Organizations: College of Computing and Data Science, Nanyang Technological University, Singapore · Key Laboratory of System Software (Chinese Academy of Sciences), Institute of Software, Chinese Academy of Sciences, and the University of Chinese Academy of Sciences · Department of Computer Science, City University of Hong Kong, Hong Kong SAR, China · Department of Computer Science & Engineering, Texas A&M University, Texas, USA
Neural implicit surface methods that couple volume rendering with signed distance functions (SDFs), such as VolSDF and NeuS, achieve high-quality multi-view reconstruction for watertight objects. However, these approaches rely on a globally consistent inside-outside partition of space. This assumption becomes fragile for thin structures (e.g., sheets, tubes, and thin walls) and can break down for sign-ambiguous geometry (e.g., surfaces with boundary, non-manifold junctions, and closely spaced surface components), often resulting in spurious closures or loss of fine structures. Unsigned distance field (UDF) formulations relax the global sign requirement and better support non-watertight geometry, but are substantially harder to optimize. We propose PhaseSurf, a neural volume rendering framework built on Metric-Phase Fields (MPFs). MPFs decompose geometry into a nonnegative metric field capturing unsigned proximity and a continuous phase field providing a soft sign cue. By coupling the two through residual phase injection, MPFs yield a signed composite implicit function with stable near-surface gradients while retaining UDF-like robustness in sign-ambiguous regions. This design enables direct iso-surface extraction using standard Marching Cubes and avoids the failure modes of both pure SDF- and UDF-based formulations. We further introduce MPF-specific training losses that enforce metric consistency, stabilize phase transitions near the interface, and suppress spurious geometry in free space. Experiments on multi-view datasets with thin structures and sign-ambiguous geometry show that PhaseSurf produces more stable reconstructions and higher-quality geometry than UDF-based methods and recent 3DGS pipelines, while avoiding artifacts typical of SDF-based approaches.
Figures & tables
Fig. 1 : MPF on a challenging toy model. The model consists of two closely spaced open sheets, four slender tubular connections, and a closed spherical component. The sheets are single-layer surfaces with boundaries, whereas the sphere admits a well-defined inside-outside partition. The attachments form non-manifold junctions, and the tubes introduce narrow passages and nontrivial topology. Together, these features pose challenges to both SDF- and UDF-based reconstruction. ( 1(a) ) Two views of the reference model. ( 1(b) )–( 1(e) ) Cross-sectional visualizations of the metric field r , phase field θ , phase indicator P , and composite field ϕ , respectively. ( 1(f) )–( 1(h) ) Reconstructions produced by NSH [ 3 ] , CAP-UDF [ 4 ] , and MPF. Both baselines struggle to recover the thin structures, resulting in incomplete or distorted geometry. In contrast, MPF more faithfully preserves the thin sheets, tubular connections, and overall structure.
Fig. 2 : Pipeline. For each 3D sample along camera rays, the MPF network predicts an unsigned metric r(x)≥0 , a phase θ(x) , and a feature f(x) . We form the signed composite field φ(x)=r(x)tanh(βθ(x))+θ(x) and use NeuS-style signed-field volume rendering to compute occlusion-aware weights. The radiance MLP predicts view-dependent color, and the volume rendering network produces RGB (supervised by input images) and accumulated opacity α (optionally supervised by masks).
Fig. 3 : Visualizations and local enlarged views of the reconstructed results on the DTU dataset [ 30 ] . For each showcased data, we present an enlarged local rendering that corresponds to the input camera view in the upper row. We render the same part of the mesh of each method in a novel angle that can better demonstrate the difference of each method in the lower row. In the top two rows, scissors and screwdrivers are stacked on top a set of bricks. All methods except our method reconstructs spurious structures that connect the tools to the surface below. In the bottom two rows, the teeth of the toy bear represents a layer of thin surface, and all methods except our method cannot faithfully reconstruct the thin plane structure and connects to the face behind the teeth. Our method is more flexible with representation of the implicit geometry and produces the best result at preventing complex structures from connecting together, as well as reconstructing thin surfaces.
Fig. 4 : Limitation: Our enhanced expressive capability may cause the reconstructed surface to have an increased tendency to dent under high specular lighting or shadow conditions, where color changes drastically at different viewing angles and lacking adequate color consistency cues.
Fig. 5 : Results on custom dataset for the real captured test cases. The umbrella scene contains thin structures, such as the umbrella rod and the retention strap, highlighted by colored boxes. The flower scene features open boundaries (e.g., petals), thin structures (e.g., the stem), and fine-scale geometric details (e.g., leaf veins). The basket scene contains dense thin lattice structures formed by narrow grid bars on the basket walls and base. NeuS and 3DGS-based baselines exhibit missing or fragmented geometry in these thin regions and struggle to recover delicate venation patterns. Finally, the cup scene is an open model and many baseline methods produce extravagant structures in such open scenes. In contrast, our method reconstructs these structures more completely and consistently, producing sharper and more faithful fine details.
Method
High-Heeled Shoe
Tank
mean (↓)
pred→gt (↓)
gt→pred (↓)
mean (↓)
pred→gt (↓)
gt→pred (↓)
GaussianUDF
10.319
4.260
16.379
7.582
5.771
9.393
GGGS
6.299
6.021
6.577
5.977
4.694
7.260
NeuS
9.707
8.936
10.477
6.442
4.925
7.959
PGSR
7.607
6.591
8.622
8.294
5.266
11.322
HF-NeuS
11.883
10.449
13.317
6.277
4.882
7.672
TABLE II : Geometry reconstruction results on the TAAS-Synthetic dataset measured by Chamfer Distance (CD, in 10−3 units). We report the directional scores from ground truth to prediction (gt→pred), from prediction to ground truth (pred→gt), and their bidirectional mean. Lower CD values indicate better geometric accuracy. Best results are shown in bold , and second-best results are underlined . “NA” indicates reconstruction failure.
Method
High-Heeled Shoe
Tank
mean (↑)
pred→gt (↑)
gt→pred (↑)
mean (↑)
pred→gt (↑)
gt→pred (↑)
GaussianUDF
89.49
94.55
84.43
61.16
63.17
59.14
GGGS
90.91
88.96
92.87
70.48
71.19
69.77
NeuS
86.31
85.03
87.59
72.76
74.54
70.99
PGSR
91.46
92.03
90.88
65.09
69.17
61.02
HF-NeuS
86.01
86.99
85.03
73.80
75.00
72.60
TABLE III : Geometry reconstruction results on the TAAS-Synthetic dataset measured by Normal Consistency (NC, %). We report the directional scores from ground truth to prediction (gt→pred), from prediction to ground truth (pred→gt), and their bidirectional mean. Higher NC values indicate better geometric accuracy. Best results are shown in bold , and second-best results are underlined . “NA” indicates reconstruction failure.
Fig. 6 : Results on the TAAS-Synthetic dataset. Red boxes highlight challenging thin or sign-ambiguous structures. None of the baseline methods (NeuS, PGSR, GaussianUDF, and GGGS) is able to recover the complete geometry: they often produce missing parts, fragmented structures, or floating artifacts. In contrast, our method reconstructs the full geometry more faithfully and preserves fine structures. GeoSVR fails to produce any mesh for these cases and is therefore excluded from the comparison.
Fig. 7 : Results of NeUDF on our dataset.
Fig. 8 : Compared to UDF-centered reconstruction methods, our method produces two-layered watertight mesh that represents a layer of thin shell around the open surface. This sidesteps two major problems with UDF. Top: Implicit UDF methods have difficulties accurately learning the zero turning point on the surface, posing challenges to UDF mesh extraction and often produces fragmented meshes; our method constructs a more complete mesh. Bottom: Implicit UDF methods require heavy smooth terms for successful convergence, resulting in loss of details. Our method can better capture the decorative details of the surface.
Fig. 9 : Qualitative results on the Ignatius test case from the Tanks & Temples dataset [ 31 ] . With the lack of the relevant view angles, only our method and Neuralangelo can correctly reconstruct the arm of the sculpture and separate the arm from the chest.
Fig. 10 : Qualitative comparison of our full model and our model without near surface regularization and free space regularization respectively. Without near surface regularization the model has difficulties learning thin structures, whereas without free space regularization the learned surface becomes noisy.
Fig. 11 : Qualitative comparison on the individual losses.
Fig. 12 : Omitting Lsurf will make the training unstable, resulting in a completely degraded reconstruction quality compared to other methods.
Method
Marching Cubes
Marching Tetrahedra
TSDF Fusion
MeshUDF
PGSR
✓
GeoSVR
✓
GaussianUDF
✓
GGGS
✓
✓
NeuS
✓
HF-NeuS
✓
TABLE IV : Comparison of mesh extraction strategies used by different reconstruction methods.
Fig. 13 : 3DGS-based reconstruction pipelines often rely on a post-processing step to clean the extracted meshes. Due to the lack of strong global geometric constraints, reconstructed components may become noisy or disconnected. Here we show the raw meshes extracted from PGSR, GeoSVR, and GGGS, where the first two contain noticeable noise and floaters, together with the corresponding meshes after the cleaning step. Although post-processing removes these artifacts, it also eliminates thin structures such as the leaves, resulting in missing geometry. In contrast, our method preserves global geometric integrity and does not require filtering or denoising post-processing.
Method
Basket
Umbrella
Cup
Flower
GaussianUDF
28.247 / 0.909
32.023 / 0.916
26.244 / 0.918
27.308 / 0.862
GeoSVR
26.492 / 0.883
28.429 / 0.930
23.440 / 0.890
26.529 / 0.869
NeuS
27.907 / 0.857
32.137 / 0.857
29.145 / 0.919
25.425 / 0.728
PGSR
26.050 / 0.880
29.053 / 0.900
23.993 / 0.887
25.659 / 0.843
Ours
28.033 / 0.861
32.128 / 0.855
28.991 / 0.917
25.734 / 0.730
Method
High-Heeled Shoe
Tank
LEGO
Figurine
TABLE V : Quantitative rendering results on the TAAS-Real (top) and TAAS-Synthetic (bottom) datasets. Each entry reports PSNR (↑) / SSIM (↑) . Best results are shown in bold , and second-best results are underlined .
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
Multi-view surface reconstruction is a core problem in computer vision. One prominent line of work represents the surface implicitly as a signed distance field (SDF), optimizing it based on the photometric loss between rendered and observed pixel colors. These approaches typically employ SDF-based volume rendering to obtain a differentiable relaxation of discontinuous visibility along rays, thereby reducing reliance on silhouette supervision. In this paper, we reformulate SDF-based volume rendering as probabilistic surface rendering, where each pixel color is modeled as a mixture distribution induced by the random first ray-surface intersection. To this end, we introduce Stochastic Signed Distance Processes (SSDP), which model the SDF along each ray as a stochastic process, inducing a first-passage-time distribution for each ray. We then derive the first-passage probability for each sampling interval based on Bayesian filtering, together with its practical approximation for parallel rendering. We further show that NeuS, an existing SDF-based volume rendering method, arises as a special case of our formulation. Experiments on the DTU and MobileBrick datasets demonstrate that our method outperforms baselines in both surface reconstruction and uncertainty quantification, supporting the effectiveness of our first-passage formulation. Our code is available at https://github.com/skmhrk1209/SSDP.
Hiroki Sakuma, Masatoshi Okutomi
Department of Systems and Control Engineering Institute of Science Tokyo
Neural implicit surface reconstruction with signed distance function has made significant progress, but recovering fine details such as thin structures and complex geometries remains challenging due to unreliable or noisy geometric priors. Existing approaches rely on implicit uncertainty that arises during optimization to filter these priors, which is indirect and inefficient, and masking supervision in high-uncertainty regions further leads to under-constrained optimization. To address these issues, we propose GPU-SDF, a neural implicit framework for indoor surface reconstruction that leverages geometric prior uncertainty and complementary constraints. We introduce a self-supervised module that explicitly estimates prior uncertainty without auxiliary networks. Based on this estimation, we design an uncertainty-guided loss that modulates prior influence rather than discarding it, thereby retaining weak but informative cues. To address regions with high prior uncertainty, GPU-SDF further incorporates two complementary constraints: an edge distance field that strengthens boundary supervision and a multi-view consistency regularization that enforces geometric coherence. Extensive experiments confirm that GPU-SDF improves the reconstruction of fine details and serves as a plug-and-play enhancement for existing frameworks. Source code will be available at https://github.com/IRMVLab/GPU-SDF
Qiyu Feng, Jiwei Shan, Shing Shin Cheng +1
Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, China. · Department of Mechanical and Automation Engineering and T Stone Robotics Institute, The Chinese University of Hong Kong, Hong Kong.