cs.CVMar 20, 2026

High-fidelity Multi-view Normal Integration with Scale-encoded Neural Surface Representation

Authors: Tongyu Yang, Heng Guo, Yasuyuki Matsushita, Fumio Okura, Yu Luo, Xin Fan

Organizations: Dalian University of Technology, China · Beijing University of Posts and Telecommunications, China · Beijing Key Laboratory of Multimodal Data Intelligent Perception and Governance · The University of Osaka, Japan

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Abstract

Previous multi-view normal integration methods typically sample a single ray per pixel, without considering the spatial area covered by each pixel, which varies with camera intrinsics and the camera-to-object distance. Consequently, when the target object is captured at different distances, the normals at corresponding pixels may differ across views. This multi-view surface normal inconsistency results in the blurring of high-frequency details in the reconstructed surface. To address this issue, we propose a scale-encoded neural surface representation that incorporates the pixel coverage area into the neural representation. By associating each 3D point with a spatial scale and calculating its normal from a hybrid grid-based encoding, our method effectively represents multi-scale surface normals captured at varying distances. Furthermore, to enable scale-aware surface reconstruction, we introduce a mesh extraction module that assigns an optimal local scale to each vertex based on the training observations. Experimental results demonstrate that our approach consistently yields high-fidelity surface reconstruction from normals observed at varying distances, outperforming existing multi-view normal integration methods.

Figures & tables

Figure 1: (a) Problem setup: Given surface normals captured at varying scales, the goal is to recover detailed 3D surfaces while addressing multi-view inconsistencies caused by scale variations. (b) Comparison with Existing Method [ XT24 ] : Our approach can handle surface normal inputs at multiple scales (close-up and regular), enabling the recovery of fine surface details, particularly in high-frequency regions.
Figure 2: Method overview. (1) We sample inscribed spheres within the cone, each with position p\mathbf{p} and scale ss , which are jointly encoded via hash grids and a scale-triplane. Interpolated features are concatenated and fed into a tiny MLP to output SDF and surface normal. (2) Pixel normals are computed via volume rendering. (3) SMEM enables mesh extraction at the optimal scale.
Figure 3: Comparison between our hybrid representation and two triplanes. Both methods use multi-resolution grids with the same finest spatial resolution.
Figure 4: The flowchart of SMEM. (a) For each vertex within a cell, we query the scale-triplane feature map at its position p\mathbf{p} , sum the features of xx , yy , and zz axes for all vertices within the cell, and select the scale with the maximum aggregated response as the cell’s final scale. (b) We visualize the scales on the extracted mesh, where the purple areas correspond to smaller scales, which is consistent with the observations from the close-up views.
Figure 5: Setup of synthetic data generation. Blue and yellow camera poses denote the regular and close-up views, respectively. We provide example views for each object.
Figure 6: Setup of our real-world experiment. (a) The target object is placed on a checkerboard and imaged on a rotation stage under 1212 lighting conditions. (b) The objects range in height from 1111 cm to 2020 cm. (c) Normal maps estimated from SDM-UniPS [ Ike23 ] .
 Mean Angular Error ↓\downarrow (novel views)L2 Chamfer Distance ↓\downarrow 
MethodGaneshaLegoMicShipGaneshaLegoMicShipRuntime ↓\downarrow
Setting I, only regular views:
SuperNormal [ XT24 ]7.577016.81513.5517.1030.25770.34760.18990.151614 mins
RNb-NeuS [ BBQ∗24 ]7.581017.06114.6557.6480.18090.56770.61320.256311 hrs
PET-NeuS [ WSW23 ]6.704213.54918.8187.1490.18370.20280.54150.163426 hrs
Tri-MipRF [ HWM∗23 ]----0.51110.74770.49060.673013 mins
Table 1: Quantitative evaluation on synthetic data. Red and orange cells indicate the best and the second best results, respectively. Results are measured in terms of MAE and CD.
Figure 7: Comparison between our method and baselines on synthetic data.
 Setting ISetting II
 MAE ↓\downarrowCD ↓\downarrowMAE ↓\downarrowCD ↓\downarrow
w/o SNSR4.6220.11195.3420.097
w/o LCSR\mathcal{L}_{\text{CSR}}4.4550.06874.4430.068
Ours4.1210.06173.7030.048
Table 2: Ablation study on SNSR and LCSR\mathcal{L}_{\text{CSR}} on synthetic data. Bold text indicates the best result.
 Setting I, only regular viewsSetting II, regular + close-up views
 GaneshaLegoMicShipGaneshaLegoMicShip
Consistent scale0.06530.14880.08450.06870.05410.13240.09090.0719
SMEM0.06170.14740.08120.07040.04830.11310.08090.0684
Table 3: Quantitative comparison between using a globally consistent scale and the proposed SMEM. Values report the CD, with bold indicating the best results.
Figure 8: Comparison between our method and baselines on real-world data. (I) corresponds to Setting I, and (II) corresponds to Setting II. We zoom in on regions covered by close-up views and highly recommend that readers enlarge the figure to observe the differences clearly.
Figure 9: Qualitative comparisons on Ganesha between our method and those without the proposed SNSR or LCSR\mathcal{L}_{\text{CSR}} .
Figure 10: Qualitative comparison of the Ship results with and without LCSR\mathcal{L}_{\text{CSR}} .
Figure 11: Qualitative comparisons of mesh extraction with and without SMEM in Setting II (regular + close-up views).
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