PrimitiveUDF: Primitive-Based Unsigned Distance Fields for Surface Reconstruction from Point Clouds¶
Conference: ECCV 2026
Paper: ECCV Official
Code: https://github.com/Spatial-Intelligence-Group/PrimitiveUDF
Area: 3D Vision
Keywords: Surface Reconstruction, Unsigned Distance Fields, Point Clouds, Spherical Reorganization, Hybrid Primitives
TL;DR¶
To resolve the fundamental failure mode of unsigned distance fields conflating nearby layers in multi-surface regions, PrimitiveUDF reorganizes Euclidean neighborhoods into 2D local charts via viewpoint-guided spherical projection and constructs hybrid triangle/segment primitives as an explicit geometric bias for distance regression.
Background & Motivation¶
Implicit geometric representations have emerged as a dominant paradigm across 3D vision, computer graphics, and robotics. While signed distance fields (SDFs) are well-suited for watertight geometries, unsigned distance fields (UDFs) predict the absolute spatial distance from any query point to the nearest surface, making them uniquely equipped to represent open, non-watertight surfaces and real-world scenes. Learning-based UDF approaches typically query local Euclidean \(K\)-nearest neighbors (KNN) around a spatial point and aggregate them into feature embeddings via permutation-invariant pooling. However, Euclidean proximity fundamentally disagrees with geodesic along-surface proximity in regions with thin structures, sharp folds, or closely spaced double layers (such as car hoods, book pages, layered pillows, or curtains). Under pure Euclidean gathering, the selected neighborhood points inevitably span across distinct and disjoint surface sheets.
Crucially, learning-based UDF networks are typically trained with scalar supervision on the final distance value alone, offering negligible pairwise guidance on which local neighboring points belong to the same underlying surface sheet. When the network attempts to aggregate features from this topologically entangled point set, conflicting geometric signals cancel or over-smooth one another, leading to fractured surfaces, blurred boundaries, artificial bridging across layers, and severe outlier artifacts. Even when attempting to establish explicit point-to-point connections locally, naive greedy linking lacks essential structural guarantees—such as manifold continuity, non-crossing, and non-degeneracy—making it fragile under noise and uneven sampling.
This paper tackles this problem from a fresh perspective: rather than expecting an MLP to disentangle mixed point sets implicitly, one should impose lightweight, explicit structural constraints prior to feature aggregation. Crucially, these primitives do not hardcode the final mesh; rather, they serve as an explicit structural bias to organize local features for learned field regression. Core idea: project Euclidean neighborhoods onto a virtual viewpoint sphere along a local PCA variation axis to unfold overlapping layers into a planar chart, and adaptively grow non-degenerate triangle patches and prune 3D direction-aligned segments to provide an explicit hybrid primitive inductive bias for query-conditioned UDF regression.
Method¶
Overall Architecture¶
PrimitiveUDF takes as input a point cloud \(P = \{(x_j, f_j)\}_{j=1}^N\) with 3D coordinates and point features, and predicts the unsigned distance \(d(q) \in \mathbb{R}_{\ge 0}\) for any 3D spatial query point \(q \in \mathbb{R}^3\). The architecture consists of three core stages: first, raw Euclidean neighborhood points \(\mathcal{N}(q)\) are reorganized into a seam-free 2D local chart through viewpoint-induced spherical parameterization and tangent-plane log-mapping; second, the hybrid primitive construction module proposes surface-adjacent 3D triangle primitives from the 2D chart traversal and extracts 3D direction-consistent segment primitives along the principal axis; third, selected primitives are encoded into primitive tokens with query-relative spatial offsets, and an attention-based regressor fuses them to decode the final scalar UDF value.
%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
A["Input Point Cloud & Query<br/>P = {(x, f)}, query q"] --> B["Stage 1: Projection-Induced Reorganization<br/>PCA-quantile virtual viewpoint + tangent-plane log-map"]
B --> C["Stage 2: Hybrid Primitive Construction<br/>Chart-grown 3D triangles + direction-pruned 3D segments"]
C --> D["Stage 3: Attentive Primitive Regressor<br/>Token pooling + cross-attention MLP UDF prediction"]
D --> E["Precise Unsigned Distance d(q)"]Key Designs¶
1. Projection-Induced Reorganization: Decoupling Overlapping Layers via Local 2D Charts
Euclidean proximity indiscriminately bundles points from adjacent surface layers into a single neighborhood set, depriving the regressor of discriminative surface-relative cues. This module maps the local neighborhood into a viewpoint-defined angular organization where points on the same surface sheet remain directionally coherent while points on distinct layers become widely separated. To avoid fragile unconstrained optimization, candidate virtual centers are restricted to a 1D sweep along the dominant local PCA axis: \(c(t) = \mu + t \vec{a}\), where \(\mu\) is the local centroid and \(\vec{a}\) is the primary eigenvector. Evaluating three preset PCA-quantile candidate offsets against a degenerate-projection check reliably yields an optimal center \(c^\star\) placed in free space away from dense point clusters. The neighborhood points are projected onto the viewing unit sphere:
On this sphere, previously entangled spatial layers separate into distinct angular bands. To eliminate the computational burden of spherical geodesics and bypass coordinate seam singularities, the projected directions are mapped onto a tangent plane using a log-map anchored at the densest directional cluster \(d_0\): \(z_i = \mathrm{LogMap}_{d_0}(d_{c^\star}(x_i)) \in \mathbb{R}^2\). This 2D chart serves solely as an efficient metric domain for proposing topological adjacency, while all actual primitive geometry remains anchored to original 3D coordinates.
2. Hybrid Primitive Construction: Co-extracting Patch-like and Elongated Hypotheses
Naive point-to-point linking lacks structural regularization and is vulnerable to noise and sampling density variations. PrimitiveUDF instead constructs an explicit hybrid primitive pool \(\mathcal{C}(q) = \mathcal{C}^{\triangle}(q) \cup \mathcal{C}^{\ell}(q)\) combining patch-like 2D manifolds and 1D elongated structures. For triangle primitives, counterclockwise propagation is initiated from the point closest to the chart origin to propose adjacent triplets \(\mathcal{A}_{\mathrm{org}}\). In 3D space, structural validation filters are applied: a non-degeneracy check \(\mathrm{NonDeg}_{3D}\) discards collinear or near-collinear triplets, while a spatial compactness check \(\mathrm{Compact}_{3D}\) rejects shortcut triangles spanning large physical gaps:
For thin rods, crisp boundaries, or severely under-sampled regions where 2D triangles break down, 3D directional segment primitives provide a complementary structural hypothesis. Points are sorted by their projection along the dominant 3D principal direction \(\hat{e}\): \(\gamma_i = (x_i - \bar{x})^\top \hat{e}\). Each point only proposes edges to a small set of subsequent neighbors \(\mathrm{Next}(i)\). Outlier and shortcut edges are pruned using a 3D Euclidean length check \(\mathrm{Local}_{3D}\) and a directional alignment check \(\mathrm{Align}_{3D}\). Finally, all candidate primitives are ranked by the Euclidean distance between their 3D center \(c_p\) and the query \(q\), and truncated to a compact budget using \(\mathcal{S}(q) = \operatorname{TopB}_{p \in \mathcal{C}(q)}(-\|c_p - q\|_2)\).
3. Attentive Primitive Regressor: Query-Conditioned UDF Decoding
To transform discrete primitive relations into continuous and differentiable distance predictions, each selected primitive \(p \in \mathcal{S}(q)\) is converted into a primitive token \(\pi_p = [f_p, \Delta c_p]\). Here, \(f_p\) aggregates the features of its constituent vertices via symmetric pooling (optionally augmented with lightweight geometric statistics), and \(\Delta c_p = c_p - q\) explicitly encodes the spatial vector from query point \(q\) to the primitive center \(c_p\).
An attention-based aggregation module processes the token sequence \(\{\pi_p\}\) to produce a query-conditioned geometric embedding \(z(q)\). Concatenated with the spatial query encoding \(\psi(q)\), this embedding is passed through an MLP regressor \(g(\cdot)\) with absolute value activation to output the unsigned distance:
Because both spherical reorganization and hybrid primitive construction are rule-driven without learnable parameters, the network maintains minimal parameter overhead while gaining strong inductive bias.
Key Experimental Results¶
Main Results¶
The method was evaluated across large-scale real-world indoor scenes (ScanNet and Matterport3D), watertight objects (ShapeNet 13 classes), open-surface non-watertight models (ShapeNet Cars), and complex CAD geometries with non-manifold edges (ABC benchmark). Across complex indoor scenes, PrimitiveUDF achieves substantial gains in Chamfer Distance, normal consistency (NC), and F-Score.
| Dataset | Metric | PrimitiveUDF (Ours) | GeoUDF | NVF | SALS |
|---|---|---|---|---|---|
| ScanNet (MC 256) | \(\mathrm{CD}_{L1} \downarrow (\times 10^{-3})\) | 1.86 | 2.05 | 2.03 | - |
| ScanNet (MC 256) | \(\mathrm{CD}_{L2} \downarrow (\times 10^{-6})\) | 6.03 | 7.84 | 11.7 | - |
| ScanNet (MC 256) | \(\mathrm{F\text{-}Score}@0.5\% \uparrow\) | 95.7 | 93.8 | 94.6 | - |
| ScanNet (MC 256) | \(\mathrm{NC} \uparrow (\%)\) | 90.1 | 89.3 | 88.9 | - |
| Matterport3D (MC 256) | \(\mathrm{CD}_{L1} \downarrow (\times 10^{-3})\) | 2.09 | 2.21 | 2.83 | - |
| Matterport3D (MC 256) | \(\mathrm{CD}_{L2} \downarrow (\times 10^{-6})\) | 7.29 | 8.33 | 11.9 | - |
| Matterport3D (MC 256) | \(\mathrm{F\text{-}Score}@0.5\% \uparrow\) | 94.1 | 92.9 | 89.5 | - |
| Matterport3D (MC 256) | \(\mathrm{NC} \uparrow (\%)\) | 95.5 | 94.2 | 93.6 | - |
| ScanNet (MC 128) | \(\mathrm{CD}_{L1} \downarrow (\times 10^{-3})\) | 2.02 | 2.36 | 2.20 | 2.02 |
| ScanNet (MC 128) | \(\mathrm{CD}_{L2} \downarrow (\times 10^{-6})\) | 7.13 | 11.9 | 11.0 | 7.49 |
| ShapeNet Cars | \(\mathrm{CD}_{L2} \downarrow (\times 10^{-4})\) | 0.110 | 0.120 | 0.134 | 0.179 |
| ShapeNet Cars | \(\mathrm{F\text{-}Score}@0.5\% \uparrow\) | 90.69 | 89.23 | 87.39 | 83.05 |
| Non-Manifold ABC | \(\mathrm{CD}_{L1} \downarrow (\times 10^{-2})\) | 0.320 | 0.333 | - | 0.330 |
| Non-Manifold ABC | \(\mathrm{F\text{-}Score}@0.5\% \uparrow\) | 85.65 | 83.69 | - | 83.63 |
Ablation Study¶
Ablations on ScanNet (using PointTransformerV2 backbone and Marching Cubes resolution 256) systematically analyze the interdependence of spherical reorganization and primitive construction, as well as the suitability of various primitive geometric families.
| Config | \(\mathrm{CD}_{L1} \times 10^{-3} \downarrow\) | \(\mathrm{CD}_{L2} \times 10^{-6} \downarrow\) | \(\mathrm{F\text{-}Score}@0.5\% \uparrow\) | \(\mathrm{NC} \uparrow\) | Params (M) | Note |
|---|---|---|---|---|---|---|
| Base (unstructured KNN) | 1.91 | 6.30 | 95.3 | 89.2 | 11.36 | Standard unstructured point set pooling |
| w/ P.C. (only primitives) | 2.11 | 8.43 | 93.1 | 88.6 | 11.37 | Primitives on raw Euclidean neighbors introduce false edges |
| w/ S.R. + P.C. (full model) | 1.86 | 6.03 | 95.7 | 90.1 | 11.37 | Full pipeline with spherical reorganization + primitives |
| Primitive: Segment | 1.96 | 6.92 | 95.2 | 89.7 | - | Pure 1D segment primitives lack planar surface support |
| Primitive: Triangle | 1.86 | 6.03 | 95.6 | 90.1 | - | Rigid 2D triangle patches best capture indoor surfaces |
| Primitive: Triangle+Segment | 1.86 | 6.03 | 95.7 | 90.1 | - | Hybrid primitives provide balanced coverage |
| Primitive: 4-Point Patch | 2.06 | 7.54 | 94.3 | 88.3 | - | Extra degrees of freedom cause severe non-planar degeneracy |
Key Findings¶
- Crucial Coupling Between Reorganization and Construction: Constructing primitives directly on raw Euclidean neighborhoods without spherical reorganization (
w/ P.C.) leads to a severe performance drop (\(\mathrm{CD}_{L1}\) deteriorates from 1.91 to 2.11). When neighborhood points from adjacent sheets are linked, false relational priors corrupt distance regression. Only when paired with spherical reorganization (w/ S.R. + P.C.) does the model achieve superior performance (1.86). - Failure of Over-Parameterized Primitives: The 4-point patch primitive exhibits significant degradation (\(\mathrm{CD}_{L1}\) increases to 2.06), demonstrating that non-coplanar ambiguity in 4-point configurations disrupts normal consistency. Triangles remain the most mathematically rigid and stable building blocks for 2D surface patches.
- Graceful Degradation Under Perturbations: In ScanNet robustness evaluations under Gaussian noise (\(\sigma = 0.005\)), GeoUDF error surges by 96.5%, whereas PrimitiveUDF increases by only 34.9%. Under severe point cloud downsampling (3,500 points, one-third of original), PrimitiveUDF preserves an F-Score of 91.6% (compared to SALS falling to 61.5%), demonstrating excellent resilience under sparse and noisy conditions.
Highlights & Insights¶
- Primitives as Feature Inductive Bias Rather Than Output Meshes: Unlike classical explicit surface reconstruction that attempts to stitch primitives into a global mesh (which often suffers from boundary seam stitching artifacts), PrimitiveUDF uses primitives strictly to structure local feature tokens. The final field continuity and resolution independence remain governed by continuous neural decoding.
- Elegance of Single-Axis Viewpoint Unfolding: Rather than performing costly global surface parameterization or high-dimensional manifold learning, sweeping virtual viewpoints along a local 1D PCA axis cleanly unfolds double layers into a 2D tangent plane chart via simple spherical projection.
- Cross-Domain Transferability: The concept of virtual-viewpoint angular decoupling can be directly transferred to other 3D representations that struggle with thin-surface transparency or double-layer bleeding, such as Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3D-GS).
Limitations & Future Work¶
- Author-Admitted Limitations: The pipeline still relies on heuristic geometric parameters (e.g., compactness thresholds and collinearity tolerances). At intricate high-order non-manifold junctions, primitive generation rules can occasionally degrade, reverting the model to point-level feature reliance.
- Identified Limitations: In severely incomplete scans with large missing holes or extreme anisotropy, local PCA axis estimation may become misaligned, impacting the quality of the tangent-plane log-map. Additionally, performing dynamic neighbor gathering and primitive pruning on CPU/GPU during inference introduces minor latency overhead.
- Future Directions: A promising direction is to learn the viewpoint candidate selection and primitive pruning thresholds end-to-end via lightweight neural modules. Integrating hybrid primitive representations directly with dual contouring meshing algorithms could also yield cleaner non-manifold edge recovery.
Related Work & Insights¶
- vs GeoUDF [33]: GeoUDF interpolates upsampled point coordinates and normals to guide distance fields, but struggles around double layers where Euclidean proximity blurs adjacent sheets. PrimitiveUDF eliminates cross-layer feature contamination via projection-induced local charts and hybrid primitive tokens.
- vs SALS [32]: SALS models 3D line segment-to-surface relations, which produces ripple-like artifacts across smooth planar regions due to a lack of 2D patch constraints. PrimitiveUDF uses rigid 2D triangles as primary surface primitives alongside 1D segments, achieving superior fidelity across both flat walls and thin edges.
Rating¶
- Novelty: ⭐⭐⭐⭐☆ The combination of viewpoint-driven chart unfolding and hybrid primitive feature tokens provides an insightful remedy for multi-surface ambiguity in UDFs.
- Experimental Thoroughness: ⭐⭐⭐⭐⭐ Comprehensive benchmarks spanning watertight, open-surface, large-scale indoor scans, and non-manifold CAD models with extensive stress tests.
- Writing Quality: ⭐⭐⭐⭐⭐ Clear mathematical formulation, insightful problem definition, and solid ablations.
- Value: ⭐⭐⭐⭐☆ Highly relevant for neural implicit surface reconstruction from messy real-world scans.