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

Tongyu Yang; Heng Guo; Yasuyuki Matsushita; Fumio Okura; Yu Luo; Xin Fan

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

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 $\mathbf{p}$ and scale $s$ , 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 $\mathbf{p}$ , sum the features of $x$ , $y$ , and $z$ 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 $12$ lighting conditions. (b) The objects range in height from $11$ cm to $20$ cm. (c) Normal maps estimated from SDM-UniPS [ Ike23 ] .

	Mean Angular Error $\downarrow$ (novel views)				L2 Chamfer Distance $\downarrow$
Method	Ganesha	Lego	Mic	Ship	Ganesha	Lego	Mic	Ship	Runtime $\downarrow$
Setting I, only regular views:
SuperNormal [ XT24 ]	7.5770	16.815	13.551	7.103	0.2577	0.3476	0.1899	0.1516	14 mins
RNb-NeuS [ BBQ∗24 ]	7.5810	17.061	14.655	7.648	0.1809	0.5677	0.6132	0.2563	11 hrs
PET-NeuS [ WSW23 ]	6.7042	13.549	18.818	7.149	0.1837	0.2028	0.5415	0.1634	26 hrs
Tri-MipRF [ HWM∗23 ]	-	-	-	-	0.5111	0.7477	0.4906	0.6730	13 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 I		Setting II
	MAE $\downarrow$	CD $\downarrow$	MAE $\downarrow$	CD $\downarrow$
w/o SNSR	4.622	0.1119	5.342	0.097
w/o $\mathcal{L}_{\text{CSR}}$	4.455	0.0687	4.443	0.068
Ours	4.121	0.0617	3.703	0.048

Table 2: Ablation study on SNSR and

\mathcal{L}_{\text{CSR}}

on synthetic data. Bold text indicates the best result.

	Setting I, only regular views				Setting II, regular + close-up views
	Ganesha	Lego	Mic	Ship	Ganesha	Lego	Mic	Ship
Consistent scale	0.0653	0.1488	0.0845	0.0687	0.0541	0.1324	0.0909	0.0719
SMEM	0.0617	0.1474	0.0812	0.0704	0.0483	0.1131	0.0809	0.0684

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 $\mathcal{L}_{\text{CSR}}$ .

Figure 10: Qualitative comparison of the Ship results with and without $\mathcal{L}_{\text{CSR}}$ .

Figure 11: Qualitative comparisons of mesh extraction with and without SMEM in Setting II (regular + close-up views).

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High-Fidelity Surface Splatting-Based 3D Reconstruction from Multi-View Images

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IIT Palakkad, India

3D Mesh Generation 3D Reconstruction Multi-View 3D Reconstruction 3D Mesh Reconstruction

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Multi-view mesh reconstruction remains a core challenge in computer graphics and vision, especially for recovering high-frequency geometry from sparse observations. Recent methods such as 3D Gaussian Splatting (3DGS) and Neural Radiance Fields (NeRF) rely on post-processing for mesh extraction, thereby limiting joint optimization of geometry and appearance. Implicit Moving Least Squares (IMLS) instead enables direct conversion of point clouds into signed distance and texture fields, supporting end-to-end reconstruction and rendering. However, existing IMLS formulations use exponential kernels that struggle with high-frequency detail. We introduce a compact polynomial kernel with local support and greater flexibility, allowing better control over frequency content and improved geometric fidelity. To further enhance fine details, we incorporate stochastic regularization with Laplacian filtering. Together, these improve the preservation of high-frequency structure while maintaining stable optimization. Experiments show state-of-the-art performance in both surface reconstruction and rendering, yielding more accurate geometry and sharper visuals from multi-view data.

Abstract

Multi-View 3D Reconstruction

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