regress each point’s unsigned distance to the surface with a learned function whose zero-level set represents that surface.
- Unlike occupancies and signed distance fields, NDF can represent open surfaces, inner structures, open manifolds, curves, and functions beyond 3D shapes.
- NDF provides algorithms for extracting dense point clouds and meshes, computing normals, and rendering images from the learned field.
- ShapeNet experiments report state-of-the-art reconstruction performance, including reconstruction of shapes with inner structures, while avoiding closed-mesh preprocessing in most comparisons.
2 Related Work
Prior shape representations trade off resolution, continuity, topology, or output flexibility, while implicit methods remain tied to closed surfaces. NDF replaces inside–outside classification with unsigned-distance regression and supports broader surface representations and extraction procedures.
- Distance fields have been used in vision, graphics, robotics, and physics for registration, fitting, inference acceleration, and skeleton extraction.
- Voxel methods face cubic memory growth, while point-cloud methods typically fix the output-point count and therefore limit effective resolution.
- Mesh-based methods may be restricted by topology, continuity, or an underlying template model.
- Occupancy- and signed-distance-based implicit methods provide continuous, resolution-independent representations but require artificially closed shapes, risking artifacts and lost interior structures.
- NDF instead regresses unsigned distance, allowing closed or open surfaces, data manifolds, and extraction of dense point clouds, meshes, and images.
- NDF focuses on reconstruction from deficient point clouds rather than neural rendering and can be trained across multiple scenes or objects.
3 Method
NDF encodes sparse inputs as continuous unsigned distance fields, enabling open and internally structured surfaces while supporting dense extraction, rendering, and multi-target regression. Its algorithms use distance gradients and modified sphere tracing to recover surfaces and evaluate functions or manifolds.
- Neural Distance Fields: Unlike occupancies or signed distance fields, NDF represent open surfaces, inner structures, open curves, manifolds, and functions without artificially closing shapes.The representation is defined for dimensions beyond 3D and does not rely on inside-versus-outside classification.
- Neural Distance Fields: NDF encodes a sparse input into a learned unsigned distance field whose zero-level set represents the surface.A 3D CNN extracts multi-scale features, and a ReLU decoder regresses nonnegative distances from those features.
- Learning: Training samples points near each ground-truth surface, computes their unsigned distances, and jointly learns the encoder and decoder with a mini-batch loss.The distance clamp δ = 10cm concentrates capacity near surfaces and provides a reported trade-off for visualization convergence.
- Dense Point Cloud Extraction: For dense point extraction, NDF projects points toward the surface using q := p − f(p) · ∇_p f(p), then repeats refinement to address approximation error and distance clamping.The negative gradient points toward the closest surface point for an exact UDF; extracted points can be meshed with classical local-connectivity methods and processed in parallel.
- Rendering: NDF rendering modifies sphere tracing by marching along rays using damped predicted distances and backward steps near the surface to reduce over-shooting.Iterations stop when the predicted distance falls below a prescribed threshold.
- Multi-target Regression: The same modified sphere tracing evaluates multiple outputs by representing a regression function as a zero-level set in one higher dimension.Setting the initial point and ray along the output coordinate allows multiple y values for fixed inputs and applies the method to curves, manifolds, and functions.
4 Experiments
Experiments evaluate NDF on closed and complex 3D shapes, open surfaces, and 2D functions or manifolds. NDF matches or exceeds prior reconstruction methods while representing structures and surfaces unavailable to conventional implicit formulations.
- 3D Shape Reconstruction of Closed Surfaces: NDF reconstructs closed ShapeNet cars with precision comparable to state-of-the-art methods and outperforms all baselines quantitatively.Training uses 3094 cars pre-processed into closed meshes, which removes interior structures.
- 3D Shape Reconstruction of Closed Surfaces: 0.05 Chamfer-L2 ×10−4 is reported for NDF on 3000-point closed ShapeNet reconstruction, versus 0.2 for IF-Net and 1.0 for DMC.
- 3D Shape Reconstruction of Complex Shape: On test cars, NDF is the only compared method reported to successfully reconstruct the full inner structure.SAL and NDF use raw data directly, whereas IF-Net is trained on closed data without inner structures.
- 3D Shape Reconstruction of Complex Shape: NDF represents open garment surfaces and visualizes them through dense point-cloud generation and direct rendering.
- Functions and Manifolds: A single NDF interpolates sparse samples of linear, parabolic, sinusoidal, and spiral functions, using sphere tracing to evaluate the recovered surfaces.The functions-and-manifolds experiment uses 1000 functions per type with an 80/20 train-test split.
- Limitations: NDF can produce dense point clouds, but meshing relies on off-the-shelf methods that can be slow.The authors also note that the method is not yet real time and suggest coarse-to-fine sampling for speed.
5 Discussion and Conclusion
The discussion presents unsigned-distance prediction as a simple representation change that broadens implicit function learning beyond closed 3D surfaces. NDF achieves state-of-the-art ShapeNet reconstruction and supports continuous outputs across several surface classes.
- Switching from occupancy or signed distances to unsigned distances broadens implicit function learning to open surfaces, inner structures, curves, manifolds, and functions.
- NDF learns directly from real-world scans without artificially closing surfaces and achieves state-of-the-art point-cloud reconstruction on ShapeNet.
- The method includes algorithms for efficient surface projection and direct rendering with a custom sphere-tracing variant.
Broader Impact
NDFs support reconstruction and completion of noisy, incomplete real-world point clouds across applications including AR/VR, robotics, and cultural heritage. The authors also flag privacy, proprietary-rights, and safety risks from sparse-input reconstruction.
- NDFs can reconstruct and complete noisy, incomplete point clouds from cameras, scanners, and lidar.The paper identifies applications including AR/VR, autonomous vehicles, robotics, virtual humans, cultural heritage, and fabrication quality assurance.
- The authors report state-of-the-art results for point-cloud completion and suggest denoising and semantic segmentation as further applications.
- Sparse or partial captures may allow NDFs to generate complete environments, scenes, and persons from general world statistics.
- Such reconstructions may violate personal or proprietary rights, and safety-critical uses must consider the risk of unreliable results.