GeoSVR: Taming Sparse Voxels for Geometrically Accurate Surface Reconstruction
Authors: Jiahe Li
Jiawei Zhang
Youmin Zhang
Xiao Bai
Jin Zheng
Xiaohan Yu
Lin Gu
Venue: NeurIPS 2025 spotlight ()
Keywords: surface reconstruction
3D reconstruction
sparse voxels
Primary area: applications
TL;DR: This work presents GeoSVR, an explicit voxel-based framework that explores and extends the under-investigated potential of sparse voxels to achieve accurate, detailed, and complete surface reconstruction with high efficiency.

Abstract: Reconstructing accurate surfaces with radiance fields has achieved remarkable progress in recent years. However, prevailing approaches, primarily based on Gaussian Splatting, are increasingly constrained by representational bottlenecks. In this paper, we introduce GeoSVR, an explicit voxel-based framework that explores and extends the under-investigated potential of sparse voxels for achieving accurate, detailed, and complete surface reconstruction. As strengths, sparse voxels support preserving the coverage completeness and geometric clarity, while corresponding challenges also arise from absent scene constraints and locality in surface refinement. To ensure correct scene convergence, we first propose a Voxel-Uncertainty Depth Constraint that maximizes the effect of monocular depth cues while presenting a voxel-oriented uncertainty to avoid quality degradation, enabling effective and robust scene constraints yet preserving highly accurate geometries. Subsequently, Sparse Voxel Surface Regularization is designed to enhance geometric consistency for tiny voxels and facilitate the voxel-based formation of sharp and accurate surfaces. Extensive experiments demonstrate our superior performance compared to existing methods across diverse challenging scenarios, excelling in geometric accuracy, detail preservation, and reconstruction completeness while maintaining high efficiency. Code is available at https://github.com/Fictionarry/GeoSVR.

GeoSVR: Taming Sparse Voxels for Geometrically Accurate Surface Reconstruction
Jiahe Li' Jiawei Zhang' Youmin Zhang² Xiao B Jin Zheng 13,5 Xiaohan Yu* Lin Gu Schooo of Computer Science and Engineering, State Key Laboratory of Complex Critical Software Environment, Jiangxi Research Institute, Beihang University
Raamantic AI State Key Laboratory of Virtual Reality Technology and Systems, Beijing MMacquarie University TTohoku University (lijiahe, baixiao, j jinzheng) (buzaang)buuaa, Obuaa edu. cn
2DGS
PGSR
(Phagges.2220)
GS2Mesh
SVRase
Geo'VR
Figure 1: Geometric Sparse-Voxx Voxel Reconstruction. Our method, abbreviated as GeoSVR, delivers high-quality surface reconstruction for intricate real-world scenes based explicit sparse voxels. Our superiority exhibited compared to the state-of-the-att approaches built upon Gaussian Splatting, which encounter rough, inaccurate, incomplete recovery problems with help from external estimators, excelling in delicate details capturing with high completeness and top-tier efficiency.
Abstract
Reconstructing accurate surfaces with radiance fields has achieved remarkable progress in recent years. However, prevailing approaches, primarily based on Gaussian Splatting, are increasingly constrained by representational bottlenecks. In this paper, we introduce GeoSVR, explicit voxel-based framework that explores and extends the under-investigated potential of sparse voxels for achieving accurate, detailed, and complete surface reconstruction. strengths, sparse voxels support preserving the coverage completeness and geometric clarity, while corresponding challenges also arise from absent scene constraints and locality in surface refine- ment. To ensure correct scene convergence, we first propose foxel-Uncertaii Depth Constraint that maximizes the effect of monocular depth cues while present- ing voxel-oriented uncertainty to avoid quality degradation, enabling effective and robust scene constraints yet preserving highly accurate geometries. Subsequently, Sparse Voxel Surface Regularization is designed enhance geometric consistency for tiny voxels and facilitate the voxel-based formation of sharp and accurate sur- faces. Extensive experiments demonstrate our superior performance compared to existing methods across diverse challenging scenarios, excelling in geometric accu- racy, detail preservation, and reconstruction completeness while maintaining high efficiency. Code is available at tuttps://gitaai www//oocoioiaaaeee httpa////.../iiiiiaarrr/e//////
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Introduction
Surface reconstruction from multi-view images has been a critical long-term problem in computer vision and graphics. In recent years, with the development of Neural Radiance Fields (NeRF) 43
60] have been shown by combining volume rendering with signed distance functions (SDF) to learn implicit fields from input images, yet are mostly computationally expensive. More recently, with the rise of 3D Gaussian Splatting (3DGS) 32] surface reconstruction with explicit sparse representation is making rapid progress [25] [2] 78 15
impressive performances [7]
59
38
62
enabling efficient and high-qualit, geometry learning for a wider range of scenarios.
While significant advancements have been achieved in these 3DGS-based approaches, the method- ological limitations emerging a bottleneck. One critical problem lies in the reliance on well-structured point clouds initialization. Typically provided by multi-view geometry (MVG) approaches [5] [52, the point clouds inevitably contain inaccurate and uncovered regions due to ap- pearance ambiguities, which further aggravates difficulties for 3DGS to refine these challenging areas accurately in geometry, becoming an inherent flaw. This spatial incompleteness further hinders the
full potential of rapidly evolving geometry foundation models [7 69 2
in attempts [15] 14 36, 64],
obstructing their ability to drive a quality revolution in surface reconstruction. Another key issue is the lack of clearly defined edges in the Gaussian primitives, making the geometry ambiguous from
both the representation clarity 288 (55 and the calculation precision trade-offs [55] 42
Exploring another possibility, this paper presents GeoSVR that tames sparse voxels to achieve accurate and delicate surface reconstruction. Unlike previous explicit approaches based 3DGS, we start with a recently proposed SVRaster (55) that combines sparse voxels with rasterization to efficiently refine the scene via level of details. Initialized with fully covered coarse voxels constantly, the full potential can be maintained to model any part inside the scene with completeness. And with clearly bounded voxels, geometric details can be better identified compared to the Gaussians or smooth neural fields. However, while obtaining distinct characteristics, challenges come correspondingly.
Despite competitive surface quality yielded by vanilla SVRaster, significant geometric distortion persists during the sparse voxels optimization, due to the absence of a strong structure prior like the point clouds used in 3DGS, hindering further surface refinement. To fully exploit the strength of the densely covered representation, we resort to the current rapidly evolving and increasingly well-established monocular depth as the geometry cue to provide dense and easy-to-fetch scene constraints. However, a key problem arises for our highly accuracy-required surface reconstruction task: how effectively utilize this good but not perfect external constraint, while preserving well- reconstructed geometries from being hurt by errors to avoid quality degradation. To address this, we first adopt the patch-wic patch-wise depth regularizer [35] to facilitate local geometry learning, and based on which, a Voxel- Uncertiity Depth Constraint is proposed, evaluating the geometric uncertainty of each voxel and adaptively determining the degree of reliance on external cues at pixel level. By modulating internal photometric and external depth supervisions for confident and ambiguous regions, our approach enables effective and robust scene constraints, even for well-reconstrructed geometries.
Investigating the voxel-based surface formation, we then focus on geometric accuracy refinement and develop Sparse Voxel Surface Regularization. Since the gradients are shared only with the nearest neighbors, challenges exist in composing these extremely local and tiny sparse voxels to we try to adopt the widely used explicit multi-view geometry constraint [26] to help build geometrically
ideal surfaces. First, inspired by previous MVG-regularized approaches 20 16 50 12.
correct surfaces. Nevertheless, the sparse voxel's extreme locality made this plane-based geometry regularization less effective in enforcing a regional geometry constraint. To enlarge the refinement of per voxel, we conduct an interval sample to randomly drop out portion of voxels to simplify the learned scene during geometry regularization, thus forcing each tiny voxel to keep global geometry consistency. Second, from the perspective of voxel's surface representation, we introduce two voxel- wise regularizations: A Surface Rectification to restrict the surface formation to be aligned with unique voxel to reduce depth bias; and according to the metioned voxel uncertainty, a Scaling Penalty to eliminate the participation of the geometrically inaccurate large voxel in the surface formation. With the help of both sharp and accurate surfaces are facilitated in the reconstruction.
In summary, our main contributions are as follows:
An exploration GeoSVR to build explicit voxel-based framework for accurate surface reconstruction, taming sparse voxels to enable delicate and complete geometry learning.

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A Moxel-Uncertainyy Depth Constraint that maximizes the utilization of external depth cue while avoiding quality degradation by the proposed voxel uncertainty evaluation, enabling effective and robust scene constraints for highly accuracy-required surface reconstruction.
A Sparse Voxel Surface Regularization for surface geometric accuracy refinement, which enlarges the global geometry consistency constraint for tiny voxels and facilitates recon- structing sharp and accurate surfaces by regularizing the voxel-based surface formation.
Extensive experiments on DTU, Tanks and Temples, and Mip-NeRF 360 datasets demon- strate that the proposed GeOSVR achieves superior performance compared to the state-of- the-arts in reconstructing accurate surfaces across diverse challenging scenarios, excelling in detail preservation and high completeness while maintaining computational efficiency.
2 Related Works
Differentiable Radiance Fields. In recent years, radiance fields have made significant progress in 3D reconstruction by learning scenes directly with differentiable rendering. Neural Radiance Fields (NeRF) 43 is one of the most important foundations, which uses a large MLP to memorize 3D scene and renders through differentiable volume rendering, yet is weak in efficiency. Later, hybird representations come by proposing neural grids 156 45 27
plane decompositions [9] 18 8, or
sparse voxels [9 39 74] with or without neural networks. However, a weakness is that these methods always assume all the grids uniform in scale, limiting the quality and scalability. More recently, 3D Gaussian Splatting (3DGS) [32] represents radiance fields by a set of anisotropic 3D Gaussians and renders with differentiable splatting using rasterization, achieving remarkably successful balances between fast and high-quality scene reconstruction 40
However, due to the complexity of tremendous intersected Gaussians, view-inconsistent rendering problem is exhibited, and is hard to fix without large efficiency trade-offs [48 42
76
Also, the reliance on sparse point clouds brings additional uncertainty. To this end, SVRaster [55 combines efficient rasterization with explicit non-uniform sparse voxels to achieve definite, robust, and high-quality scene representation, with less mandatory dependency on structure prior as well. Nevertheless, its potential for accurate geometry learning has not been fully explored, which is an open yet invaluable problem for 3D reconstruction.
44
Surface Reconstruction with Learnable Fields. Reconstructing surfaces from multi-view images
has been a long-standing problem. While multi-view stereo- basee methods 226 81
52 70 rely on a
modular pipeline with multiple decoupled stages, earlier neural approaches 772 47 proposed
to represent surfaces implicitly with an MLP to learn geometry directly from images. Further advancements such as UNISURF [46). NeuS [9,, VolSDF 71] represent implicit surfaces by signed distance functions integrated with differentiable volume rendering and achieve better reconstructed
details. Based on these, methods with improvements like geometry regularizations [16] 77 20 58)
and efficient grid representations (38 65) extended the quality and available scenarios. However, the trade-off between training time and quality for complex scenes is still serious challenge.
More recently, Gaussian- baased surface reconstruction has arisen with 3DGS by offering better explicit geometry with much higher efficiency. SuGaR 255 first focuses extracting Gaussians mesh surfaces with alignment regularization. Then, more efforts appear by integrating 3DGS with SDF [3] 66, 79 361 or improved representations 22 78
[1]. significantly progressing the surface quality. Specifically, 2DGS (28) and GSurfel [3] propose squeezing Gaussians as 2D surfels for a better aligned surface, and GOF creates an opacity field allow dense and detailed mesh extraction. However, due to the loose geometry constraint and photometric ambiguities, challenges in accuracy still exist. For the SDF-integrated approaches, since additional MLP and also grid are usually required, problems of over-smoothness (79] and limitations for large unbounded scenes [41] may
occur. To conquer the accurate reconstruction on challenging regions, following previous successes (20 16 12), PGSR inherits the idea of surfels and incorporates the multi-view geometry constraint 26 which widely used in multi-view stereo, to regularize planar accuracy, but the production leans to be over-smooth, due to the unsharp Gaussians similarly in 2DGS 41 75 Meanwhile, some
attempt to resort external geometry cues from geometry foundation models 17 2 69 for regularization. However, the performance is still far from what the cues could fully provide, mainly caused by the methodological bottleneck in the strict demand of high-quality initial points, for which the effect of special densification is also limited [1] 14]. Instead, this work explores another sparse voxel representation to escape the strict initialization requirement and pursue a clearer geometry representation, achieving superior accurate, detailed, and complete surface reconstruction.
works 15
36 62
3

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Youd Replaricatin
Replartation
Surfice
Spare
Mosel Derpos
Reotifiaatio
Serize
Regaliiiction
Sealing Perudty
Netwer
D togis E Dospot
(s) Stene Coustraitt
Vind Unnee soceesirryy Rowaaattte Cestion
Sparie Vixel
Map
Maxlosi
Bad vax Dopthas
Vioriellaserattty Dack Conntrazil
Depis
Inport RGB Tmaage
Depth
Aecondrrctta
Figure Overview of GeoSVR. Our method starts from constantly initialized sparse voxels, optimized with RGB images. (a) To enforce correct scene convergence while avoiding accuracy degradation, we apply Voxel-Uncertainty Depth Constraint by evaluating geometric uncertainty to determine the degree of reliance monocular depth cue. (b) Voxel Dropout is introduced to enlarge the global geometry consistency for tiny voxels during the explicit geometry regularization. (c) For fine-grained surface refinement, align the voxel-level density field to the surfaces with Voxel Regularization, facilitating accurate and sharp surface formation.
3 Method
3.1 Preliminaries: Sparse Voxels Rasterization
Representation. Sparse Voxels Rasterization (SVRaster) [55] represents scene with density field based on sparse voxels, which are organized in an Octree of the size w. E R and center W. E R$ Each voxel keeps separately on the eight voxel corners to model trilinear inside density field for geometry. voxel is identified with the index == {i.j. k} at Octree level I, and its size V, and center Ve are given as:
of SH coefficients Vih for voxel color, and densities Vgen [0, +xx|2xxx2 2x2x2
x 2-
0.5 x Ws + X
Rendering, During rendering, SVRaster adopts a-blending similar to NeRF and 3DGS. Inside each voxel, SVRaster evenly samples K points in the ray segment of length A/ between the ray-voxel intersections, and composes voxel-wise a with trilinear interpolation interp(-) by volume rendering. Then, the a-blending available to render the pixel-wise color C that corresponds to the ray:
C= C=EM Mays, T, II," ay); a == exp(
At
interp( qk)), (2)
1-=
K
where at and e; are alpha and siew-dependent color of the i-th intersected voxel, and qu is the local position of the k-th sample point the voxel. According to a- a-blending, pixel-wise normal N and depth D. The pixel-wise depth D can be given similarly via per-point distance rendering. For voxel's normal, the analytical gradient is calculated the voxel center qe:
render the
normalize (Vg interp (Vgeu: qe))
Adaptive Octree Control. To adaptively adjust the scene Octree during training, SVRaster prunes the voxels with the least blending weight To, and accumulates an a-weighted priority based on loss gradients to select the voxels that need to be subdivided to the next level to represent finer details.
Challenges in Surface Reconstruction. Despite strengths in geometric completeness and clarity, challenges exist correspondingly: 1) With little native constraint, the optimization often encounters heavy geometry distortion and blocks further improvement. 2) The impact scope of a single voxel could be quite local, which is unfavorable to accurate surface formation. Exploring tackling these two challenges, present GeoSVR for high-quality voxel-based surface reconstruction, in Figure 2
3.2 Voxel Geometric Uncertainty for Scene Constraint
Unlike previous approaches based on SDF 20 77 or 3DGS 28 14
that benefit from
32 the highly expressive and constant-inittalizzed sparse voxels require an essential scene constraint effectively ensure the geometry converges approximately correct surfaces, preparing for a further accuracy refinement.
structure constraints from geometric 1 sparse points initialization

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Problem in Monocular Depth Cue. Inspired by previous works [77 64 we turn attention to the increasingly well-established monocular depth [ 21 67 69,, which provides dense, efficient, and full-time available constraints for scene geometry optimization. Moreover, this dense cue natively matches the spatially complete voxels to fulfill its potential for compensating appearance ambiguities.
However, the problem of how to maximally utilize this attractive but not perfectly accurate prior in the highly accuracy-required surface reconstruction remains a long-standing difficulty. Despite considerable relevant studies [77] 58
64 62 36], solution is still absent to evaluate the
learned geometry's confidence determine external cue reliance, which causes only werr-onnerrvative strategies to be available, but could still degrade the quality by the included errors [77 14.
Voxel Geometrie Uncertainty. In this work, aim to solve the problem by evaluating geometric uncertainty from the representational capability: 1) In SVRaster, each voxel contains a trilinear density field to represent the geometry of the cube space with length of Vs W, x 2-1 Then, the accuracy for an under-captured geometry is strictly limited, negatively related to the level of corresponding voxels. 2) During optimization, SVRaster progressively subdivides voxels at with largest gradients to the next level [+1 1. Consequently, the voxels at lower levels denote either regions with fewer texture constraints or less view coverage, both associated with high uncertainties.
Inspired by these two tight couplings of uncertainty and voxel's level, we abstract a level-aware geometric uncertainty that explicitly correlates with Octree level I to guide identifying scene constraint targets. For a voxel t at level I, its base and geometric uncertainties Ubsse and Ugcom are given by:
Ubase (1)
Ugeom (v) Ubase (1) (1 exp (-Vgeo))
3(++
where ( is a scaling factor, combined with Octree size wa as global scene scale. to the starting level. Geometric uncertainty Ugcom()) is composed of the level-dependent base uncertainty Ubsse and the voxel density, indicating a voxel at low level with critical geometry leads higher uncertainty. Derived in the Appendix Section B, we simplify powers and exponents while preserving the same trend to prevent numerical blowup in later applying.
Depth Constraint. Based on the uncertainty, we next design the constraint enable effective and reliable monocular depth integration. To effectively apply the monocular depth as supervision, we resort to patch-wise global-local depth loss (35) for better scale alignment and facilitating the geometry knowledge learning. Then, integrating the geometric uncertainty into the pixel-wise constraint, we first render an Octree level map L for efficient pixel-wise uncertainty calculation, directly gathering the volume density term of Eq. with a of Eq. via rasterization:
L L-Σ
i=1 Taahi a a-1-exp Al
N
Σ
K
interp(Vgeor g)))
(5)
K
Next, converting uncertainty to weight, produce pixel-wise modulation depth constraint. To ensure adaptive and robust constraints for various stages and scenarios, we obtain statistics of L to set the hyperparameters in Eq. 4.. Specifically, for scale- indee--nddeeedeeeee let the scale term of wa/B equal to pir-view global level scale w| = max(L) - min(L), and set Io = min(L) to define the coarsest level of the view. Then, derived from U Ue the geometry uncertainty weight W une follows:
W1
W
W| = max (L) - min
max max L,
mi))
Finally, given the estimated monocular depth D as the constraint for the rendered depth D, W Wanc is applied to the patch-wise depth loss DDppatch (35) for per-pixel constraint reweight:
LD- DD. Wine LD-patch DD.
As result, Voxel-Uncertaingg Depth Constraint LD-wns pays minimal attention to the voxels with low uncertainty to be confident of the native photometric constraint, while enhancing highly uncertain ones to rely on external cue for solving geometry ambiguities. The effect can be illustrated in Figures 2 and 6 where level map L is shown to obtain more uniform range of values for better visual effect.
3.3 Sparse Voxel Surface Regularization
Despite the scene constraint exerted, a coarsely correct reconstruction does not exhibit the full potential of sparse voxels. Therefore, we next investigate the capability of sparse voxels for highly accurate surface formation under explicit geometry constraint and finer voxcl-level regularizations.
5

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Geometry Regularization with Voxel Dropout. Serving an explicit and strict constraint, homography patch warping has shown great effect in classical MVS [22 53 81 and recent related works (20 16
12 58 which we also try to apply in our method. Typically, considering source view and reference view with image I, and I, we warp the image point x' in the pixel patch P of I to the image point x in I, of the reference view by the plane-induced homography H [53]
II
50
x Hx', H KR + R. (R,'t RR,ttt
(8)
n n"p
where p is the intersected 3D point calculated from depth D. and the normal n is from Eq. P
K is
camera intrinsics, and [R. t] the extrinsies of each view. Then, an occlusion-awand NCC loss is applied between the warped P and its target in I, However, we observe that despite improvements brought, this technique does not work as ideally as in previous approaches. Due the extreme locality of the tiny voxels that connect to only the nearest neighbors by few corners, the planar constraint becomes less effective, leading to redundant wrong structures being produced.
To solve this problem, our idea is to enlarge the regularization for each voxel by breaking these incor- rectly organized geometries, enforcing the tiny voxels obey more global geometry consistency instead of only their own tiny scopes. During the process, we conduct an interval sample of the voxels with random ratio in [?, 1] while calculating the full-scale depth D and normal N. Therefore, only a subset of voxels is used to represent the scene, while the others are temporally dropped out. Then, the regularization enforces each voxel to respond the geometry consisteney of larger area, including where the dropped-out voxels belong, for a forced break and correction of the ill geometries.
Surface Rectification. Subsequently, focus on the bias between the trilinear voxel density field and the weight contribution in rendering, which causes mis- aligned surfaces from rendering and voxel density. As in Figure D] due to the trilinear local-linked voxel fields, the density increase of one voxel will implicate the neighbors, resulting decentralized densities that makes the highest rendering weight w biased to the side regions but not the correct highest density position, like Figure 3 a.
(a) Surface Formation
(b) Surface Rectify
To this end, we propose Surface Rectification, a voxel- level regularization conducted during rendering. In the process, we first calculate an enter voxel alpha Ope and out Opo from the density of the intersected enter and out points Pe; Pa: denoted red cross in Figure 3 to model the first-time intersection for surface checking, and select the voxels with critical change density between P. and P. cross a threshold T. (set 0.5 in this work) as the surface voxels Vy:
Figure 3: Illustration of Surface Rectifica-
tion and the visualized process on voxels.
1/3 {v Ope < Ta < Opo): where Opeeoo - exp(- -t interp( goos Peio)
Then, for these voxels, we penalize the density at Pe but encourage at to form sharp segmentation of the surface and empty spaces, with a penalty term including the voxel's rendering contribution wt
Reee w I(u V.) (interp(y geo Pa) interp(Vgeo. (vgep P.)),
Ta.
(10)
Since then, the surface in rendering can be rectified to be aligned to the density, as in Figure 3 a.2.
Scaling Penalty. Inspired by the voxel geometric uncertainty in Sec. 3.2 we present simple yet effective regularizer that penalizes the voxels occupying a long sampling distance, which denotes a less accurate geometry modeling. Normalized with globally minimal voxel size min(v.), vs), it follows:
At
Rap = w interp(V q.) maxx(0, loga
min(v.) }), where q. = (0.5, 0.5,0.5)). 0.5). (11)
3.4 Loss Function
The total objective is composed of the photometric loss Ephoto from SVRaster, the depth constraint LD-mne from Eq. 77. NCC loss for geometry regularization, and the voxel regularizations in See. 3.3
L = C + D + TLxce + M1 Rie Ryp.
(12)
In this work, set the weights of ' 0.1, 7 0.01, μr 10-5, 5, and #2 10-6, respectively.

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Table Quantitative Comparison on the DTU [1] Dataset. Bests are in highlight. Our GeoSVR
achieves the highest reconstruction quality on the Chamfer distance while retaining fast training.
110
114
118
122
Maa
VoIDDE F1
1.14
1.26
0.70
0.72
1.18
0.66
1.08
0.42
0.61
0.55
0.86
> 12hh
Implex
NeuS 30g
1.00
1.37
0.93
0.45
110
0.65
0.57
1.48
1.09
0.83
0.52
1.20
0.35
0.49
0.55
0.84
>. 1.2h
Neuralaggelo
33
0.37
0.72
0.35
0.35
0.87
0.54
0.53
1.29
0.97
0.73
0.47
0.74
0.32
0.41
0.43
0.51
+125h
Gev-Neud
20
0.38
0.54
0.34
0.36
0.50
0:45
0.41
1,03
0.84
0.55
0.46
0.47
0.29
0.36
0.35
0.51
112h
MonoSDPP
0.41
0.37
0.51
0.73
2DGS
0.52
0.77
baplict
SVRaster
551
0.61
0.74
0.41
0.36
0.93
0.75
0.94
1.33
1,40
0.61
0.63
1.19
0.43
0.57
0.64
0.76
0.1h
G82Mesh
[0]
0.59
0.79
0.70
0.38
0.78
1.00
0.69
1.25
0.96
0.59
0.50
0.68
0.37
0.50
0.46
0.68
0.3h
VCR-GauS [c]
0.55
0.91
0.40
0.43
0.91
0.95
0.84
1.39
1.30
0.50
0.76
0.92
0.44
0.75
0.54
0.80
-1h
Mens<iSDF
B-45
0.65
0.36
0.36
0.94
0.70
0.67
1.27
0..99
0.63
0.44
0.84
0.39
0.53
0.47
0.65
brs
PGSR 11]
0.58
0.59
0.54
0.30
0.36
0.34
0.52
0,5h
GeoNVR (Chors)
Reference
Ge (Oun)
PGSR
SVRuster
VCR-GauS
GOF
Figure 4: Reconstructed Mesh Visualization on the DTU (31] Dataset. Our GeoSVR achieves superior reconstruction both accuracy and completeness, handling difficult regions well by geometry cue constraints while still preserving fine-grained details. Better visualized with zoom in.
4 Experiments
Implementation Details. Our code implemented with PyToorch and CUDA kemells, built upon SVRaster (55) In the experiments, we train each model with 20, 000 iterations, with the learning rates for density and SHs degree 0 and the others of 0.05, 0.01, and 0.00025 in Adam 33 optimizer.
We use DepthAnything V2 [69 to provide the depth cues. The patch size of 7 x is used for patch warping, and y in voxel dropout is set 0.5 and 0.3 for DTU and TnT datasets. The Octree setups keep the same as in [55], and the prune interval is increase to 2, 0000 for finer expression. In our method, we use TSDF for mesh extraction. All experiments are conducted on RTX 3090 Ti GPUs.
4.1 Comparision
Dataset. We use the prevailing DTU, Tanks and Temples (TnT), and Mip-NeRF 360 datasets for evaluation. The scene selections of DTU and TnT are consistent with previous works [ 59 38 28
preprocessed following 2DGS (2 and Neuralangelo [38]. The voxel size of TSDF set to 0.002 for DTU and is calculated for TnT following PGSR ΠII. The images in DTU and TnT are downsampled 2x, and in Mip-NeRF 360 are downsampled 2x or 4x following
for indoor and outdoor scenes.
Baselines. We take the ofate-of-the-art surface reconstruction approaches as baselines, including implicit (e.g.. NeuS [59], Neuralangeo [38], Geo-NeuS (00 and explicit methods (e.g., 2DGS (28,,
GOF 78 PGSR [1].. Among them, MonoSDF (77). GSurfel [5]. VCR-GauS [14, GS2Mesh
62. and MonoGSDF (36) take external geometry cues from pre-trained depth and/or normal models
for regularization. Basic representations like 3DGS (32 and SVRaster (55) are also included.

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Table 2: Quantitative Comparison on the Tanks and Temples [4]
Dataset. GeoSVR achieves the
best on the Fl score, demonstrating superior reconstruction quality on various real-world scenarios.
Implicit Neuralangelo Geo-NeuS
Explicit
NeuS
MonoSDF
2DGS
SVRaster
VCR-GauS MonoGSDF
PGSR
GeoSVR
Barn
0.29
0.33
0.35
0.66
Caterpillar
0.29
0.36
0.26
0.31
0.23
0.41
0.33
0.26
0.38
0.44
0.49
Courthouse
0.17
0.28
0.12
0.12
0.16
0.28
0.29
0.19
0.29
0.20
0.34
Ignatius
0.83
0.89
0.72
0.78
0.51
0.68
0.69
0.61
0.72
0.81
0.83
Meetingroom
0.24
0.32
0.20
0.23
0.17
0.28
0.19
0.19
0.25
0.33
0.37
Truck
0.45
0.48
0.45
0.42
0.45
0.59
0.54
0.52
0.62
0.66
0.66
Mean
0.35
Time
>24h
>128h
>12h
16m
24m
1
53m
45m
68m
Reference
GeoSVR (Uur)
PGSR
SVRaster
Reference
GeoSVR (Oun)
VCR-GuuS
GOF
Figure 5: Reconstructed Mesh Visualization on the Tanks and Temples GeoSVR stands out by reconstructing accurate surfaces even for difficult scenes like complex buildings and weak texture regions, delivering intricate details well as precise flats.
34 Dataset. Our
Surface Reconstruction. To evaluate surface reconstruction performance, we make comparisons the DTU and TnT datasets with Chamfer distance and Fl scorr.. The results are reported in Table D and On the DTU dataset, our method outperforms all the baselines in the overall accuracy, exceeding previous SDF and 3DGS-based SOTA methods Geo-NeuS and PGSR, and also all the methods leveraging external geometry cues well. On the TnT, method also achieves the best in F1-score, and gets better results in most scenes compared to the SDF-based Neuralangelo, monocular depth-hinted (i.e., Depth Anything V2) MonoGSDE, and geometry regularized PGSR.
On the two datasets, our method also retains fast training comparable to the DDGGS-aaee meth- ods. In Figure 4 and [ we visualize the re- constructed meshes from ours and competitive baselines. Our productions obtain both the best accuracy and completeness. And due to the ba- sis of the initial frior-free and densely covered sparse voxels, GeoSVR can handle the reflec- tive regions and areas with insufficient coverage, where the 3DGS-based methods are limited, due to insufficient initialization points. Additionally, GeoSVR performs better than previous geome- try cue-rcliant methods (e.g., VCR- (CR-GauS) that may lead to oversmoothing and underfitting.
Table 3: Quantitative Results Mip-NeRF 360 Dataset. The best scores for surface reconstruction methods are highlighted with colors.
Outdoor Scone SSIM
Indaor Scrne
LPIPS
PSNR
SSIM
NeRF
21.16
0.158
0.515
26.84
0.790
0.370
Deep Blending
21.54
0.524
0.364
26.40
0.844
0.261
NGP
0.566
Mip-NeRF 360
24.47
0.691
0.283
31.72
0.917
0.180
JDGS
24.67
0.728
0.240
30.96
0.924
0.187
SVRaster
24.68
0.738
0. 0.206
30.65
0.927
0.161
BakedSDF
22.47
Suracs Ro00
SuGak
22.93
0.629
0.356
29.43
0.906
0.225
2DGS
24.34
0.717
0.246
30.40
0.916
0.195
GOF
24.82
0.750
0.202
30.79
0.924
0.184
0.707
PGSR
24.76
0.752
0.203
30.36
0.934
0.147
Appearance Reconstruction. Achieving accu- rate geometry reconstruction, our method main-
GooSVR (Ouns)
24.83
0.738
0.218
30.46
0.931
0.172
tains the capability for high-quality novel view synthesis as well. In Table 3 we compare our methods on the Mip-NeRF 360 dataset with the baselines the aspect of rendering quality. Our method exhibits competitive performance among the surface reconstruction methods as well as the NVS- specific baselines such as our basis SVRaster. Due to the lack of geometry ground-truth, we do not evaluate the surface reconstruction quality. Qualitative comparisons can be found in the Appendix.
8

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4.2 Ablation Study
In this section, we verify the effect of our designs on the Tanks and Temples 34 dataset and report the mesh reconstruction metrics. The quantitative scores reported in Table As references, the reproduced SVRaster and PGSR with TSDF are reported in the comparison. Additionally, we summarize the baselines with external cues in Table to exhibit the effect of the methodology itself.
Table 4: Ablation Study on the Tn' Dataset.
Table 5: Accuracy Comparison to Baselines with External Cues.
Items
Settings
Precision
Recall
Score 1
SVRaster (Base)
PGSR (Reference)
0.383
0.509
0,560
0.421
0.527
Method
Goo.
Init& Cues
TnT DTU FL.
C1.1
PGSR
wise Depth (Reference)
0.517
MonoSDF
SDF
Mono Depth
Narmall
A. Sparse Points
0.363
0.409
0.382
SIM pts
A. + Inverse Depth
0.383
0.421
0.398
Gortel h3
GS
Mono Normal
0.88
A. Patch-wise Depth
B. Multi-view Reg.
0.474
0.520
0.438
0,568
0.538
0.449
GS2Mesh X
GS
Stareo Depth
SIM pts
0.68
B. Multi-view Reg Voxel Dropout
0.533
0.569
0.546
VCR-Gom
Mono Normal
SIM pts
C. Surface Rectif,
C. Surface Rectif, Scaling Peaalty
0.536
0.538
0.577
0,572
0.552
0.549
MonoGSDF
GS+
SDF
SIM
Depth
0.17
0.65
D. Voxel-Uncertainty Depth (Ouns)
0.549
0.581
0.560
Ours
Voxel
Mono Depth
0.56
0.47
Scene Constraint. Scene constraint dominates an essential start for further refinement. In Table 4 we observe that regularizations of sparse depth from SiM points and monocular depth with inverse loss both help less, while the patch-wise depth loss of Table 4 breaks through to improve the geometry effectively. A step further, even though the reconstruction already achieves a high quality (0.552 in F1), our -nce-tnnerta Depth Constraint still remarkably recognizes the uncertain regions and refines the geometry and preserving the well-reconstructed parts, as shown in Figure and Table
Ounoc Level Map
wio Von! Uncomtitty Depth
w/ Vonel Ulccertiitty Depth
wio Suriace Roxiil
Sulfac Mocil:
Reloxase
Figure 6: Qualitative Studies for the Voxel-Uncertainty Depth. Recognizing regions with uncertain voxel geometry, the challenging inaccurate surfaces can be effectively fixed.
Figure 7: Qualitative Studies for the Surface Rectification. Facilitation for sharp and accurate surfaces is made.
Multi-view Regularization. Based on the scene constraint, we then analyse the multi-view regular- ization part. Consistent with the conclusions like in previous works (20, [6] [T] adding the explicit multi-view geometry objective can hugely improve the geometry accuracy, yet by relieving the local trap of sparse voxels, our Voxel Dropout strategy further improves the multi-view consistency to higher level and exceeds the patch-warping regularized reference method with monocular depth.
Voxel Regularization. To further facilitate the surface-depth consistency, we apply the Surface Rectification and Scaling Penalty for the voxels to get finer surfaces. As shown in Table and Figure 7 the voxel regularization designs benefit the formation of accurate surfaces from the perspective of voxel-based representation, therefore improving the geometry both quantitatively and qualitatively.
Conclusion
In this work, we have presented GeoSVR, an explicit voxel-based framework that explores and extends the investiiveet potential of sparse voxels to deliver accurate, detailed, and complete surface reconstruction with high efficiency. Our study first analyzes voxel uncertainty in geometry representation to distinguish the confidence of learned geometry, enabling effective and robust scene constraint from external cues. Next, we investigate the problem of voxel-based surface refinement, reconstructing surfaces with superior quality by our solution. the future, will be interesting to explore enhancing voxel's globality to conquer challenges like varying lights and textureless regions.

---

Acknowledgments and Disclosure of Funding
This work supported by the National Natural Science Foundation of China 62276016, 62372029. and Key R&D Program of Jiangxi Province, China (20232BBE50019), Lin Gu is supported by JST Moonshot R&D Grant Number JPMJMS201 Japan.
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Appendix
A Ablation Study
A.1 Scene Constraint
To better verify and demonstrate the effect of scene constraint, we con- duct an additional ablation study by solely disabling the scene constraint on our full GeoSVR and ablate its ef- fect with more monocular models, in- cluding DeythAng (68), Depth- Pro (6) and DepthAnythingV2 [69].
Table 6: Additional Ablation Study Scene Constraint. The absence of scene constraint leads to obvious distorted geometry (red). This drawback can be solved via our proposal.
Backhone
Monocular Model
Uncertainty
Precision
Recall
Fl- FI-Score
POSR
None
NIA
0.509
0.560
0.527
DepthAnything
0.576
None
N/A
0.511
0.549
0.523
As analysed in our main paper, un- like 3DGS or SDF that natively ob- tain geometric hypothesis for better convergence, the absence of scene constraint of SVRaster leads unde- sirable and heavily distorted surfaces.
DepthAnything
V
X
0.526
0.539
0.568
0.574
0.540
0.551
GeoSVR
DepthPro
X
0.537
0.574
0.549
V
0.546
0.579
0.557
DepthAnything22
X
0,538
0.577
0.552
Although a competitive accuracy on partial regions can gained after applying our efforts of Sparse Voxel Surface Regularization, the distorted geometry leads to lot of inaccurate reconstructions and drags the overall performance improvement compared to the SOTA 3DGS based approach PGSR [ quantitativlly and qualitatively shown in T and Figure 8 By introducing monocular depth as a solution, can be observed that this drawback the representation has been well addressed.
SIM Phini Cloods
POSK
POSR Pudloile Death
GeoSVR w/o Some Corsraion
GeoSVR Fill
Figure 8: Comparison of Challenging Region Reconstruction without/with Scene Constraint.
Despite the rich geometric eues provided, previous 3DGS-based approaches are much more limited in exploiting monocular depths for improvements, which demonstrates the advantage of our explored sparse voxels. For demonstration, we apply the monocular depth with our used patch-wise loss to the SOTA PGSR and adjust the coefficient to fit the best Fl-score, and visualize the reconstructed surfaces in Figure S It can be observed that for challenging areas that are difficult to reconstruct through multi-view consistency, 3DGS-based approaches even when applying monocular depth constraints, mainly limited by their heavy reliance on the initial SfM points. Notably, PGSR also applies specific densification technique AbsGS [3 relieve this limitation, but this is still marginal for such cases. Instead, when just applying the less advanced DepthAnythingg, our method gets much larger improvements, especially equipped with the proposed Voxel-Uncere -ncertaitty Depth Constraint. With DepthPro that is less robust for outdoor scenes, our method still retain high-quality reconstruction, exhibiting the effectiveness and robustness of method.
hardly recover the accurate geometry
A.2
Voxel Dropout
In the main paper, we have quantitatively veri- fied the effect of Voxel Drouput, which improves the release of the power of geometry regulariza- tion for the local voxels significantly. Due the space limitation of the main paper, we supple- ment the qualitative comparisons here help demonstrate its effect in Figure 9 As shown, different from the situations in SDF or 3DGS where smooth surfaces are reconstructed by ap- plying the homography patch warping, several redundant geometric structures remain in local voxel-based representation when not applying
Reference
wea Vonel Dropout
w/ Vosel Drepont
Figure 9: Effect of Voxel Dropout Strategy.
22

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voxel dropout. Analysing these geometric artifacts, we found that despite the geometry regularization can recognize and penalize these regions, the effect is marginal because the effect scope is quite small for tiny voxel and it does not receive the gradient from the distant neighbors, whereas it can not move as the primitives in 3DGS, making local minima between the appearance supervision and geometry regularization. Getting inspiration from the classic dropout (54) that solves the overfitting from complex parameters, which is similar to our problem, we simplify the voxel-based scene representation by dropping out parts of the voxels, and make each voxel obtain large responsibility for geometric consistency during geometry regularization. This proposal finally relieves the problem.
A.3 Surface Rectification
In Table 4, we ablate the Surface Rectification on the TnT datasets show its effect, and report the com- parison on DTU in Figure 7. Acting as a fine-gran une-grrined regularization technique on tiny voxels with critical density changes, its effect can be better exhibited on the DTU dataset, which focuses on the evaluation for highly accurate surface reconstruction. For better demonstration, we report the quantitative ablation results on DTU in Table Compared to the TnT dataset, the improvement on it is more significant to bring about 0.01 improvement Chamfer distance. This is even close to the entire gap between some previous methods (e.g., 0.51 from Geo-Neus 0.52 from PGSR) in Table 1, especially considering the quality is already quite close to the ground truth, which demonstrates our technique's effectiveness in accurate surface refinement.
Table 7:
Additional Ablation Study on Sur- face Rectification on the DTU [3] dataset.
Setting
d2s 4
s2d 1.
cf-dist
w/o Surface Rectif.
0.433
0.521
0.477
w/ Surface Rectif.
0.426
0.511
0.468
B Derivation of Voxel Geometric Uncertainty
Here we provide the detailed derivation of the Voxel Geometric Uncertainty in Eq. (4).
Derivation. Review the representation, the scene geometry is represented with the composition of non-overlapping trilinear voxels, of which the density inside a voxel is trilinearly weighted by the corner points with a density value of each. Therefore, the geometry representation capability for single voxel is constant and scale-independent, which we denote as a constant value Gmax to indicate the maximum quantity of information of each voxel for geometry representation.
Then, consider local region of the quantity of information Pgoo in geometry per unit volume that needs to be learned. For voxel with the length of v, in it, the desired quantity of information Q for representation should be:
Q = Pgen v3 8.1. V. W. x 2-1
Q - Pgeo
W 2
(13)
In most situations, the sparse voxel model can not fully capture the geometry information with unlimited resolutions due to the limited computational resources. Therefore, for the underfitted regions, the maximum information retention ratio 7/max can be given:
Gmax
Gmax
2
7max
E (0.1).
(14)
Q
Pgau
After getting the ideal upper-bound, we focus on the common cases for the uncertainty.
First, considering Eq. 14 only gives the maximum retention ratio, while we try to estimate the actual voxel uncertainty, the local target for different voxels should be considered. Then, based on the retention ratio 7mmx our goal is to model proper base to weight the uncertainty that is only relevant to the voxel's characteristic. Therefore, we build the voxel uncertainty based on an inverse 7) to indicate the information loss, which ensures the weight does not shrink to O to cause failure when the ideal Gmax meets the target Q, and introduce a coefficient g(v) to adjust the local target for different voxels. The voxel geometric uncertainty U in the initial follows:
Gmax g(v)
Gmax
)3, W
2! U(v) = -
1 Gmax
Wa 3 (gg
. Pgep g(v).
(15)
Pgen
g(v)
Coefficient Definition and Approximation. Turn to the real situations, since it's difficult to precisely define the value of constants Gmax and Pooss and variance gv. denote the constant Gmax
23

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Reference
SVRaster
2DGS
PGSR
GeoSVR (Ours)
Figure 10:
Qualitative Comparison on Mip-NeRF 360 dataset. Our GeoSVR provides more detailed and complete surface reconstruction for the real-world captured scenes.
coefficient that relates glocal geometry scale, and take the sampled voxel density approximate represent the term Pgeu g(u) to reflect the local quantity of geometric information, reasonably assuming the already learned densities in voxels have already been approximately accurate during the past optimization and are positively correlated to their local quantity of geometric information.
Therefore, based Eq. 15 the approximated voxel geometric uncertainty Unperi given by:
Vapp(())
exp (-Vgon))
(16)
where interp(-) not shown indicate non-specific sampling. Considering further probable involvement in various calculations, given the values of Octree level may increase to be up to 16 or even larger, Unper can easily cause numerical blowup to an extremely extensive data range due its contained power and exponent in (2 and thus brings instability. Therefore, keeping the same trend and also suitable data range weight for later, we cancel the overall power of 3 and replace the term / with 1/1. additionally compensate for the degree value variation, we introduce a bias la on the Octree level to help control the shape of the function. Consequently, the final formulations of the Voxel Geometric Uncertainty Eq. (4) are derived:
Ws
Usase (1)
U Ugeom(() (v) = Ubase (1) exp (-Vgeo))
(17)
B(I lo)'
C Qualitative Comparison on Mip-NeRF 360
Here supplement the qualitative comparison Mip-NeRF 360 3 dataset. As shown in Figure 10 our GeoSVR provides more detailed and complete surface reconstruction for the real-world captured images. As discussed in the main paper, both 2DGS and PGSR suffer from the geometry representation ambiguity from the Gaussians, and thus lead to over-smooth surfaces and a lack of details. Instead, method overcomes the geometry distortion in SVRaster while preserving high-quality details with completeness to deliver accurate surface reconstruction.
D Experimental Details
D.1 Datasets
We use the DTU Tanks and Temples (TnT) J and Mip-NeRF 360 3 datasets for evaluation.
Specifically, we follow the previous works to select 15 scans with ids of 24, 37, 40, 55, 63, 65, 69,
https://roboimggenn compute..eccmceeeoecoocccc. dtu. wwtp////e/dddaa.3/
org/
https://jonbarron http://www...iooooooeeeff//////
24

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83. 97. 105, 106. 110, 114, 118, 122, and use the half-resolution images as the training data. The DTU dataset used in the experiment is preprocessed from 2DGS [28 through COMLAP [1
In Th'T dataset, we follow previous work to use 6 high-quality scenes from the Training Data split that provides publicly accessible ground truth for evaluation. The camera poses and scene boundary are translated by the script provided by Neuralangelo [8] For Mip-NeRF 360, we use all 9 scenes for evaluation. The images are downsampled 2x or 4x following [32] for indoor scenes ("bonsai", "counter", "kitchen", "room") and outdoor scenes ( ("bicycle", "garden", "flowers", "stump", "trechill"). The camera poses are provided along with the dataset.
D.2 Baselines
In experiments, our baselines mainly involve: 1) implicit SDF-based methods: NeuS (59
Neuralan- 28 GOF GS2Mesh
geo [38] Geo-NeuS (20,, MonoSDF [77), and 2) explicit methods: 2DGS
62 VCR-GauS [4), PGSR [II, MonoGSDF [36] and SVRaster 155 In the latter, SVRaster is
based on sparse voxels and others are based on 3DGS, while MonoGSDF also uses a hybrid SDF.
Baselines Involving Geometry Models. Among them, MonoSDF 77 GSurfel [5], VCR-GauS
[4]. GS2Mesh [2]] and MonoGSDF (named G2SDF in the earlier 36 take external geometry cues from pre-trained depth and/or normal models for regularization. Specifically, MonoSDF uses pre- trained Omnidata [17 models to estimate monocular depth and normal, and GSurfel uses normal from Omnidata for supervision. GS2Mesh takes pre-trained stereo model [80] to extract surfaces from well-trained 3DGS model directly from the synthesized views. VCR-GauS leverages monocular normal (2) and conducts multi-view check to estimate the estimation confidence of the normal maps for better regularization. MonoGSDF takes monocular depth from DepthAnything V2 [69] which is the same as we use, to supervise the rendered depth with some learnable adjustment terms.
For qualitative results, we report the official scores from the published or up-to- date arXiv papers if available. For Geo-NeuS that does not have an official score on TnT dataset, we take the results reported by Neuralangelo for comparison. For qualitative results, we prioritize using the officially provided checkpoints or results if available. Otherwise, we use the official codebase to reproduce the results following the corresponding scripts on the same processed datasets as used for our method, which does not contain error poses like the processed TnT from 2DGS and GOF, for fairness. The reported training time is from the corresponding papers. And since MonoGSDF has not reported the training time on DTU nor open-sourced their code, we marked it as "hrs" through an approximated estimation from the provided training time of TnT.
Source of Results.
D.3 Metries
Following prevailing settings 7 38 for DTU dataset, and F1-Score for the overall quality for TnT.. Especially, we take the off-the-shelf evaluation toolkits 7 with the corresponding version of dependencies (c.g., Open3D 0.9.0 for TnT)
28 78,, we use Champer distance to measure the accuracy
in measurement for fairness. For Mip-NeRF 360 dataset, we inherit the metrics with implementations
used in 3DGS
32 to keep aligned with previous works 778
E Inference Speed
Besides delivering high-quality surface reconstruction, GeoSVR also retains high efficiency. While the training times are reported in the main paper, we list the rendering speed on different datasets in the experiments in Table It's shown that our method achieves a fast inference speed,
Table 8: Average Rendering Speed.
Dataset
360 [3]
DTU [31
TnT (34
FPS
83.1
143.8
142.0
inheriting from SVRaster [55) by keeping its concise representation without introducing any heavy modules at inference. The typical time of mesh extraction is within minutes, depending on the required scale. Overall, GeoSVR achieves top-tier efficiency competitive with GS-based methods.
25

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Bar
MeetingRoom
Ignatios
Caterpillar
Truck
Figure 11: Visualization of Reconstructed Meshes on TnT 34 Dataset.
bicycle
bonsai
counter
flower
garden
kitchen
room
stump
treehill
Figure 12: Visualization of Reconstructed Meshes on Mip-NeRF 360 3 Dataset.
26

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scan24
scan37
scan40
scan55
scan63
scan65
scan69
scan83
scan
scan105
scan106
scan110
scan114
scan118
scan
Figure 13: Visualization of Reconstructed Meshes DTU 31 Dataset.
Robha
scan24
scan37
scan40
scan55
scan63
scan65
scan69
scan83
scan97
scan105
scan106
scan110
scan114
scan118 118
acan122
Figure 14: Visualization of Reconstructed Meshes with Vertex Color DTU 31 Dataset.
27

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F Efficiency Analysis
In Table 9 we report the efficiency metrics corresponding the ablation study Table 4. From the results, it can be observed that all of the components maintain high efficiency in all aspects, including inference FPS, memory, and the required number of voxels, except the multi-view regularization that contributes most to the increasing training time consumption. According to our analysis, this is mainly caused by the less efficient code implementation, which we plan to solve in the future.
In terms of GPU consumption, it can be observed that our proposed components exhibit superior efficiency, which seldom increases GPU memory occupancy under similar number of voxels. Especially, this achievement is contributed by our efficiency-focuser designs in constraint selec- tion, restrained voxel-level regularizations, and combined with the efficient coding implementation. Moreover, while our proposed techniques effectively enforce correct geometry to be learned, the artifacts, redundant voxels, and distorted surfaces can be removed well corrected, therefore, the GPU memory requirement could even decrease along with the number of used voxels reduced.
Table 9: Efficiency Analysis of the Ablation Study.
Items
Settings
Voxels (M) +
FPS
Peak GPU Mem І
F1-Score
Training Time
A. Base (SVRuster)
9.3
132.9
12.3 GB
0.397
23.8 min
B.
A. Patch-wise Depth
9.1
138.2
10.5 GB
0.449
24.2 min
B. Multi-view Reg.
9.1
138.7
11.4 GB
0.538
65.1 min
B. Multi-view Reg. + Voxel Drupout
9.1
137.3
11.5 GB
0,546
68.3 min
C. Surface Rectif.
8.8
146.4
11.1 GB
0.549
64.4 min
C. Surface Rectif. Scaling Penalty
9.0
142.4
0.552
67.3 min
Voxel-Unnertainty Depth (Ours)
8.8
142.0
11.2
0.560
67.5 min
G Additional Visualization Results
Here we show the additional visualization of the reconstructed meshes on the three datasets. In Figure an [2] we show the reconstructed scenes in the TnT and Mip-NeRF 360 datasets. Our proposed GeoS VR reconstructs high-quality meshes in these complex and intricate scenes. In Figure [3 we reported the reconstructed objects DTU datasets, and additionally show the colored rendering in Figure 14 These results prove the capability of GeoSVR to reconstruct vivid objects with accurate detail, which further proves its practical value in real-world applications. For intuitive comparison, additionally provide supplementary video and kindly invite the reader to watch.
H Societal Impacts
Our proposed method provides high-quality surface reconstruction from images. So far, we have not discovered the direct negative societal impact, but it's notable that the accurate 3D reconstructions may be used maliciously. And the accurate reconstructions from real-world data may raise potential privacy concerns. During use, these societal impacts should be treated with caution.
I Discussion
In this work, we present GeoSVR to achieve high-quality surface reconstruction with state-of-the-art accuracy, completeness, and detail preservation. Moreover, our investigation goes further step for the possibility of recovering accurate geometry via the voxel-based representation, and also reveals a potential better utilize the growingly important and well-established geometric foundation models
688 69
2
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4
besides the Gaussian Splatting-base based approaches 36 14 35 15)
Nevertheless, the limitations still exist, mainly in 1) regions with serious reflections, 2) textureless areas, and 3) transparent surfaces. Due to the heavy misleading of the photometric inconsistency and the limited representation capability for ray tracing, these regions often cause suboptimal geometry.
Typically, it's a common phenomenon that the rendering quality slightly drops when the model is forced to learn the accurate geometry. This mainly lies in that the captured multi-view images from
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the real world do not always retain an ideal photometric multi-view consistency that matches the correct geometry, such as the reflective regions and transparent materials, especially the current radiance fields for surface reconstruction seldom consider complex ray tracing, but mostly only once forward. that situation, a distorted geometry in a local minimum may be better than the correct one to express an approximately accurate appearance.
In the future, introducing more efficient ray tracing techniques 223
improved voxel globality, and solutions for transparency 37] 29] could be of help to solve these challenging issues.
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Reviews:
[{"review_id": "a6KK6mPpjm", "reviewer": "Reviewer_gVE6", "summary": "An explicit voxel-based framework is proposed for surface reconstruction from RGB images. To better constrain surface reconstruction, a voxel-based uncertainty weighting is introduced which adaptively selects whether to rely on multi-view photometric cues or external monocular depth cues for guiding accurate surface reconstruction. To further constrain reconstruction, a multi-view geometry loss is leveraged and a form of voxel dropout is proposed when rendering depth and normals for the patch-based warping to help encourage the regularization to act more globally on the tiny voxels. Finally a surface rectification regularization is proposed for encouraging sharper surface boundaries. The proposed method builds off of SVRaster, demonstrating large improvements over SVRaster on surface reconstruction while also outperforming recent implicit and explicit surface reconstruction methods on several datasets.", "questions": "**Questions:**\n- It seems like SVRaster needs to be run first to obtain the initial sparse voxel grid from RGB images. If SVRaster fails to provide a decent initialization will this cause the proposed approach to fail?\n\n**Suggestions:**\n- Would be good to add a description of color coding (i.e., red = best) or at least describe lower CD is better and higher F1 is better in Tables.", "limitations": "yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n- The proposed method demonstrates strong surface reconstruction results:\n    1) Significant improvement on surface reconstruction over the method the approach is based on (SVRaster), while not sacrificing performance in novel view rendering quality.\n    2) Quantitatively outperforms all the other recent explicit and implicit surface reconstruction methods \n    3) Qualitatively produces reconstructions that are more complete / contains less holes, results in sharper geometry, and suffers from less warped / distorted surfaces.\n    4) While only slightly outperforming PGSR quantitatively, the proposed approach produces noticeably better reconstructions from the qualitative results in the main paper and supplemental.\n- The proposed voxel geometric uncertainty seems like a sound way to weight whether to rely on solely photometric cues or use additional monocular depth cues, as large voxels (lower levels in octree) likely indicate regions with low overlap or low photometric consistency in images and therefore need additional supervision from depth to accurately locate surfaces. Moreover, the proposed uncertainty weighting seems to be effective regardless of foundation depth model used which further demonstrates its usefulness.\n\n**Weaknesses:**\n- It is not completely clear to me that the proposed surface rectification is an effective way to solve the issue of increasing density in one voxel causing an increased density in the neighboring voxels. While I understand the proposed surface rectification can help produce a sharper boundary, encouraging the surface to be pulled toward the \"out\" point seems like it may potentially shrink the geometry. Can’t this lead to undesirable artifacts or is this unlikely as the voxel sizes are typically very small? Moreover, the surface rectification seems to have very little impact quantitatively (Table 4) and qualitatively (Figure 7).\n- Writing could use some improvement:\n    1) Surface rectification section (lines 229 - 233) could be improved. In line 230, $\\alpha_{p,e}$ and $\\alpha_{p,o}$ are called voxels but then in Figure 3 $p_{e,o}$ look like crossing points between voxels, and then in Eq. 9 $\\alpha_{p,e/o}$ is defined as the standard alpha term from volume rendering, which is confusing to read.\n    2) Some sentences have grammatical errors (line 177, end of line 182 and beginning of 183, line 187)", "was_revised": true, "final_justification": "After reading the other reviews and the authors rebuttals, I have raised my score to accept. The authors addressed my major concerns in their rebuttal, and overall I think the paper offers good technical contributions while demonstrating quantitative and qualitative performance improvements over existing works.", "rebuttal": "### **Responses to Reviewer gVE6**\n\nWe sincerely thank Reviewer gVE6 for recognizing our work and providing valuable comments. We noticed that the main concerns from the reviewer are the performance and explanation of the Surface Rectification design, improvements on the writing and the relation to SVRaster in initialization. Here, we address the questions individually:\n\n------\n\n\n\n> **Q1: Robustness and Effectiveness of the Surface Rectification.**\n\n> - Will Surface Rectification cause inaccurate shrunk geometry by over-pulling the surfaces to the \"out\" direction?\n\nOur proposed Surface Rectification aims to address the biased surface problem at voxel level, **offering robust correction in the whole optimization process**. It can prevent the over-shrunk geometry problem in two aspects: **1)** First, while a typical effect of Surface Rectification is to solve the front-biased surface by pulling it toward the out direction, as illustrated in Figure 3, **our design does not restrict the rectification direction** but is to encourage a sharp density variation inside of one voxel by both penalizing the front density value meanwhile encouraging the after one. Therefore, in some cases, the Surface Rectification can even help fix unexpected hollows to be smooth and complete (e.g., when the density value of the enter point $\\mathbf{P}_e$ has already been small but the out point  $\\mathbf{P}_o$ is not large enough). The surface would not be blindly pulled towards a certain incorrect direction. **2)** As noticed by the reviewer and analyzed in our paper, an accurate surface is always formed by tiny voxels rather than the large ones. As our Surface Rectification is conducted inside specific critical voxels, its direct effect is limited to its target and the nearest neighbors. Thus, for the tiny voxels that are important to form the final accurate surfaces, **restrained yet effective rectification is adopted**, while the large voxels are still in the stage of coarser optimization with the photometric and geometric supervisions. We'll add more explanations in the revision to better clarify the working principle of Surface Rectification.\n\n> - The quantitative and qualitative effect of the Surface Rectification.\n\nSurface Rectification brings **a significant and critical improvement in high-precision surface refinement** in reconstruction accuracy, especially playing an irreplaceable role **in situations where the reconstruction results have already been very close to the ground truths**.  Different to the proposed contributions like Voxel-Uncertainty Depth that has a large and macro influence with large geometric changes to adjust the obvious errors, Surface Rectification is an important and necessary technique for **pursuing the challenging target of extremely high-precision surfaces**, which works mainly in the stages of an almost well-reconstructed geometry to certify the delicate and difficult details, such as shown in Figure 7. Especially, its effect can be well demonstrated on the DTU dataset quantitatively, as shown in Table 8 in the supplementary material. Besides the critical accuracy improvement in high-precision cases, we believe the revealed problem behind this technique can also deliver novel insights to inspire more advancements to facilitate the development of the field.\n\nThanks for the feedback from the reviewer! To help the readers better understand, we'll add clear guidance in the main paper to the related additional experiments in the supplementary material, and provide more qualitative results for better demonstration.\n\n------\n\n\n\n> **Q2: Writing problems.**\n\nWe sincerely appreciate your careful notice to help improve our paper! In line 230, we have missed a word of \"alpha\" during writing, and we are sorry for causing the confusion. The correct descriptions should be \"... an enter voxel alpha $a_{\\textbf{p,e}}$ and the out  $a_{\\textbf{p,o}}$ ...\", which is calculated following Eq. (9). And following the comment, we have checked our paper thoroughly and corrected the grammatical errors, and fixed unclear expressions that may lead to misunderstanding. \n\nSpecifically, for the problems pointed out by the reviewer, we have made the corrections, such as:\n\n- Line 177: \"Geometric $U_{\\text{geom}}(v)$ is composed of $U_{\\text{base}}$ from level with voxel density, ...\" -> \"Geometric uncertainty $U_{\\text{geom}}(v)$ is composed of the level-depended base uncertainty $U_{\\text{base}}$ and the voxel density, ...\";\n- Lines 182-183: \"..., we resort to a patch-wise global-local depth loss for better scale alignment and facilitate the geometry knowledge learning.\" -> \"..., we resort to a patch-wise global-local depth loss for better scale alignment and facilitating the geometry knowledge learning.\";\n- Line 187: \"To ensure adaptive and robust for various stages and scenarios, we obtain ...\" ->  \"To ensure adaptive and robust constraints for various stages and scenarios, we obtain ...\".\n\nThese revisions and the other unlisted writing refinements will be updated in the revised version.\n\n------\n\n\n\n> **Q3: Relation to the initialization from vanilla SVRaster.**\n\nIndeed, **our method does not inherit reconstruction results from vanilla SVRaster**, and is able to **perform high-quality reconstruction for the challenging cases that SVRaster may fail**. We'd like to note that the pipeline of GeoSVR is not linked to the initial voxels produced by vanilla SVRaster, and is robust in situations where SVRaster can only reconstruct seriously inaccurate surfaces. As described in Section 1 and Figure 3, both our method and SVRaster adopt initialization of constant voxels that depend on the range of camera trajectory to cover the whole scene, and the reconstruction processes would go differently once the optimization starts. As shown in the first scene in the supplementary video, and comparisons of Figure 11 in the supplementary material, GeoSVR has successfully reconstructed the regions that are extremely biased from the ground truth in SVRaster, demonstrating the superior robustness of GeoSVR. Due to the restriction on the rebuttal, we are not allowed to upload more typical cases here with images, but we will add the results in the revised version to help declare the performance relation between our method and SVRaster.\n\n------\n\n\n\n> **Q4: Better clarity of the highlighting and metrics.**\n\nThanks for the suggestions! Following the comments, we have conducted a thorough double-check of our paper, especially on the unclear descriptions, and refined it, including adding the explanations of the color marks in Tables 1, 2, 3, and declaring the directionality of the metrics in Tables 1 and 2 in the captions. The updates will be shown in the next chance of paper uploading. We thank the reviewer again for helping us make the paper easier to read with better clarity."}, {"review_id": "gti5sAtScU", "reviewer": "Reviewer_fLdW", "summary": "This paper is a subsequent work of SVRaster, focusing on improving the geometry reconstruction quality for the voxel-based 3D representation. This task is very important and this work paves a solid step in this direction. Specifically, the author employs the prior from DepthAnything v2 to selectively guide the poorly optimized region. This idea should be generalizable across different 3D representation. Furtherly, this paper proposes some geometry-friendly regularizations, including the voxel dropout, Surface Rectification, etc.. According to the experiments, this paper outperforms others in reconstruction quality.", "questions": "1. Please provide more thorough analysis on the depth design.\n2. Whether will the Voxel Dropout design encourage larger and more redundant voxels?", "limitations": "yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths:\n+: Each design is simple yet effective, accompanying with a detailed analysis, making it convincing.\n+: The qualitative and quantitive results outperform baselines.\n\nWeakness:\n-: The memory consumption is not clear. The author adopts some new losses, regulations, constraints, although they lead to an improvement in the geometry, it would be better to add the increasing in memory consumption to better justify. \n-: The key design is the voxel-uncertainty depth guidance. While there is no direct comparison between naive depth guidance and the voxel-uncertainty version. \n-: How can the method deal with the case when the depth prediction network totally fails? Where the per-scene optimization pipeline can still provides with a not bad lower bound.", "was_revised": true, "final_justification": "I keep my original score for acceptance because the rebuttal addressed most of my concerns and the proposed method is very effective.", "rebuttal": "### **Responses to Reviewer fLdW**\n\nWe sincerely thank Reviewer fLdW for the positive evaluation and insightful feedback. We noticed that the reviewer’s main concerns involve analysis of computational overhead, ablation detail for depth constraint, and robustness in failure scenarios. Here, we address the questions from the reviewer individually:\n\n------\n\n\n\n> **Q1: Memory consumption of the proposed method.**\n\nThanks for the constructive suggestion! Our method **maintains similar or even less GPU memory overhead compared to SVRaster, and practically is able to reduce over 8% of GPU memory** (over 1.1 GB in the original 12.3 GB) in the experiments on TnT datasets on average. Here we supplement the metrics of running overheads corresponding to the ablation study of Table 4 to show the consumption of each component. From the reported results, it can be observed that our proposed components exhibit superior efficiency in GPU consumption, which **seldom increases GPU memory occupancy under a similar number of voxels**. Especially, this achievement is contributed by our efficiency-focused designs in constraint selection, restrained voxel-level regularizations, and combined with the efficient coding implementation. Moreover, while our proposed techniques effectively enforce a correct geometry to be learned, the artifacts, redundant voxels, and distorted surfaces can be removed or well corrected, **therefore, the GPU memory requirement could even decrease along with the number of used voxels reduced**. This demonstrates the high efficiency and effectiveness in improving the surface reconstruction quality in the methodology, but not solely an efficiency-quality trade-off. We'll add these results in the revised version to support a more comprehensive justification.\n\n| Item Notation | Settings                                | Inference FPS | # Voxels (Million) | Training Peak GPU Mem (GB) |\n| ------------- | --------------------------------------- | ------------- | ------------------ | -------------------------- |\n| A.            | Base                                    | 132.9         | 9.3                | 12.3                       |\n| B.            | A. + Patch-wise Depth                   | 138.2         | 9.1                | 10.5                       |\n|               | B. + Multi-view Reg.                    | 138.7         | 9.1                | 11.4                       |\n| C.            | B. + Multi-view Reg. + Voxel Dropout    | 137.3         | 9.1                | 11.5                       |\n|               | C. + Surface Rectif.                    | 146.4         | 8.8                | 11.1                       |\n| D.            | C. + Surface Rectif. + Scaling Penalty  | 142.4         | 9.0                | 11.2                       |\n| E.            | D. + Voxel-Uncertainty Depth (**Ours**) | 142.0         | 8.8                | 11.2                       |\n\n\n\n------\n\n\n\n> **Q2&Q3: Comparison with naive depth constraint. & Robustness when the monocular depth prior fails.**\n\nThanks for the feedback from the reviewer. From Table 4 in the main paper and Table 7 in the supplementary material, and the corresponding qualitative results in Figure 6  in the main paper and Figure 9 in the supplementary material, **our method, along with the Voxel-Uncertainty Depth Constraint, can be well verified to be effective and robust in various cases with comprehensive validations**. Here we provide our analysis.\n\n> - Q2: Comparison with naive depth constraint.\n\nIn the ablation study of Table 4, we first compared the performance between the two alternatives to apply the depth priors (i.e., Sparse Points and Inverse Depth in the table), and found that our used Patch-wise Depth performs best, which is the foundation for the following ablation settings. To show the impact of our proposed Voxel-Uncertainty Depth Constraint, **we directly compared the two situations** with or without this technique in Table 4 by Item D and E. As analyzed in Section 4.2, this technique can remarkably recognize the uncertain regions and refine the geometry while preserving the well-reconstructed parts, even though the reconstruction already achieves a high quality. Recognizing the importance of a comprehensive verification, we additionally provided **a fine-grained ablation study for the depth constraint** in Section A in the supplementary material, including various comparisons on different depth estimators between no depth constraint / without Voxel-Uncertainty Depth Constraint /  with Voxel-Uncertainty Depth Constraint. According to the table, our proposed technique **consistently delivers obvious improvements in both accuracy and completeness**, and outperforms the other situations regardless of the quality of the provided depth priors, which demonstrates its effectiveness and robustness.\n\n> Q3: Robustness when the monocular depth prior fails.\n\n Although it's extremely rare to be entirely invalid for the advanced depth estimators that are trained on large corpus, our method still support the capability for high-quality reconstruction with totally no depth priors involved, as verified in **Table 7**, which shows that **our method can still achieves a comparable performance than the previous SOTA method PGSR in such an unusual case.** Notably, in this comparison, PGSR still relies on an SfM point cloud as the prior, while our method doesn't require it. Besides this extreme case, a more common challenging situation is that the provided depth prior is of a much lower quality than expected. To verify our performance on this case, we ablate our method in Table 7 by not using the SOTA monocular estimators but the relatively old DepthAnything V1, which is much weaker in accuracy, robustness, and detail prediction than DepthAnything V2 and DepthPro, to stimulate the situation.  We find that even in this case, our method can still provide high-quality surface reconstruction, mainly thanks to our Voxel-Uncertainty Depth Constraint that successfully protects the well-reconstructed parts not influenced by the errors in the monocular depth priors, while still applying effective geometry constraints to the uncertain areas. **In summary, our method is robust for different failure cases of the depth priors.** \n\n\n\nTo better guide the readers to locate the additional experiments, we'll add clearer reminders in the main paper to the related supplementary material.\n\n\n\n------\n\n\n\n> **Q4: Will the Voxel Dropout design encourage larger and more redundant voxels?**\n\nThanks for your insightful question! According to the efficiency ablation results from the table in the response to Q1 and observations like Figure 10 in the supplementary material, **our Voxel Dropout will not cause evidently redundant or larger voxels to be produced and harm the reconstruction quality**. This robustness can be ensured from two aspects: **1)** In our representations, the size of the voxels is strictly controlled to be unidirectional, which can only become smaller by subdivision. Therefore, the Voxel Dropout can be safely applied without the risk of distorting the voxels to fit a larger space by becoming abnormally bigger in size. **2)** In the implementation, we have separated the gradient from Voxel Dropout from the accumulated gradient indicator for voxel subdivision. As a result, the incorrect voxels that suffer from large impacts will not unexpectedly divide into a set of redundant small voxels, ensuring the sparsity control of voxels stays controllable but not worsened by the enforced regularizations. We'll add these explanations of Voxel Dropout in the revised version to help the readers better understand our method."}, {"review_id": "6DFMCr05Yq", "reviewer": "Reviewer_dj1z", "summary": "This paper proposes a method for improving sparse voxel-based surface reconstruction. Building upon the existing work Sparse Voxels Rasterization (SVR), it introduces two key enhancements: (1) a voxel-uncertainty depth constraint to leverage monocular depth cues, and (2) a surface regularization module to improve geometric consistency. Experiments on various datasets demonstrate the effectiveness of these improvements.", "questions": "Please see Weakness.\n\nMy main concern is Table 4 indicates most improvement stems from Multi-view Regularization [7] and Patch-wise depth [27], casting doubt on the novelty of the other components.", "limitations": "Yes, no problems here.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths:\n* The work is well-motivated and builds naturally on recent developments in the community.\n* The proposed method is clearly positioned within existing literature, and experiments across multiple datasets demonstrate its effectiveness.\n\nWeakness:\n* The proposed method integrates five distinct loss components. While Table 4 provides quantitative ablation results, Figures 6 and 7 only visualize the effects of two main components. As a result, the qualitative impact of the remaining loss terms remains unclear. Including more targeted visualizations—particularly for the lesser-emphasized losses—would better illustrate their contribution and justify their inclusion. Additionally, Figure 7 does not clearly demonstrate improvements in surface sharpness.\n\n* According to Table 4, most performance gains are attributed to the Multi-view Regularization module (borrowed from [7]), which raises concerns about the novelty and technical contribution of the remaining components. A deeper analysis or improved visualization would strengthen the case for the proposed method’s overall contribution.\n\n* The proposed method introduces additional components that improve rendering quality, but it is reported to be roughly 10× slower than the baseline SVRaster. However, this significant runtime overhead is not clearly reflected in Table 4. I suggest including time comparisons in Table 4.", "was_revised": false, "final_justification": "", "rebuttal": "### **Responses to Reviewer dj1z**\n\nWe sincerely thank Reviewer dj1z for the time and effort in the constructive and encouraging review. We found the reviewer’s main concerns are related to how the contributions of various loss terms and runtime overhead. Here, we address the specific questions from the reviewer individually:\n\n------\n\n\n\n> **Q1: Reported visualized effects of only two components in Figures 6 and 7. It's better to provide more visualizations.**\n\nThanks for the constructive suggestion! In our submission, we visualized the ablation results for the three most insightful components in **Figures 6 and 7** of the main paper, and **Figures 9 and 10** of the supplementary material, along with detailed analysis in **Section A.1 and Section A.2**. We believe these visualizations can provide comprehensive support for justifying the effects of Voxel-Uncertainty Depth Constraint,  Voxel Dropout, and Surface Rectification.\n\n\nSpecifically, **1)** for the Voxel-Uncertainty Depth Constraint, Figure 6 in the main paper and Figure 9 in the supplementary material have shown an obvious improvement is brought in constraint the scene geometry; **2)** For the Voxel Dropout, due to the space limitation, we reported the visualization in the Figure 10 in the supplementary material and made analysis in the Section A.2; **3)** For the Surface Rectification, some visualizations were reported in the Figure 7, just as noticed by the reviewer. Especially, we'd like to briefly explain here that our Surface Rectification is designed for **pursuing the challenging target of extremely high-precision surfaces** reconstruction. It works mainly in the stages of an almost well-reconstructed geometry to certify the delicate and difficult details, and thus affects mainly in the details that is not as obvious in visualization as the other techniques that aims to reshape a coarsely correct geometry from a worse start, but this does not equals a lower importance, **especially considering the raising difficulty and criticalness in accuracy improvement the situation that the reconstruction results have already been very close to the ground truths**. \n\nWe agree with the reviewer that more visualization results would be beneficial to justify the inclusion of the components, and will add the visualized comparisons for the remaining Scaling Penalty technique in the revised version. Due to the official restriction of the rebuttal in forbidding images, we are sorry that the materials can not be presented immediately, but will be included along with the next chance of paper update.\n\n------\n\n\n\n> **Q2: Performance Gaining of Multi-view Regularization and Patch-wise Depth.**\n\n> - Explanation and analysis of the performance in the ablation study.\n\nThanks for your thoughtful feedback! We'd like to clarify that Multi-view Regularization and Patch-wise Depth **did not provide the key improvement in performance**. From the ablation study in Table 4, it's notable that although Multi-view Regularization and Patch-wise Depth work well, the improvements are based on a weak initial performance and have achieved an upper-bound of 0.538 in F1-Score, which is limited by the insufficient capacity to address the valuable problems our paper has revealed and aimed to solve. Notably, this score is only comparable to the previous SOTA method PGSR with depth prior added, **which has not shown the advancement that our GeoSVR achieved**. Based on this start, the results from settings of C, D, and E show that notable improvements have been brought by our proposed Voxel-Uncertainty Depth Constraint, Voxel Dropout, Surface Rectification, and Scaling Penalty, and achieve a remarkable 0.560 F1-Score. Combined with our reported visualization results, **the critical and irreplaceable effect of each component can be well justified.**\n\nBesides notable improvements have been achieved by our technical contributions, we'd like to discuss that **the progress made in different cases should be evaluated distinguishably, which correspond to different difficulties**, Especially, in the situation where GeoSVR exhibits its advancements, the scenes are already nearly well reconstructed, and the remaining problems are much more difficult and challenging to solve. In this case, **the progress we make is particularly critical and important, and is of great value for inspiring the pursuit of higher-precision reconstruction in the future.**\n\nWe'd like to note that Multi-view Regularization and Patch-wise depth are not the core contributions of our work, which has been clearly described in our paper. **These two classic and general techniques are adopted to provide a basic capability to support our advanced research, but do not act as the critical innovations of our work.** We express our sincere respect for these great prior works and reported their effects in the ablation study to ensure the transparency, but would like to emphasize that the patch-warping based multi-view consistency is a long-standing effective technique for accurate geometry learning that has been widely used in many previous works for over years [18, 44, 65, 16, 12, 7, 41, 8, 47], which has become a common and standard solution for the field; and we regard the patch-wise depth just as one of an under-investigated loss function in the field of surface reconstruction for our selected monocular depth constraint, which should be well introduced in the paper.\n\nAs recognized by the reviewers, **the contribution of GeoSVR mainly lies in the proposed Voxel-Uncertainty Depth Constraint, Voxel Dropout, Surface Rectification, and Scaling Penalty**. The Voxel-Uncertainty Depth Constraint, which is highly praised by the reviewers, is an insightful and sound way to maximize the effect of monocular depth cues while presenting a voxel-oriented uncertainty to avoid quality degradation. It innovatively analyzes the geometric uncertainty based on the voxel representation, enabling effective and robust scene constraints while preserving highly accurate geometries. Then, we systematically analyzed the problems in voxel-based surface formation, and targetedly proposed the Voxel Dropout, Surface Rectification, and Scaling Penalty in the aspect of multi-view geometry regularization and the bias in surface-voxel alignment. **Our investigation of high-quality sparse voxel-based surface reconstruction brings new understanding to the community.** With the thorough problem analysis and our insightful solution, GeoSVR is composed and demonstrates strong performance across various benchmarks. And besides the state-of-the-art performance achieved, **the revealed problems also bring fresh insights and could inspire more advancements to facilitate the development of the field.**\n\n\n------\n\n\n\n> **Q3: Runtime overhead of Table 4.**\n\n\n\n| Item Notation | Settings                                | # Voxels (Million) | Inference FPS | Training Peak GPU Mem (GB) | F1-Score | Training Time |\n| ------------- | --------------------------------------- | ------------------ | ------------- | -------------------------- | -------- | ------------- |\n| A.            | Base (SVRaster)                         | 9.3                | 132.9         | 12.3                       | 0.397    | 23.8 min      |\n| B.            | A. + Patch-wise Depth                   | 9.1                | 138.2         | 10.5                       | 0.449    | 24.2 min      |\n|               | B. + Multi-view Reg.                    | 9.1                | 138.7         | 11.4                       | 0.538    | 65.1 min      |\n| C.            | B. + Multi-view Reg. + Voxel Dropout    | 9.1                | 137.3         | 11.5                       | 0.546    | 68.3 min      |\n|               | C. + Surface Rectif.                    | 8.8                | 146.4         | 11.1                       | 0.549    | 64.4 min      |\n| D.            | C. + Surface Rectif. + Scaling Penalty  | 9.0                | 142.4         | 11.2                       | 0.552    | 67.3 min      |\n| E.            | D. + Voxel-Uncertainty Depth (**Ours**) | 8.8                | 142.0         | 11.2                       | 0.560    | 67.5 min      |\n\n\n\nThanks for the constructive suggestion! Here we provided the efficiency metrics of the ablation study Table 4. From the results, it can be observed that the multi-view regularization contributes most to the training time consumption increasing, while the other components **maintain high efficiency in all aspects, including the inference FPS, memory overheads, and the required number of voxels**. According to our analysis, this is mainly caused by the less efficient code implementation of the regularization, which we plan to solve in the future. The training time of the base SVRaster is a bit different from the official result in Table 1, which is caused by a slight hyperparameter adjustment to obtain an ideal reconstruction accuracy, which is consistent with the details we reported in lines 245-251 and is the same as the other ablation settings. We'll add the results in the revised version following the suggestion."}, {"review_id": "fo5f1dMVVz", "reviewer": "Reviewer_ZuxM", "summary": "This paper proposes GeoSVR, a method that explores accurate surface reconstruction by building upon Sparse Voxels Rasterization aka SVRaster (Sun et al, CVPR 2025). SVRaster is similar to 3D Gaussian Splatting but encodes colors and densities within a sparse voxel grid instead of anisotropic 3D Gaussians.\n\nGeoSVR improves SVRaster's surface reconstruction via separate regularizers, most notably a patch-wise depth/normal regularizer based on a pretrained monocular depth estimator (DepthAnythingV2). A challenge of this strategy is how to best handle inaccurate predictions from the depth estimator, which the paper suggests solving with downscaling the regularization loss with pixel-wise \"uncertainty\". The uncertainty score is calculated as a function of the voxel sizes used to volume-render the given pixel - the intuition is that since SVRaster progressively divides voxels at level l with large gradient to level l+1, voxels at lower levels are less constrained / should have higher uncertainty. GeoSVR also uses voxel dropout regularization to encourage a better global structure, a \"surface rectification\" term that encourages sharp boundaries between surfaces and empty spaces, and a scaling penalty that penalizes voxels occupying long sampling distances.\n\nGeoSVR is evaluated against commonly used implicit benchmarks (VolSDF, NeuS, etc), and explicit methods (2DGS, SVRaster, GOF, etc). On DTU, it generally outperforms baselines with regards to Chamfer distance and on Tanks and Temples with regards to F1 score. The results for appearance quality on MipNeRF 360 are more mixed (best PSNR on outdoor scenes, 0.5db worse on PSNR than 3DGS and >1db than Mip-NeRF 360 on indoor scenes) but generally competitive.", "questions": "I currently feel positive about the paper, and am happy to maintain/increase my rating if the authors can address my concerns about the evaluation section. The other outstanding question I have is what GeoSVR's rendering speed looks like compared to SVRaster and 3DGS.\n\nTypos:\n\nLine 72-73: \"An exploration GeoSVR to build explicit voxel-based framework for accurate surface reconstruction, taming sparse voxels to enable delicate and complete geometry learning.\"\nLine 187-188: \"To ensure adaptive and robust for various stages and scenarios, we obtain statistics of L to set the hyperparameters in Eq. (4).\"\nLine 235: \"renderng\" -> \"rendering\"", "limitations": "Right now the paper tangentially mentions \"conquering challenges like varying lights and textureless regions\" in the conclusion without explicitly calling out limitations of the current method. I recommend expanding upon this in an explicit limitations section along with a discussion of why appearance does not quite match existing SOTA in several cases.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "One of the core ideas behind this paper (using patch-wise depth downweighed by uncertainty) seems like a clear, easy-to-understand, and effective idea, and I like how simple it is to define \"uncertainty\" as a function of voxel size. Some of the other regularization terms (namely the \"Geometry Regularization with Voxel Dropout\") are less intuitive to me, but seem to help as shown in the ablation.\n\nThe evaluation section could be improved. The metrics in Tables 1 and 2 are different and would feel less \"cherry-picked\" if both Chamfer Distance and F1 Score were reported in both cases. The visual metrics (PSNR/SSIM/LPIPS) should also be reported for DTU and TnT as the takeaways from the MipNeRF 360 dataset are unclear. More discussion around the appearance reconstruction results (beyond merely stating that GeoSVR is \"competitive\") and why it performs worse on indoor scenes relative to 3DGS/M360 would strengthen the paper.\n\nAlso, as the paper emphasized how 3DGS methods are constrained by inaccuracy of SfM initialization, it would be worthwhile to compare to MCMC (\"3D Gaussian Splatting as Markov Chain Monte Carlo\", NeurIPS 2024) as a popular 3DGS variant that claims competitive results without initialization.", "was_revised": true, "final_justification": "Thank you for answering my questions. I remain positive about the paper and will maintain my accept rating.", "rebuttal": "### **Responses to Reviewer ZuxM**\n\nWe sincerely appreciate Reviewer ZuxM's time and efforts for the positive comments and thorough suggestions. We notice that the concerns mainly relate to the metrics selection across datasets, analysis about the rendering quality, comparison with the related approach, and the running overhead. Here, we address the questions raised by the reviewer individually:\n\n------\n\n> **Q1: Metric consistency across DTU, TnT and Mip-NeRF 360 datasets.**\n\n> - The selection of Chamfer Distance and F1-Score on DTU and TnT datasets.\n\nWe agree with the reviewer that adding more comprehensive and consistent metric evaluation across different datasets is extremely important for the community, but it may be particularly difficult to implement currently. In our work, we separately adopt F1-Score and Chamfer Distance for TnT and DTU datasets **following the standard settings in previous works with no manual selection** to produce fair and persuasive comparisons. We'd like to note that these two dataset-metric bindings are generally considered as **the prevailing standard settings for surface reconstruction currently**, which have been widely used and accepted by the famous works like VolSDF, NeuralWarp, NeuS, Neuralangelo, 2DGS and etc. for years. Especially, F1-Score is the officially specified metric for the TnT dataset equipped with an official evaluation toolkit; meanwhile, using Chamfer Distance to evaluate DTU datasets with the officially provided distance calculation process has also been a well-recognized tradition in the field of surface reconstruction.  Although a unified metric setting would be better, ideally, designing and implementing a fair, objective, and robust evaluation tool of a new metric for a specific dataset from scratch indeed requires a lot of effort and time, which may be out of the scope of this paper.\n\nWe fully understand the concern from the reviewer and sincerely appreciate the provided thoughtful suggestions. Currently, considering exhibiting strong performance in the most prevailing and well-accepted standard settings across the two mainstream and challenging datasets TnT and DTU, combined with the rendering quality evaluation on Mip-NeRF 360 and various reported visualization results, **we believe the contribution of our work can be well verified and recognized by the provided fair, comprehensive and objective supports in the paper.**\n\n> - Additional rendering performance on DTU and TnT datasets.\n\nThanks for your constructive suggestion and thorough consideration. We'd like to express that evaluating rendering performance on the TnT and DTU datasets with the surface reconstruction task is not common in the field, mainly because these reconstruction settings are different from the novel view synthesis task (like the one applied to Mip-NeRF 360 setting), of which **the formers use all the captured views as the inputs in the training to reconstruct a surface model for evaluation, therefore there's not an unseen test set of the RGB views left for a fair and objective evaluation**. Considering a potential value of justification, following the comments, we provide a comparison here that conducts the rendering quality evaluation on the training set. But we want to note that these results should be interpreted with caution because these data have not been isolated during the training. Therefore, they can not fairly and justly reflect the performance of each method. We sincerely recommend referring to the results in the Mip-NeRF 360 setting for a fair, objective, and persuasive comparison.\n\n\n *Table R1. Rendering Quality on DTU and TnT datasets. **(The evaluation can be only conducted on the training set as no test set is available, and should be interpreted with caution.)***\n\n| **Methods** | TnT||| DTU|||\n| ----- | ------ | ----- | ------ | ------ | ------ | ----- |\n|| PSNR $\\uparrow$ (Training Set) | LPIPS $\\downarrow$ (Training Set) | SSIM $\\uparrow$ (Training Set) | PSNR $\\uparrow$ (Training Set) | LPIPS $\\downarrow$ (Training Set) | SSIM $\\uparrow$ (Training Set) |\n| SVRaster    | 24.68| 0.149| 0.866| 35.13| 0.092| 0.955|\n| 2DGS| 25.26| 0.200| 0.850| 34.32| 0.168| 0.938|\n| PGSR| 24.57| 0.150| 0.872| 33.78| 0.152| 0.945|\n| GeoSVR| 23.49| 0.150| 0.853| 32.49| 0.103| 0.949|\n\n------\n\n> **Q2: Analysis on the novel view synthesis performance.**\n\nThanks for the constructive suggestion! While achieving the core target of high-quality surface reconstruction, the experiments of novel view synthesis in Mip-NeRF 360 datasets show that our method also maintains a strong capability in appearance reconstruction, striking a great balance between these two tasks. Typically, it's a common phenomenon that the rendering quality slightly drops when the model is forced to learn the accurate geometry (e.g., SuGaR, 2DGS, VCR-GauS, PGSR compared to 3DGS). This mainly lies in that the captured multi-view images from the real world do not always retain an ideal photometric multi-view consistency that matches the correct geometry, such as the reflective regions and transparent materials, especially the current radiance fields for surface reconstruction seldom consider complex ray tracing, but mostly only once forward. In that situation, **a distorted geometry in a local minimum may be better than the correct one to express an approximately accurate appearance.** Especially, in Mip-NeRF 360, these kinds of regions are **more common in the Indoor Scenes**, like the metal and glasses in Counter, a large reflective television screen in Room, etc. Therefore, our performance in the Indoor categorization is worse than that in Outdoor, and may also **perform lower rendering quality than the baseline methods with relatively less accuracy in geometry**. \n\nFollowing the suggestion, these discussions will be added in the revised version, and we'll explore achieving better consistency between the accurate geometry and challenging appearance cases in the future.\n\n------\n\n> **Q3: Comparison with 3DGS-MCMC.**\n\nFollowing the suggestion, we provide an additional comparison with 3DGS-MCMC here, where **GeoSVR still achieves SOTA performance, which further enhances the advancement and significance of our GeoSVR to explore and achieve high-quality surface reconstruction on the under-investigated representation**. 3DGS-MCMC makes important progress by reformulating 3DGS as MCMC sampling for optimization, improving the rendering quality and robustness of initialization for novel view synthesis. Considering it was not designed for surface reconstruction initially, we made the evaluation by applying it to the SOTA 3DGS baseline PGSR for fairness. As shown in Table R2, while 3DGS-MCMC relieves the reliance on initial SfM point clouds by enabling random initialization, our method still performs the best in the comparison. Due to the different focus of the tasks, some designs in 3DGS-MCMC, like the noise-driven SGLD, can bring significant improvements in appearance fitting, but may not quite match the goal of accurate surface formation currently.\n\n*Table R2. Comparisons with 3DGS-MCMC on TnT dataset. (\"SfM\" and \"Random\" denote the initialization type, and \"Depth\" indicates that Patch-wise Depth loss is adopted. We marked the changes of replacing the initialization from \"SfM\" to \"Random\".)*\n\n|| Barn| Caterpillar| Courthouse | Ignatius| Meetingroom| Truck|\n| ---- | ---- | ----- | ---- | ---- | ---- | ---- |\n| PGSR (SfM)| 0.655| 0.486| 0.238| 0.811| 0.319| 0.652|\n| 3DGS-MCMC + PGSR (SfM)| 0.633| 0.406| *Unconverged*| 0.802| 0.315| 0.632|\n| 3DGS-MCMC + PGSR (Random)| 0.633 (+0.000) | 0.392 (-0.014) | *Unconverged*| 0.802 (+0.000) | 0.326 (+0.011) | 0.625 (-0.007) |\n| 3DGS-MCMC + PGSR (SfM+Depth)| 0.666| 0.422| *Unconverged*| 0.745| 0.327| 0.633|\n| 3DGS-MCMC + PGSR (Random+Depth) | 0.655 (-0.011) | 0.397 (-0.025) | *Unconverged*| 0.767 (+0.022) | 0.324 (-0.003) | 0.600 (-0.033) |\n| **GeoSVR (Ours)**| **0.681**| **0.494**| **0.340**  | **0.826**| **0.368**| **0.655**|\n\n------\n\n> **Q4: Rendering speed comparison.**\n\nOur method **keeps a high efficiency in the rendering FPS, outperforming the 3DGS baselines in most cases**, and is even slightly faster than SVRaster in practice. In Section E of the supplementary material, we briefly discussed the rendering speed of GeoSVR and its relation to SVRaster. As analyzed, since our method does not introduce any burden during inference, its rendering speed is theoretically the same as SVRaster under the same number of voxels. Here we additionally compare our method with SVRaster and the 3DGS baselines on the three datasets in Table R3, and report the inference speed of our ablation study in Table R4. These results have shown the superior inference speed of GeoSVR compared to various baselines. And by forcing an accurate geometry to be learned, the voxels can be utilized more efficiently by removing distorted surfaces and artifacts, which further improves the advantage of GeoSVR in terms of efficiency.\n\n\n*Table R3. Comparisons on Inference FPS.*\n\n| Methods    | Mip-NeRF 360  | DTU| Tanks and Temples   |\n| ---- | :----: | :----: | :---: |\n| 2DGS| 25.8 | 114.9 | 88.6  |\n| GOF| 9.2  | 20.8  | 15.8  |\n| PGSR| 40.1 | 162.6 | 54.5  |\n| SVRaster   | 82.7 | 114.4 | 132.9 |\n| **GeoSVR** | 83.1 | 143.8 | 142.0 |\n\n\n*Table R4. Comparisons on Inference and Number of Voxels on TnT dataset.*\n\n| Items | Settings| # Voxels (Million) | Inference FPS |\n| ----- | ---- | ----- | ---- |\n| A.| Base (SVRaster)| 9.3| 132.9|\n| B.| A. + Patch-wise Depth| 9.1| 138.2|\n| C.| B. + Multi-view Reg. + Voxel Dropout| 9.1| 137.3|\n| D.| C. + Surface Rectif. + Scaling Penalty  | 9.0| 142.4|\n| E.| D. + Voxel-Uncertainty Depth (**Ours**) | 8.8| 142.0|\n\n------\n\n> **Q5: Writing problems.**\n\nThanks for your careful notice and pointing out the problems! We have fixed these errors and checked the paper thoroughly to ensure writing quality. The revisions will be included at the next opportunity to upload the paper."}]

Author rebuttal:

Meta-review: The final scores for this submission are 5/5/4/4. After the rebuttal period, all reviewers expressed a positive attitude toward the paper and acknowledged that the authors had addressed their main concerns. The main strengths of this work are its strong surface reconstruction performance and the simplicity and effectiveness of the proposed method. By carefully reviewing both the paper and the rebuttal, I recommend accepting this submission.
Decision: Accept (spotlight)