Path Matters: Unveiling Geometric Implicit Bias via Curvature-Aware Sparse View Optimization
Authors: Canran Xiao
Liaoyuan Fan
Yanbin Li
Jing Tang
Peilai Yu
Venue: ICLR 2026 Poster (2026)
Keywords: 3D Gaussian Splatting
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: 3D Gaussian Splatting (3DGS) has recently emerged as a powerful approach for novel view synthesis by reconstructing scenes as sets of Gaussian ellipsoids. Despite its success in scenarios with dense input images, 3DGS faces critical challenges in sparse view settings, often resulting in geometric inaccuracies, inconsistencies across views, and degraded rendering quality. In this paper, we uncover and address two key implicit biases of 3DGS reconstruction algorithm in sparse-view: (1) the model has a stronger demand for supervision signal toward regions of high curvature, and (2) the model is sensitive to the smoothness of the trajectory of the input views. To tackle these issues, we propose a novel framework that optimizes camera trajectories to maximize curvature coverage while enforcing smooth motion, and we further enhance the informativeness of data through a synthetic view generation process. Extensive experiments on Mip-NeRF 360, DTU, Blender, Tanks & Temples, and LLFF datasets show that our method substantially outperforms state-of-the-art solutions in sparse-view scenarios, both in rendering quality and geometric fidelity. Beyond these empirical gains, our investigation uncovers the subtle ways in which data representation and trajectory planning interact to shape 3DGS performance, offering deeper theoretical insights into the algorithm’s inherent biases.

Published as a conference paper ICLR 2026
PATH MATTERS: UNVEILING GEOMETRIC IMPLICIT BIAS
VIA CURVATURE-AWARE SPARSE VIEW OPTIMIZATION
Canran Xiao t+ Liaoyuan Fan Yanbin Li Jing Tang', Peilai Yu
Shenzhen Campus of Sun Yat-sen University, UUniversity of Hong Kong
BBijjnng University of Post and Telecommunications, "Huazhong University of Science and Technology
"I Ludwig Maximilian University of Munich xiaocr 1 1. sysu. .du.cn
ABSTRACT
3D Gaussian Splatting (3DGS) has recently emerged as powerful approach for novel view synthesis by reconstructing scenes sets of Gaussian ellipsoids. Despite its suc- cess in scenarios with dense input images, 3DGS faces critical challenges in sparse view settings, often resulting geometric inaccuracies, inconsistencies across views, and de- graded rendering quality. In this paper, we uncover and address two key implicit biases of 3DGS reconstruction algorithm sparse-view (1) the model has a stronger demand for supervision signal toward regions of high curvature, and (2) the model is sensitive to the smoothness of the trajectory of the input views. To tackle these issues, we propose a novel framework that optimizes camera trajectories maximize curvature coverage while enforcing smooth motion, and we further enhance the informativeness of data through synthetic view generation process. Extensive experiments Mip-NeRF 360, DTU, Blender, Tanks & Temples, and LLFF datasets show that our method substantially out- performs state-of-the-ar solutions in sparse-vien scenarios, both in rendering quality and geometric fidelity. Beyond these empirical gains, our investigation uncovers the subtle ways in which data representation and trajectory planning interact to shape 3DGS perfor- mance, offering deeper theoretical insights into the algorithm's 's inherent biases.
INTRODUCTION
In recent years, 3D Gaussian Splatting (3DGS) (Kerbl et al.
2023 Chen & Wang 2024 Fei et al. 2024) has
emerged as powerful approach for novel view synthesis, leveraging Gaussian ellipsoids to model scenes more flexibly than traditional representations (Zhang et al. (023). 3DGS has broad application prospects fields such as autonomous driving, embodied intelligence, and world models (Xiao al. 2025 Ni et al..
2025
Zhao et al. 2025 Wang et al. 2025a b. Zhhng et al. 2024b).
The efficiency of 3DGS approximating complex geometries and lighting scenarios makes it particularly appealing for niel rendering tasks in VR and AR (Zhai et al. (024)) as well as film production (Peng ltt al. 2024a| Zhang et al. [202cc] 2026). However, a common challenge in applying 3DGS in the real world is the sparse- View scenario, where collecting dense viewpoint data is noisy, impractical or impossible (Feng 2024 Ni et al. (025). Enhancing the performance 3DGS with a few input images offers compelling direction for improving the capabilities of 3DGS.
et al. 2022 Lu et al.
*Corresponding author
These authors contributed equally this work

---

Published as a conference paper at ICLR 2026
However, 3DGS in such sparse-view scenarios presents deeper challenges beyond reliance on dense sam- pling (Cheng et al., 2024). A key issue is the algorithm's s sensitivity to input data distribution and qual- ity, which can severely degrade performance when data is limited or unevenly sampled (Yao et al. [024] Liu et al. (025). This often manifests in geometric inaccuracies, inconsistencies across views, and errors in spatial and photometric appreentationn-lmiaaaiin servations. To mitigate these issues, some methods have been proposed that enhance supervision during training. These approaches primarily use multi-view consistency to create pscudo labels for unseen rays by re-projection (Zhang et al.) 2022, Pan al. 2023 Zhang et al. 2024a) warping (Xu et al. 2022 Chen et al. 2025 Zhang et al.J 2025a) 3D points to unseen viewpoints. While these techniques offer improve-
that become especially pronounced with sparse ob-
ments, they do not fully address the underlying weaknesses of 3DGS in handling sparse and suboptimal data
distributions, particularly the inherent constraints and biases that lie in the algorithm that arise due to the complex interplay between data distribution and scene representation.
Data collection trajectory
Corrected sampling trajectory
views synthetic views
49 views
views
Figure 1: We focus on the problem of 3D reconstruction from sparse views using 3D Gaussian Splat- ting(3DGS). Our work identifies that sparse view 3DGS is prone to geometric inaccuracies, decreased geo- metric consistency, and inaccuracies in spatial and photometric properties. This study proposes a framework that enhances the performance of 3DGS in sparse view scenarios, achieving state-of-the-art results.
Although often subtle (Li et al., 2024 Yao al. 2023), these biases could undermine reconstruction qual- ity when data is limited or unevenly sampled. The interplay between how the scene representations are reconstructed and how viewpoints are arranged remains underexplored. Furthermore, recognizing and miti- gating these geometric implicit biases and further reducing these biases to improve the overall reconstruction performance by adapting the learning process is promising direction in sparse-view -iew reconstruction.
We tackle the above challenges by introducing novel framework that significantly boosts 3DGS perfor- mance in sparse data environments by optimizing the camera trajectory of pseudo labels. Specifically, we reveal how factors like the coverage of scene surface from the synthetic viewpoints and the smoothness of synthetic viewpoints sampling trajectory collectively affect the reconstruction quality under limited obser- vations, and further design strategies, including an optimized path planning method and a synthetic view generation procedure, to mitigate their effects. Beyond simply improving empirical results, our work pro- vides theoretical understanding of how method reduces the subtle biases underlying 3DGS.
The key contributions of this paper are as follows: (i) We are the first to identify and analyze the inductive biases inherent in Sparse View 3DGS, revealing how biases related geometric detail prioritization and trajectory smoothness impact the quality of 3D reconstruction from sparse datasets. (ii) We propose an op- timized camera trajectory framework that maximizes surface curvature coverage while maintaining smooth-
2

---

Published as a conference paper ICLR 2026
ness, thereby improving the accuracy and consistency of scene reconstruction in sparse view scenarios. (iii) We demonstrate the superiority of our approach through extensive evaluations on benchmark datasets, where our method consistently outperforms existing techniques, achieving significant improvements in rendering quality and geometric fidelity.
2 RELATED WORK
3D Gaussian Splatting. 3D Gaussian Splatting (3DGS) rasterizes anisotropic 3D Gaussians directly onto 2D screen via a splatting-centric approach (Zwicker et al. 2002), determining pixel colors through depth sorting and alpha blending instead of expensive ray marching. Despite its near-instant rendering, 3DGS sensitive to sampling rates; changes in zoom or viewing distance can introduce distortions, mitigated by low-pass filtering (Yu et al. 2023) or multi-level Gaussians (Yan et al. (023).. Moreover, 3DGS often inflates Gaussians beyond true scene geometry, increasing both redundancy and memory usage. Certain approaches manage the impact of Gaussians on the rendering outcome by assessing their size (Lee et al., (023) or their detectability across different viewpoints (Fan et al., 2023). leading the elimination of less impactful Gaussians. Alternative strategies minimize the memory footprint of Gaussian parameters through a quantization approach (Navaneet et al.] (2023) or by deducing Gaussian attributes from the attributes of a structured lattice (Morgenstern et al. 2023; Lu et al. 2023). Some other works focus broader aspects of 3DGS models, such as the uncertainty estimation (Li & Cheung 2002).. active learning (Lee et al.! 2022), or
the copyright protection (Huang al. 2024
Sparse View Rendering. Synthesizing novel views from sparse images is a significant challenge, as conventional techniques often require an impractically high number of views. Early strategies (Tucker & Snavely 2020; Zhou et al., 2018) (Srinivasan et al. 2019) utilize multi-plane images (MPls) for depth- based re-rendering. Recent methods leverage the NeRF framework, broadly categorized into ap- proaches. The first, exemplified by DietNeRF (Jain et al. (02T), enforces semantic consistency across views. RegNeRF (Niemeyer al. (2022) and ViP-NeRF (Somraj & Soundararajan, 2023) focus on color, depth consistency, and visibility across views. The second approach integrates depth priors, as seen in SparseNeRF (Wang et al. (023). which uses pre-trained depth estimation for depth regularization, and DSNeRF (Deng et al. (022)). which relies on SfM-derived camera poses for depth guidance. Additionally, Neo 360 (Irshad et 2023) adopts a tri-plane feature representation enhance 3D feature understanding.
3 GEOMETRIC IMPLICIT BIASES IN SPARSE VIEW 3D GAUSSIAN SPLATTING
In training 3DGS model, the distribution of training cameras would influence the model fitting, with the abrupt trajectories causing uneven sampling and increased reconstruction errors. This underscores the need investigate how trajectory smoothness affects training outcomes, motivating our exploratory work.
3.1 EXPLORATORY EXPERIMENTAL SETUP
order to uncover potential inductive biases the 3DGS process, we designed a series of experiments focusing on different sampling strategies and camera trajectory configurations. The experiments aim to evaluate how these factors influence the quality of 3D reconstruction under sparse view conditions. We conducted experiments using a subset of 9 images selected from a total of 106 available images in the Blender (Mildenhall et al. 2021) dataset's LEGO excavator scene. These images were chosen to capture diverse angles and perspectives of the scene, ensuring that key geometric features were represented despite the sparsity of the views. The selected images were used to train the 3DGS model under various conditions, including different image sequences and trajectory paths.
3

---

Published as a conference paper ICLR 2026
Metric
Green
Red
Blue
Orange
Erec (MSE)
0.02
0.08
0.07
0.10
Sae (SSIM)
0.95
0.85
0.88
0.82
Cvioe
0.94
0.81
0.78
0.74
Suaj
0.98
0.65
PSNR (dB)
24.22
20.15
21.78
19.63
Figure 2: The results of novel view synthesis across different trajectories. The smooth green trajectory yields the best overall reconstruction quality. The red trajectory exhibits geometric inaccuracies, with loss of details in complex or occluded structures. The blue trajectory suffers from decreased geometric consistency across views, leading to poor reconstruction. The orange trajectory displays inaccurate reconstruction, highlighting challenges in sparse view reconstruction without bias correction mechanisms.
3.2 OBSERVATIONS
The experimental results in Figure the impact of camera trajectory Sparse View 3DGS reconstruc- tion. The red trajectory, with sharp twists and low smoothness, resulted in high error. The blue trajectory, with uneven height variations, led moderate performance. The orange trajectory, with distortions and noise, showed the worst reconstruction. In contrast, the green trajectory, with smooth motion, achieved the best new view quality. The analysis of the experimental results presented in Figure indicates the following key observations:
Geometric Detail Prioritization Bias the model by reducing the reconstruction errors in these geometrically complex areas. This is evidenced by the higher reconstruction error for the red trajectory than the blue trajectory, where the sampling was less focused on these critical regions (Zhang et al., 20256). The corresponding poor reconstruction of surface details reconstructed by the red trajectory further validates this bias. This demonstrate that appropriately dense sampling in high curvature areas significantly improves reconstruction quality.
Dense sampling object regions of high curvature would benefit
Trajectory Smoothness Bias Smooth camera trajectories contribute to improved reconstruction stability by minimizing geometric inconsistencies caused by abrupt changes in camera position. This is supported by the fact that minimizing the second derivative of the trajectory would influence the reconstruction quality. The green trajectory, with the highest smoothness score, achieved the best overall reconstruction perfor- mance. In contrast, the orange trajectory, with the lowest smoothness, resulted in the poorest new view quality. These findings confirm that smoother trajectories reduce the impact of noise and irregularities on the reconstruction, leading to higher fidelity.
4 A FRAMEWORK FOR SPARSE VIEW 3D GAUSSIAN SPLATTING
In this section, we describe our proposed framework, which addresses the challenges of 3DGS in sparse view settings by optimizing the camera trajectory and constructing synthetic views to enhance scene recon- struction accuracy. Shown in Figure 3, our method consists of two major components: (1) Optimal Camera Trajectory Generation and (2) Synthetic Camera View Construction.
4

---

Published as conference paper ICLR 2026
Synthetic
Camera View Construction
Optinal Trajectery
Lamor
Symtert
Outaki
views
Vanilla 3DGS
poses
Camera poses
Operation
Figure 3: Overview of our Sparse View 3D Gaussian Splatting (3DGS) pipeline. The process starts with sparse camera poses used to generate an optimized camera trajectory, maximizing curvature coverage and ensuring smoothness. Synthetic views are then constructed along this trajectory, enhancing data density. These refined inputs are then processed by the 3DGS framework to reconstruct the final 3D scene.
4.1 OPTIMAL CAMERA TRAJECTORY GENERATION
The goal of our camera trajectory optimization is to maximize the coverage of surface curvature in the scene while ensuring the trajectory's smoothness. Given sparse sequence of images {(V, T,, 4)) where V; represents the camera position of the i-th image. 1 is the corresponding image, and t, is the timestamp, we can construct an initial camera trajectory. This trajectory (t(() is defined the piecewise linear path connecting the camera positions in the sequence.
N -
(o())
= Σ 1=1
P.
t++
+ Pi+1
t
4++1 44
1 4
where P, represents the camera position 4, To allow for flexible optimization, the initial trajec- tory (o()) is parameterized using B-spline curve. This spline is defined by a set control points Q (Q1, Q...... Qm) and knot vector {to, fo......... }m where the control points initialized based on the original camera positions! P..
The B-spline trajectory 7() is given by:
(()) Σ N2(1)
(2)
where (t) are the B-spline basis functions.
Curvature and Geometric Feature Calculation To optimize the trajectory for capturing important geo- metric features, we compute the surface curvature at various points on the object's surface. Let x represent a point the surface, and n(x) be the normal vector at that point.
The principal curvatures Hi (x) and (2(x) at x are the maximum and minimum curvatures obtained by projecting the surface onto planes that include n(x). The mean curvature H(x) and Gaussian curvature
5

---

Published as conference paper ICLR 2026
K (x) are then defined
H()) xI(x) =2()))
2
For the trajectory optimization, focus mean curvature (x) it effectively captures regions with significant geometric features such as edges and corners. We then define the curvature at a point on the trajectory (t) =(r(t)) (x(()))))) where x(>(t)) is the point on the object's surface corresponding to the trajectory point (t).
Optimization Problem Formulation The optimization problem is then defined to improve this initial trajectory by maximizing the curvature coverage x((((t) while adhering smoothness constraint. The optimization variables are the positions of the control points Qj. The optimization problem is formulated
as:
L ((((())))(()))
Maximize Q
Subject to:
J. IN
11 S;
(1:)) = V, for i 1,2,
(5)
[n(())] 2 Umia for all E [ti,ta]
x()(t)) 2 Kiiin for specific regions
L. AN (1h((I)l (16( de 8
where w(y(t)) = a x(x)((())))------- B is the curvature- ourvature-eeighted function based the computed mean curvature k(r(t)), [t)] represents the speed along the trajectory, and e a smoothness threshold. The constraint ((4) = V ensures that the optimized trajectory passes through the original camera positions. Additionally, Umin enforces a minimum camera speed to prevent the trajectory from stagnating, 6minn imposes a minimum curvature constraint in regions of high geometric complexity enhance sampling, and limits the deviation from the initial trajectory (t), ensuring that the optimized path remains reasonably close to the original.
4.2 SYNTHETIC CAMERA VIEW CONSTRUCTION
Sampling along the optimized path. Given the optimized trajectory (t),), we sample M timestamps {4))/1 by arc-length parametrization to ensure approximately uniform baselines. Each synthetic camera pose is
= K,), 7)))"(t)) R₁ SLERP (R.,, Rs; A5);
where (R., Rs) are the two neighboring real orientations bracketing ty and Aj E [0, is the normalized interpolation weight. Unless stated otherwise, Kj is inherited from the temporally nearest real view.
For warping-based synthesis we require per-pixel depth map for each real source view I;- We obtain and refine these depths in two stages, please refer for details.
View Synthesis via Parallax-Basss Interpolation For each real source (I,, Vi) with refined depth D we warp pixels to the synthetic view V/", Let ú; [uu, 0e, 1]T and K; be the intrinsics. The 3D point in camera-i coordinates is
x; (u, D,(u;) K, uu
6

---

Published as a conference paper ICLR 2026
Transforming to camera-j and projecting:
xj= R,y x, tij.
ú ,,, u, = I 2gy 2u,) [x,
(8)
where (Ryj, tiy) is the relative pose and II denotes homogeneous normalization. We obtain the color (u;)) by sampling 1, at the pre-image of u, with bicubic interpolation.
The final synthetic image is depth- and visibility-weighte blend of all warped sources:
(u) = Ei=wing why (u) (u) En wir(m)
(u) = Mi)( e Aa [u)( max (0, (Vs, Vz)):
(9)
where v,, Vj are view directions and My z-buffer visibility mask computed with small tolerance suppress ghosting. Small holes after blending are filled by edge-aware, depth-guided inpainting.
5 EXPERIMENTAL RESULTS
5.1 EXPERIMENTAL SETUP
Dataset. We evaluate our method on the DTU dataset (Jensen et al. 2014), which contain various mate- rials, textures, and complex geometry shapes. Originally, each scene contains 49 or 64 images. We also reconstruct all scenes from the Blender dataset (Mildenhall et al.] 202T) using our method. Each scene the Blender dataset contains 100 training images, and scenes generated from physical- rendering engine and include effects such as reflections. Moreover, we also evaluate our method on the Mip-NeRF 360 dataset (Barron et al., 2022), which is composed of nine distinct scenes, with five outdoors and four in- doors. We also evaluate our method on the LLFF (Mildenhall et al. (019) and Tanks & Temples (Knapitschi 2017) dataset.
Implementation Details. Our implementation extends the 3D Gaussian Splatting (3DGS) frame- work (Kerbi et al. (023) with enhancements tailored for sparse view challenges. We parameterize the initial camera trajectory with B-spline curves, optimized via L-BFGS (Berahas et al. 2016) to maximize surface curvature coverage and maintain smoothness while adhering to the original path. Gaussian param- eters {p, c, at were estimated directly from sparse views. Optimization used the Adam optimizer with a learning rate of 10-4, training for 150k iterations with a batch size of 2048 on NVIDIA A100 GPUs.
Number of Images. This paper analyzes how reconstruction quality changes with varying image counts, particularly in low-image scenarios. Unlike prior studies that used a fixed number of images per scene, we employ proportional approach, introducing the ratio to represent the fraction of images used relative to the total dataset. The dataset is split, with 70% for training and 30% for testing. Subsets with a set at 20%. 30%, and 40% are used for image rendering and surface reconstruction assessments. For the Mip-NeRF 360 dataset, we utilize 12 views for each scene.
5.2 EXPERIMENTAL RESULTS
5.2.1
QUANTITATIVE PERFORMANCE
As shown Tables T and 2 and further validated by our Blender dataset results, our method consistently out- performs state-of -ttehhhertt approaches across datasets and training ratios. On DTU with 0.4, it achieves the highest PSNR (27.89) and lowest Chamfer Distance (CD) (3.01), demonstrating superior image qual- ity and mesh accuracy. Even with fewer training images, it remains competitive, outperforming SparseGS, Dngaussian, and MatSparse3D, especially on complex geometries. On Mip-NeRF 360, our method leads with PSNR of 27.05 and the lowest LPIPS (0.4209), ensuring high-fidelity synthesis with strong perceptual
7

---

Published as conference paper ICLR 2026
Table Quantitative comparison on Mip-NeRF 360 (12 views) and Tanks Temples (3 views).
Model
Venue
Mip-NeRF 360 (12 views)
Tanks & Temples (3 views)
PSNR
SSIM
LPIPS
PSNR
SSIM
LPIPS
NeuS (Wag et
2021
NeurlPS'21
18.75
0.50
20.10
0.64
0.34
NeuralAngelo La 2023
CVPR'23
18.52
0.48
0.47
20.50
0.66
0.33
3DGS Kerbl
SIGGRAPII
15.14
0.40
0.56
17.90
0.55
0,40
Sparse(TS Xiong
2023
arXiv'23
15.93
0.42
0.46
22.00
0.72
0.30
DNGaussian
2024
CVPR'24 24
15.66
0.41
0.48
20.80
0.67
0.33
MatSparse Maa el al. 2024
CVPR'2 24
15.95
0.41
0.47
21.30
0.69
0.31
InstantSplat (Fan F 2024
arXiv'24
17.90
0.46
0.48
22.10
0.73
0.29
SuGar (Guédnn &
Lepetti & 2124
CVPR'S
19.02
0.51
0.46
22.70
0.75
0.27
VCR-GauS (Chen
20/44
NeurIPS"24
19.21
0.51
22.90
0.76
0.25
PGSR (Chen
20/40
TVCG'24
19.17
0.51
23.00
0.25
SCGaussian [Peng
2024b
NeurlPS'24
19.70
0.55
0.43
22.17
0.75
0.26
MVPGS (Xu al. X124
FCCV"24
19.85
0.55
0.44
25.57
0.85
0.14
NexusGS (Zhngg ct. 2025
CVPR'25
19.40
0.54
0.43
25.20
0.84
0.15
3DGS Ours
19.95
0.56
0.42
26.41
0.86
0.14
SCGaussian Ours
20.05
0.56
0.41
23.02
0.77
0.24
MVPGS Ours
20.15
0.56
0.42
26.10
0.86
0.13
Table Quantitative comparison on DTU with different training ratios a (Used/All). Lower better for CD and LPIPS. LPIPS is computed with the standard VGG-based LPIPS.
Model
PSNR
CD
LPIPS
PSNR
CD
LPIPS
PSNR
CD
LPIPS
NeuS (Wang
2021
23.72
4.50
0.31
24.55
3.98
0.28
25.49
3.67
0.26
NeurafAngelo L. at. 202.3
24.10
4,30
0.30
25.12
3.80
0.27
26.20
3.50
0.25
3DGS Kerbl six 2025
22.14
5.64
0.37
23.31
0.33
24.64
3.29
SparseGS Xlong
25.23
4.42
0.26
26.19
3.45
0.23
26.56
3.71
0.24
DNClussian [T
4024
24.61
4.12
0.28
24.89
4.36
0.29
25.33
3.99
0.27
MatSpurse3D MMao al
2024
25.75
5.49
0.27
25.86
4.64
0.25
25.99
4.23
0.24
InstaniSplat (Fan
0.32
24.23
SuGar (Gúédon & Lepelit 2024
24.80
4.20
0.27
25.48
3.60
0.24
26.55
3,44
0.23
VCR-GauS (Chen cl 2024b
25.02
4.18
0.26
25.90
3.50
0.24
26.70
3.40
0.22
(Chen 2074h]
3.42
NexusGS (Zning 2025
26.10
3.65
0.22
26.65
3.28
0.21
27.10
3.18
0.20
Ours
27.05
3.49
0.21
27.38
3.07
0.19
27.89
3.01
0.18
Furthermore, we demonstrate the model-agnostic nature of our approach by integrating with ex- isting frameworks. As detailed in Table combining our method with MVPGS and SCGaussian (denoted as MVPGS + Ours and SCGaussian + Ours) yields consistent performance gains (e.g., boosting SCGaussian by 0.85 dB on Tanks & Temples), verifying that curvature-awan optimization and synthetic densification strategy can serve as a plug-and-pla. module to enhance various Gaussian splatting backbones.
accuracy.
We further conduct experiments with only 3 input views the DTU and LLFF datasets. comparing method with recent advanced approaches. As shown in Table our method achieves notable performance both datasets with extremely sparse viewpoints. Specifically, for DTU (3 views), method attains the highest PSNR (20.65) and SSIM (0.891) among all baselines, demonstrating robustness in reconstructing detailed geometry from limited inputs. On the LLFF dataset views), our method also achieves the highest PSNR of 20.93.
5.2.2 QUALITATIVE PERFORMANCE
Fig. 4 shows qualitative comparisons on the real-world Mip-NeRF 360 scenes Bicycle and Bonsai. Across all viewpoints, our method produces renderings that are perceptually closer to the ground truth than MAtCha
8

---

Published as conference paper ICLR 2026
GT
Bicycle
Ours
MAtCha Gaussians
GT
Bomsal
Bonaa
Ours
MAtCha Gaussians
Figure The visualization results on the MipNeRF 360 dataset. We visualize the reconstruction results on testing views with 12 total views.
Gaussians (Guédon et al. 2025). In the Bicycle scene, our reconstruction better preserves thin structures such the wheel spokes and the slats of the bench, while maintaining a sharper grass gravel boundary and more faithful foliage textures. MAICha Gaussians exhibits noticeable blurring and mild color shifts in these high- frequency regions. In the Bonsai scene, our method more accurately reproduces textured tablecloth, and matches the global exposure of the room and background objects, whereas MAtCha Gaussians tends to under-cxpose the scene and oversmooth small structures. These visual results indicate that our approach yields Mip-NeRF 360 scenes, especially for high-frequency details and challenging real-world backgrounds. More qualitative results can refer to appendix D
fine floral details and the
accurate geometry and appearance reconstruction complex, baseline
9

---

Published as conference paper ICLR 2026
Table 3: Three-vien comparison on DTU and LLFF.
DTU (3 views)
LLFF (3 views)
Method
Venue
PSNR
SSIM t
LPIPS
PSNR
SSIM
LPIPS
SparseNeRF Wang et al., 2023
CVPR 23
19.55
0.77
0.20
19.86
0.62
0.33
SPARF Truong al. 5205
CVPR
17.75
0.68
0.33
20.20
0.63
MVPGS et 2024
ECCV'24
20.54
0.88
SCGaussian [Peng
2024b
NeurIPS'24 24
20.56
0.86
0.12
20.77
0.71
0.22
NexusGiS Zheng et
CVPR 25
20.40
0.88
0.26
20.80
0.77
0.24
MA1Cha Gausstans Guedon et 2025
CVPR 25
20.52
0.86
0.27
20.74
0.75
0.24
DIFIX3D+ (Wu 2025
CVPR 25
20.60
0.87
0.26
20.91
0.76
0.25
Ours
20.65
0.89
0.24
20.93
0.78
0.23
5.2.3 ABLATION STUDY
We conducted an ablation study on DTU to assess each component's impact (Table 4ap. Removing key elements significantly degrades 3D reconstruction under sparse views. Omitting Optimal Camera Trajectory Generation drops PSNR from 27.05 to 24.20 (20% training ratio) and increases CD, highlighting the need for curvature coverage and smoothness. Excluding Synthetic View Construction further reduces PSNR and raises CD, especially at higher training ratios. Removing the Trajectory Smoothness Constraint lowers PSNR to 26.84. Most critically, without Occlusion Handling, PSNR drops by 2.5 and CD increases by 0.5, underscoring its importance. Visual results are in the supplementary material.
5.2.4 EFFICIENCY ANALYSIS
We evaluate efficiency on indoor/outdoor scenes (Table 4b). Compared to MVS-initializeed 3DGS, our method improves rendering quality with minimal training overhead. Outdoors, we refine sparse Gaussians, gaining +2.11 PSNR while keeping real-time FPS. Indoors, our compact distribution captures details with- out noise, reaching 35.44 PSNR 75 minutes faster than 3DGS at similar FPS. This balances fidelity and efficiency.
Table 4: Results of Ablation Experiments and Efficiency Analysis (b) Efficiency Analysis
(a) An ablation study on the DTU dataset shows the per- formance of our framework with various components re- moved
Scene
Strategy
PSNR
Ganssians
Training Time
FPS
Outdoor
3DGS Init)
640k
Toein (Ale
0.3
3DGS (MVS Init)
35.74
1612k
245 min
70
Mrttes
PSNI
CD
15N8
CT)
PSNR
(3)
Ours (SfM
37.23
980k
50 min
110
Outimal Trajestor Genetation
3DGS Init)
1505k
25.01
3DGS (MVS Init)
33.65
1775k
265 min
85
wis Oxzieein Rendling
Tryystor Smowhhree Comuiin Conamint
36.38
34.94
1.30
1.46
36.12
1.64
3.51
35:06
26.81
563
3.5
Ours (SfM
1402k
75
Ous
27.05
3.49
27.38
3.07
27.39
301
6 CONCLUSION
This paper is the first to reveal inductive biases in Sparse View 3D Gaussian Splatting (3DGS), identifying key biases in geometric detail prioritization and trajectory smoothness that affect 3D reconstruction from sparse data. We propose novel framework integrating optimal camera trajectory generation and synthetic camera view construction, improving accuracy by maximizing curvature coverage and ensuring smooth paths. Experiments four datasets show significant gains.
This work adheres to the ICLR Code of Ethics. Our study does NOT involve human subjects, personally identifiable information, sensitive attributes.
Ethics Statement
10

---

Published as conference paper ICLR 2026
REFERENCES
Jonathan T. Barron, Ben Mildenhall, Dor Verbin, Pratul P. Srinivasan, and Peter Hedman. Mip-nerf 360: Unbounded anti-aliased neural radiance fields. CVPR, 2022.
Albert Berahas, Jorge Nocedal, and Martin Takác. A multi-batch I-bfgs method for machine learning. Advances in Neural Information Processing Systems, 29, 2016.
Danpeng Chen, Hai Li, Weicai Ye, Yifan Wang. Weijian Xie, Shangjin Zhai, Nan Wang, Haomin Liu, Hujun Bao, and Guofeng Zhang. Pgsr: Planar-based gaussian splatting for efficient and high-fidelity surface reconstruction. IEEE Transactions on Visualization and Computer Graphics, 2024a.
Guikun Chen and Wenguan Wang. A survey on 3d gaussian splatting. arXiv preprint arXiv:2401.03890, 2024.
Hanlin Chen, Fangyin Wei, Chen Li, Tianxin Huang, Yunsong Wang, and Gim Hee Lee. Ver-gaus: View consistent depth-normal regularizer for gaussian surface reconstruction. Advances in Neural Information Processing Systems, 37:139725-13978 2024b.
Zhangquan Chen, Puhua Jiang, and Ruqi Huang. Dv-matcher: Deformation-based non-rigid point cloud matching guided by pre-trained visual features. In Proceedings of the Computer Vision and Pattern Recog- nition Conference, pp. 27264-27274, 2025.
Kai Cheng, Xiaoxiao Long, Kaizhi Yang, Yao Yao, Wei Yin, Yuexin Ma, Wenping Wang, and Xuejin Chen. Gaussianpro: 3d gaussian splatting with progressive propagation. In Forty-first International Conference on Machine Learning. 2024.
Kangle Deng. Andrew Liu, Jun Yan Zhu, and Deva Ramanan. Depth-supervised NeRF: Fewer views and faster training for free. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), June 2022.
Zhiwen Fan, Kevin Wang, Kairun Wen, Zehao Zhu, Dejia Xu, and Zhangyang Wang. Lightgaussian: Un- bounded 3d gaussian compression with 15x reduction and 200+ fps. arXiv preprint arXiv:2311.17245, 2023.
Zhiwen Fan, Wenyan Cong, Kairun Wen, Kevin Wang. Jian Zhang, Xinghao Ding, Danfei Xu, Boris Ivanovic, Marco Pavone, Georgios Pavlakos, et al. Instantsplat: Unbounded sparse-view pose-free gaus- sian splatting in 40 seconds. arXiv preprint arXiv:2403. 20309, 2(3):4, 2024.
Ben Fei, Jingyi Xu, Rui Zhang, Qingyuan Zhou, Weidong Yang, and Ying He. 3d gaussian splatting as new era: survey, IEEE Transactions on Visualization and Computer Graphics, 2024.
Chen Feng, Georgios Tzimiropoulos, and Ioannis Patras. SSR: An Efficient and Robust Framework for Learning with Unknown Label Noise. In 33rd British Machine Vision Conference (BMVC), 2022.
URL. htt.pp://bb.c////tttttttt httpv//w2222222 mpm-mpiiii inf www.pp....... 372/
Antoine Guédon and Vincent Lepetit. Sugar: Surface-aligned gaussian splatting for efficient 3d mesh re- construction and high-quality mesh rendering. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition, pp. 5354-5363, 2024.
Antoine Guédon, Tomoki Ichikawa, Kohei Yamashita, and Ko Nishino. Matcha gaussians: Atlas of charts for high-quality geometry and photorealism from sparse views. In Proceedings of the Computer Vision and Pattern Recognition Conference, pp. 6001-6011, 2025.
11

---

Published as a conference paper at ICLR 2026
Xiufeng Huang, Ruiqi Li, Yiu-ming Cheung, Ka Chun Cheung, Simon See, and Renjie Wan. Gaussian- marker: Uncertainty-awant copyright protection of 3d gaussian splatting. Advances in Neural Information Processing Systems, 0-:33037-33066 2024.
Muhammad Zubair Irshad, Sergey Zakharov, Katherine Liu, Vitor Guizilini, Thomas Kollar, Adrien Gaidon, Zsolt Kira, and Rares Ambrus. Neo 360: Neural fields for sparse view synthesis of outdoor scenes. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 9187-9198, 2023.
Ajay Jain, Matthew Tancik, and Pieter Abbeel. Putting nerf on a diet: Semantically consistent few-shot view synthesis. In Proceedings of the IEEF/CVF International Conference Computer Vision (ICCV), pp. 5885-5894, October 2021.
Rasmus Jensen, Anders Dahl, George Vogiatzis, Engil Tola, and Henrik Aanæs. Large scale mueti-view stereopsis evaluation. In 2014 IEEE Conference on Computer Vision and Pattern Recognition, pp. 406- 413, 2014. doi: 10.1 10.11099/2..2
Bernhard Kerbl, Georgios Kopanas, Thomas Leimkühler, and George Drettakis. 3d gaussian splatting for real-time radiance field rendering. ACM Transactions Graphics 42(4), July 2023. URL https:
//repo- sam. sam.-aa..inns.e inriiiiiii....
Arno Knapitsch, Jaesik Park, Qian- Yi Zhou, and Vladlen Koltun. Tanks and temples: Benchmarking large- scale scene reconstruction. ACM Transactions Graphics (ToG), 36(4):1-13, 2017.
Joo Chan Lee, Daniel Rho, Xiangyu Sun, Jong Hwan Ko, and Funbyung Park. Compact 3d gaussian representation for radiance field. arXiv preprint arXiv:231 131681, 2023.
Soomin Lee, Le Chen, Jiahao Wang, Alexander Liniger. Suryansh Kumar, and Fisher Yu. Uncertainty guided policy for active robotic 3d reconstruction using neural radiance fields. IEEE Robotics and Automation Letters, 2022.
Jiahe Li, Jiawei Zhang, Xiao Bai, Jin Zheng, Xin Ning, Jun Zhou, and Lin Gu. Dngaussian: Optimizing sparse-view 3d gaussian radiance fields with global-local depth normalization. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 10775-20788 2024.
Ruiqi Li and Yiu-ming Cheung. Variational multi-scale representation for estimating uncertainty in 3d gaussian splatting. Advances in Neural Information Processing Systems, 37:87934-88 87958, 2024.
Zhaoshuo Li, Thomas Müller, Alex Evans, Russell H Taylor, Mathias Unberath, Ming-Yu Liu, and Chen-
Hsuan Lin. Neuralangelo: High-fidelity neural surface reconstruction. In Proceedings of the IEEF/CVF Conference on Computer Vision and Pattern Recognition, pp. 8465, 2023.
Wenyu Liu, Tianqiang Huang, Pengfei Zhang, Zong Ke, Minghui Min, and Puning Zhao. High dimen- sional distributed gradient descent with arbitrary number of byzantine attackers, 2025. URI. https:
7/arxiv. www.vvorg/aaa. abs/ 22//2220..111333
Tao Lu, Mulin Yu, Linning Xu, Yuanbo Xiangli, Limin Wang, Dahua Lin, and Bo Dai. Scaffold-gs: Struc- tured 3d gaussians for view-adaptive rendering, arXiv preprint arXi::2312.00109 2023.
Zhicheng Lu, Xiang Guo, Le Hui, Tianrui Chen, Min Yang. Xiao Tang. Feng Zhu, and Yuchao Dai. 3d geometry-aware deformable gaussian splatting for dynamic view synthesis. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 8900-8910. 2024.
Shi Mao, Chenming Wu, Ran Yi, Zhelun Shen, Liangjun Zhang, and Wolfgang Heidrich. Generating -awee 3d models from sparse views. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 1400-14400 1409, 2024.
12

---

Published as a conference paper ICLR 2026
Ben Mildenhall, Pratul P Srinivasan, Rodrigo Ortiz-Cayon Nima Khademi Kalantari, Ravi Ramamoorthi, Ren Ng. and Abhishek Kar. Local light field fusion: Practical view synthesis with prescriptive sampling guidelines. ACM Transactions on Graphics (ToG), 38(4):1-144 2019.
Ben Mildenhall, Pratul Srinivasan, Matthew Tancik, Jonathan T' Barron, Ravi Ramamoorthi, and Ren Ng. Nerf: Representing scenes neural radiance fields for view synthesis. Communications of the ACM, 65 (1):99-106, 2021.
Wieland Morgenstern, Florian Barthel, Anna Hilsmann, and Peter Eisert. Compact 3d scene representation via self-organizing gaussian grids. arXiv preprint arXiv:2312.13299 2023.
KL Navaneet, Kossar Pourahmadi Meibodi, Soroush Abbasi Koohpayegani, and Hamed Pirsiavash. Com- pact3d: Compressing gaussian splat radiance field models with vector quantization. arXiv preprint arXiv:2311.18152 2023.
Chaojun Ni, Guosheng Zhao, Xiaofeng Wang. Zheng Zhu, Wenkang Qin, Xinze Chen, Guanghong Jia, Guan Huang, and Wenjun Mei. Recondreamer--l:: Enhancing reinforcement learning via diffusion-basee scene reconstruction. arXiv preprint arXiv:2508. 08/00, 2025.
Michael Niemeyer, Jonathan T. Barron, Ben Mildenhall, Mehdi S. M. Sajjadi, Andreas Geiger, and Noha Radwan. Regnerf: Regularizing neural radiance fields for view synthesis from sparse inputs. In Proc. IEEE Conf. on Computer Vision and Pottern Recognition (CVPR), 2022.
Xiaochao Pan, Jiawei Yao, Hongrui Kou, Tong Wu, and Canran Xiao. Harmonicnerf: Geometry-informeed synthetic view augmentation for 3d scene reconstruction in driving scenarios. In ACM Multimedia 2024, 2023.
Hao- Yang Peng, Jia-Peng Zhang, Meng- Hao Guo, Yan-Pei Cao, and Shi-Min Hu. Charactergen: Efficient 3d character generation from single images with multi-view pose canonicalization, ACM Transactions on Graphics (TOG), 43(4):1-13, 2024a.
Hao-Yang
Rui Peng. Wangze Xu, Luyang Tang, Jianbo Jiao, Ronggang Wang, et al. Structure consistent gaussian splat- ting with matching prior for few-shot novel view synthesis. Advances in Neural Information Processing Systems, 37:97328-9753 2024b.
Nagabhushan Somraj and Rajiv Soundararajan. Vip-nerf: Visibility prior for sparse input neural radiance fields. In ACM SIGGRAPH 2023 Conference Proceedings, pp. 1-11, 2023.
Pratul P. Srinivasan, Richard Tucker, Jonathan T. Barron, Ravi Ramamoorthi, Ren Ng, and Noah Snavely. Pushing the boundaries of view extrapolation with multiplane images. CVPR, 2019.
Prune Truong, Marie-Julie Rakotosaona, Fabian Manhardt, and Federico Tombari. Sparf: Neural radiance fields from sparse and noisy poses. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 4190-44000 2023.
Richard Tucker and Noah Snavely. Single-view view synthesis with multiplane images. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 551-560, 2020.
Boyuan Wang, Xinpan Meng, Xiaofeng Wang, Zheng Zhu, Angen Ye, Yang Wang. Zhiqin Yang, Chaojun Ni, Guan Huang, and Xingang Wang. Embodiedreamer: Advancing real2sim2real transfer for policy training via embodied world modeling. arXiv preprint arXiv:2507.05 19,, 2025a.
Guangcong Wang. Zhaoxi Chen, Chen Change Loy, and Ziwei Liu. Sparsenerf: Distilling depth ranking for few-shot novel view synthesis. IEEE/CVF International Conference Computer Vision (ICCV), 2023.
13

---

Published as a conference paper ICLR 2026
Peng Wang, Lingjie Liu, Yuan Liu, Christian Theobalt, Taku Komura, and Wenping Wang. Learning neural implicit surfaces by volume rendering for multi-view reconstruction. arXiv preprint arXiv:2106. 10689, 2021.
Neus:
Zihan Wang, Jeff Tan, Tarasha Khurana, Neehar Peri, and Deva Ramanan. Monofusion: Sparse-view 4d reconstruction via monocular fusion. In Proceedings of the IEEE/CVF International Conference on Com- puter Vision, pp. 8252-8263, 2025b.
Jay Zhangjie Wu, Yuxuan Zhang. Haithem Turki, Xuanchi Ren, Jun Gao, Mike Zheng Shou, Sanja Fidler, Zan Gojcic, and Huan Ling. Difix3d+: Improving 3d reconstructions with single-step diffusion models. In Proceedings of the Computer Vision and Puttern Recognition Conference, pp. 26024-26035, 2025.
Canran Xiao, Liwei Hou, Ling Fu, and Wenrui Chen. Diffusion-basee self-supervised imitation learning from imperfect visual servoing demonstrations for robotic glass installation. In 2025 IEEE International Conference Robotics and Automation (ICRA), pp. 10401-10407. IEEE, 2025.
Haolin Xiong, Sairisheek Muttukuru, Rishi Upadhyay, Pradyumna Chari, and Achuta Kadambi. Sparsegs: Real-time 360 {'deg) sparse view synthesis using gaussian splatting, arXiv preprint arXiv:2312.00206,, 2023.
Dejia Xu, Yifan Jiang, Peihao Wang, Zhiwen Fan, Humphrey Shi, and Zhangyang Wang. Sinnerf: Training neural radiance fields on complex scenes from a single image. arXiv preprint arXiv:2204.00922 2022.
Wangze Xu, Huachen Gao, Shihe Shen, Rui Peng. Jianbo Jiao, and Ronggang Wang. Mvpgs: Excavating multi-view priors for gaussian splatting from sparse input views. In European Conference on Computer Vision, pp. 203-220. Springer, 2024.
Zhiwen Yan, Weng Fei Low, Yu Chen, and Gim Hee Lee, Multi-scale 3d gaussian splatting for anti-aliase rendering, arXiv preprint arXi:2331.11788/ 2023.
Jiawei Yao, Chuming Li, Keqiang Sun, Yingjie Cai, Hao Li, Wanli Ouyang, and Hongsheng Li. Ndc- scene: Boost monocular 3d semantic scene completion in normalized device coordinates space. In 2023 IEEE/CVF International Conference on Computer Vision (ICCV), pp. 9421-943) IEEE Computer Soci- ety, 2023.
Jiawei Yao, Chuming Li, and Canran Xiao. Swift sampler: Efficient learning of sampler by 10 parameters. Advances in Neural Information Processing Systems, 37:59030-59053, 2024.
Zehao Yu, Anpei Chen, Binbin Huang, Torsten Sattler, and Andreas Geiger. Mip-splatting: Alias-free 3d gaussian splatting. arXiv preprint arXiv:2311.16495 2023.
Hongjia Zhai, Xiyu Zhang, Boming Zhao, Hai Li, Yijia He, Zhaopeng Cui, Hujun Bao, and Guofeng Zhang. Splatloc: 3d gaussian splatting- based visual localization for augmented reality, arXiv preprint a4Xiv:2409. 14067 2024.
Haoliang Zhang. Samuel Cheng, Christian El Amm, and Jonghoon Kim. Efficient pooling operator for 3d morphable models. IEEE Transactions Visualization and Computer Graphics, 30(7):4225 4233, 2023.
Haoliang Zhang, Xintong Li, Jonghoon Kim, Samuel Cheng, and Christian El Amm. Neural qslim for mesh autoencoders. In International Conference Artificial Neural Networks, pp. 51 51-65. Springer, 2025a.
Haoliang Zhang, Samuel Cheng, and Christian El Amm. Unsupervised landmark discovery via karcher means for non-rigid shape correspondence. The Visual Computer, 42(1):105, 2026.
14

---

Published as conference paper ICLR 2026
Haoting Zhang, Haoxian Chen, Donglin Zhan, Hanyang Zhao, Henry Lam, Wenpin Tang, David Yao, and Zeyu Zheng. Socrates: Simulation optimization with correlated replicas and adaptive trajectory evalua- tions, arXiv preprint arXiv:2511.00683 2025b.
Jian Zhang, Yuanqing Zhang, Huan Fu, Xiaowei Zhou, Bowen Cai, Jinchi Huang, Rongfei Jia, Binqiang Zhao, and Xing Tang. Ray priors through reprojection: Improving neural radiance fields for novel view extrapolation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 18376-13888 18386, 2022.
Jiawei Zhang. Jiahe Li, Xiaohan Yu, Lei Huang, Lin Gu, Jin Zheng, and Xiao Bai. Cor-gs: Sparse-view 3d gaussian splatting via co-regularization. arXiv preprint :Xiv:2405.1121100 2024a.
Xiaofeng Zhang, Fanshuo Zeng, Yihao Quan, Zheng Hui, and Jiawei Yao. Enhancing multimodal large language models complex reason via similarity computation. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pp. 10203-10211, 2025c.
Yunkai Zhang, Donglin Zhan, Haoting Zhang, Zuo-Jun Max Shen, Zeyu Zheng, and Qing Zhu. Does attention in transformers help wildfire prediction? Available at SSRN 4929315, 2024b.
Guosheng Zhao, Chaojun Ni, Xiaofeng Wang, Zheng Zhu, Xueyang Zhang, Yida Wang, Guan Huang, Xinze Chen, Boyuan Wang, Youyi Zhang, al. Drivedreamer4d: World models are effective data machines for 4d driving scene representation. In Proceedings of the Computer Vision and Pattern Recognition Conference, pp. 12015-12026, 2025.
Yulong Zheng, Zicheng Jiang, Shengfeng He, Yandu Sun, Junyu Dong, Huaidong Zhang, and Yong Du Nexusgs: Sparse view synthesis with epipolar depth priors in 3d gaussian splatting. In Proceedings of the Computer Vision and Pattern Recognition Conference, pp. 26800-2800000 26800022689...00 2025.
Tinghui Zhou, Richard Tucker, John Flynn, Graham Fyffe, and Noah Snavely. Stereo magnification: Learn- ing view synthesis using multiplane images. arXiv preprint /rX.vv/8050098// 2018.
Matthias Zwicker, Hanspeter Pfister, Jeroen Van Baar, and Markus Gross. Ewa splatting. IEEE Transactions on Visualization and Computer Graphics, 8(3):223-25 228, 2002.
15

---

Published as conference paper ICLR 2026
A SUPPLEMENTARY TECHNICAL DETAILS
A.1 DEFINITION OF THE METRICS IN TABLE
To systematically evaluate the impact of different configurations, we used several key metrics: reconstruction error Exee (measured by mean squared error), surface detail preservation Sae (using Structural Similarity In- dex, SSIM), view consistency Cview (quantifying alignment across perspectives), and trajectory smoothness Suaj (assessed by the second derivative of the camera path).
Reconstruction Error Erec: Reconstruction error quantifies the difference between the predicted and ground truth positions of key points in the 3D model. It is typically measured using Mean Squared Er- ror (MSE). The formula is defined as:
N
1
Eyee
lp
pred
1
(10)
N
1=1
where po is the predicted position of the i-th key point, p the ground truth position, and N is the total number of key points.
Surface Detail Preservation Sde:: Surface detail preservation assesses the sharpness and fidelity of re- constructed edges and corners, using the Structural Similarity Index (SSIM). The SSIM index is computed as:
(2 + ei) (20 + +2)
Sae
(11)
(m2 11 + c oz + +
where μl and My the mean intensities, of and of are the variances, and Dzy is the covariance of the pixel values in the predicted and ground truth images. e1 and 02 are constants to stabilize the division.
View Consistency Cview: View consistency measures the alignment and coherence of reconstructed sur- faces when viewed from different angles. It can be quantified by comparing the depth maps or point clouds across multiple views:
M
Cview
peed jj
d 12
(12)
M
where V is the number of views, M is the number depth points in each view, d.f is the predicted depth of the j-th point in the i-th view, and dit is the corresponding ground truth depth.
Trajectory Smoothness Spaj: Trajectory smoothness ensures that the camera path does not exhibit abrupt changes direction. It assessed by evaluating the second derivative of the camera trajectory:
Suaj
(t)
(13)
where 7(4) is the camera trajectory as function of time I, and and (() is the second derivative of the trajectory with respect to time, which represents the acceleration curvature of the path.
These metrics comprehensively evaluate the performance of 3D reconstruction by considering both geomet- ric accuracy and photometric consistency across views.
16

---

Published as conference paper ICLR 2026
Table 5: Full per-scene metrics at three curvature- levels. Higher PSNR/SSIM and lower Chamfer- D/P2S indicate better quality.
PSNR (dB)
SSIM
Chamfer-D x10
P2S
Scene
54.8%
73.6%
88.9%
54.8%
73.6%
88.9%
54.8%
73.6%
88.9%
54.8%
73.6%
88.9%
Garden
22.74
25.06
26.13
0.522
0.566
0.579
5.12
3,93
3.28
1.81
1.48
1.32
Kitchen
23.13
25.55
27.26
0.534
0.589
0.620
4.55
3.62
3.14
1.39
1.26
Stump
23.56
25.78
27.46
0.550
0.594
0.617
4.86
3.64
3.37
1.46
1.34
Bicycle
23.29
25.24
27.36
0.559
0.579
0.615
5.09
3.93
3.17
1.76
1.44
1.25
A.2
DETAILED SETTINGS FOR THE SIANATURE-COVERANE STUDY
Trajectory generation
The starting trajectory 7²: : [0, 1R
3 is a cubic B-spline
71(1) = Σ (t) Q₁ M 24,
(14)
where {Naa} are uniform B-spline basis functions of degree 3 and Q3 E R the control points optimised by our full method ($4, Eq. (5)). The curve is anchored the N Neam Constraints
12 sparse imput poses (V,) via soft
V
1) Step 1 - sub- sub-sampled control-point sets. For level k (1,2,3,4 we form an index mask Js {il
j mod 2* 0), i.e. we retain every 2 control point of y* and delete the rest, Let Q( (Q) jeje
M2 [Tk = 24/2
Step re-optimisation with fixed smoothness. We re-optimise Q(A) ()) by solving
{ (((((a(t)))l dt +deury L (+)( de + Anccor
Num
min Q(ky
(h) V.ll"
(15)
coverage term
smootthesss
where "/k denotes the spline with control points Q(k) and the same knot vector as y Crucially, the smooth- ness weight is kept identical (Auurv 10-2)0220000 for all k, that the only DoF influencing curvature coverage is the number of control points Mç-
3) Step3 measuring curvature coverage. Let Snigh be the set of high-curvature triangles described in App. A.2 and Sao (1%) A E Stigh 3t: frustum(m) ()) n A + 2}- Coverage is then
Scov (74) 100%.
C
(16)
Snigh|
The above procedure yields the five monotone coverage levels: C' {88.9, 84.7, 73.6, 64.1, 54.8)% for k = 0...4, 4, respectively.
Curvature computation After training with we extract a 1.5 M-face mesh via marching cubes. Mean curvature (x) is computed at each vertex using the cotangent Laplacian; triangles whose average H ex- ceeds the 9hth percentile are marked "high-curvature". Coverage C is the percentage of these marked trian- gles intersected by at least one camera frustum.
Training hyper-parameters For every " keep: Adam optimiser, learning rate 1 10-4, batch size 2048, 150k iterations, Gaussian init identical to the main method. Training one model on an NVIDIA A100 takes 80 min; the entire sweep (5 trajectories x scenes) required 2 GPU-days.
17

---

Published as conference paper ICLR 2026
Expanded quantitative tables level.
Tables list full image and geometry metrics per scene and per coverage
Correlation analysis Pearson coefficients averaged over the four scenes are FPSNR = 0.96, FSSIM = 0.94, TCD -0.93, confirming the near-linear dependency between and reconstruction quality.
A.3 PSEUDOCODE
The pseudocode of our method In our framework, the Sparse View 3D Gaussian Splatting (3DGS) optimiza- tion process is detailed in Algorithm[] while the GPU software rasterization of 3D Gaussians is outlined in Algorithm
The goal of the optimization is to adjust the control points Q of the B-spline curve (t) to maximize the geometric detail captured by the trajectory while maintaining smoothness. The trajectory is parameterized as:
7()) = Σ N,01))
(17)
where (t) are the B-spline basis functions, and Q2 are the control points.
The objective function maximize the coverage of geometric features is defined as:
J(n) = f/a fx (()(t))l)
J6)==
(18)
where w()(t)) = x()(()) + 8, x(>(t)) is the mean curvature at point 7(t), and [|)((t) represents the speed along the trajectory. The optimization problem is thus:
Q arg max (J(7))
(19)
Q
The optimization employs the constrained L-BFGS method, which requires the computation of gradient of the objective function with respect to the control points Q;-
The gradient of the objective function J(7) with respect Q given by:
0J(7)
1/M AN (Dw(((() [b( w(r(t)) 01)((11 aQ, dt
(20)
iQ;
-QQ,
iQ,
where:
@vl(((1) ax(((1))
(21)
iQ,
aQ,
and:
18

---

Published as conference paper ICLR 2026
(|))(())] (t))) (+(( iQ,
24,
(22)
(t)lll
The curvature x(r(tt) at point (t) can be expressed in terms of the first and second derivatives of (())
<(>(1)) (t((t) x (()l))
(23)
(1)(1))
Thus, the gradient @u(((()) 8Q,
be derived
0x(7(t)) aQ
(T((t) (I1'00) x
(24)
aQj
This involves the computation of the derivatives of the cross product and the norms with respect to the control points Qj. which is achieved using the chain rule and the properties of cross products and dot products.
A.4 WHERE THE DEPTH COMES FROM
For warping-basee synthesis we require per-pixel depth map for each real source view 4; We obtain and refine these depths in two stages:
(i) Bootstrapping (datasct-dependent):
DTU Telt/Tann&Teennn Temples: We compute dense depths D using COLMAP PatchMatch stereo from the calibrated multi-view sets.
LLFF / Mip-NeRF 360 / Blender: We predict monocular depths DQO) with pre-trained
model (c.g., DeT/ZoeDetth). To fix the unknown global scale, we align each D to the sparse SfM points by robust median ratio:
SSM (1)
S median
(25)
D. (u)
(ii) 3DGS-consistent refinement: After short warm-up of 3DGS on real images, render expected depth D, via alpha compositing of sorted Gaussians:
T (u) ax (u) D.(u) = Σ (u(u) (u), āx(u)= Σm T' Tm-i(u) (u) am (u)
(26)
where Tk-1 is the accumulated transmittance up to the (A-1)-th Gaussian. We then fuse D and Dj with uncertainty-aware weights (photometric residual pt or predictor variance af):
Te.2 (u)
(u) = 7)s (u) D. (u) (1 --m(u)) (1(),, na(u) =
(27)
प,¹² (u)
gs. uu)
19

---

Published as conference paper ICLR 2026
Algorithm 1: Sparse View 3D Gaussian Splatting with Trajectory Optimization and Densification
Input: Training image dimensions w, h; Initial camera poses (V)): Sparse view images [Tt); SIM points M
Output: Optimized Gaussians M, C, A for 3D reconstruction
M, S, C, A InitAttributesO::
// Init positions, covariances, colore, opacities // Iteration counter
i 0:
(t) < Initial trajectory( (Vi));
// Initial camera trajectory // Optimize trajectory
Y (t) < Traneiioo/
while converged de
V, + CampleTraiiing View()
// Sample camera and image // Basterize using Aigorithm 2
1 < Rasterize S, C)
L <- Loss(I, i)
// Compute loss
M, S. C, A Adam(VE) VL)) if (RRefinemenntherationn) then foreach Gaussian (1,, L, c, a.) in (M, S, A) do
// Update Gaussians
if < e or IsTooLarge(p, 2.) then
RemoveGaussian(;
if V
L
Tp then
if S| > Ty then
SpliGaussian(y, C,
// Split
(overr-reconstruction)
else
(4,
// Clone (underr
8 4- + 1;
Algorithm 2: GPU Software Rasterization of 3D Gaussians
Input:
Image dimensions w, h; Gaussian means and covariances M, S; Colors C; Opacities A; Camera view V
Output: Rasterized image
Function Raster ze (w, M,M,,,,CAAVI
CullGaussian(p, V)
// Frustum culling of out-of-bounds Caussians
S' ScreenspaceaaussianMMM....
// Transform Gaussians screen
space
T CreateTiles(u, h):
// Create tiles for rasterization // Create indices and keys for sorting // Global sort of tiles R + Identify TileRanges(T, K); // Identify tile ranges for rasterization // Initialize output image
L, K t
SortByKeys K, L):
1 0:
foreach Tile in I do
foreach Pixel in do
// Get Gaussian range for this tile [ + BlendInOrder(i, L,r, K, M', St, S), // Blend Gaussians into the pixel
GerTileRange R.t):
return I;
20

---

Published as conference paper ICLR 2026
B THE PSEUDOCODE AND THEORY OF OUR METHOD
B.1 PROOF CONVERGENCE AND EFFECTIVENESS
To rigorously demonstrate the effectiveness of our optimized camera trajectory relative the original 3DGS method, we focus on three key aspects: convergence of the optimization process, balance between trajectory smoothness and curvature coverage, and comparative effectiveness in capturing geometric details.
B.1.1 CONVERGENCE OF THE OPTIMIZATION PROCESS
We aim to prove that our method of optimizing camera trajectories is both convergent and effective compared the original 3DGS method. We will proceed by establishing several key propositions and lemmas, which will culminate in the proof of the main theorem.
B.1.2 DEFINITIONS AND ASSUMPTIONS
Consider the trajectory (()) parameterized by control points Qj of B-spline curve. The objective function for the optimization problem is defined as:
J(x) = S,
AN (a (a.x((((t)+++ + (n) dt
(28)
where x()(t)) represents the curvature, and [t)( denotes the speed along the trajectory. We make the following assumptions:
Assumption 1: Continuity and Differentiability of the Objective Function. We assume that the objec-
tive function (r),, defined as
AN (a (oc.((7()) + (111 ((7) = L/m
(29)
is continuous and differentiable with respect to the trajectory (t). Formally, this means that for any feasible trajectory (t) in the domain of J (r), the function J C2 (²(tt, tN] + E is C2, i... possesses continuous first derivatives with respect to all the components of >(t) and its derivatives.
Assumption 2: Convexity of the Smoothness Constraint. The smoothness constraint CJ, given by
C 1r(()e
(30)
is assumed to define a convex set in the space of admissible trajectories (t). This implies that for any two feasible trajectories (1(t) and (t), and for any X [0, 1]. the trajectory (x(t) Xn(() (1 ()
also satisfies C1. Mathematically, this means the functional form of the constraint is convex:
(D + (1) de S
(31)
for all À e [0.
21

---

Published as conference paper ICLR 2026
Assumption 3: Feasibility of the Initial Trajectory. The initial trajectory (t(),, which is the starting point for the optimization, is assumed to be feasible. This means that (t satisfies all the imposed con- straints:
70(() EF,
(32)
where FF is the feasible set defined by the constraints C1 to Cg. Formally, this implies that:
16 de e,
(t():) = V, for all = I,
(33)
[1) 2 Umin
(()) Kmin in specified regions,
(l)(()) - (tr(t)l
S 6,
where (t) is some reference trajectory (potentially the initial estimate).
Convergence of the Optimization: We define the objective function for the optimization problem as:
J(7) = S.a (an()(()) (1)(( dt,
(34)
where (t) represents the trajectory parameterized by the B-spline control points Q₁. The optimization problem aims to minimize J(x) subject to the smoothness constraint:
G : J (t
(35)
Using the Lagrangian function, the problem can be expressed as:
J(7) - do (,,T de)
(36)
The first-order optimality condition (KKT condition) requires:
/ AN
V.) - - V
(t"( 0.
(37)
Substituting the expressions for the gradients, we obtain:
a vv,((T(t) + =2
=
(38)
Given the convexity of ( and <(>(1)), we begin by considering the objective function J(7) defined as:
1/h Ax (a])>"(0)1? + 3x(r(t))) dt.
J(7) =
(39)
22

---

Published as conference paper ICLR 2026
The convexity of the terms (+)] and k()())) ensures that J()) is also convex. The L-BFGS algorithm is employed to minimize this convex objective function, which satisfies the Wolfe conditions, specifically:
J() - (()(t) + sp) (sufficient decrease condition),
(40)
VJ(("((t) pl S C2 (t)( Tpl (curvature condition).
where 7() + sp is the updated trajectory in the L-BFGS iteration, and the step size that satisfies the line search criteria.
By the nature of convex optimization, the L-BFGS algorithm guarantees convergence a local minimum (t), such that:
(t)" S J (73Das(t)) (t)),
(41)
where 73DGs( (t) denotes the trajectory obtained by the original 3DGS method.
Expanding (ny (4)), we have:
1/me Fx
dt
(42)
$ 1/m (all (t)l1 + Br((30oo((t)) dt,
S AN
(t)l dt + B 1Tm (t) dt pN
or equivalently, a
(43)
sa S dN
11 (1)l di + 1.
x(7sDas(1) dt.
[t)] [1 and xt) 2 x(Y3Dos(t)).
(44)
which leads to:
J( (1)) I (TaDos(()).
(45)
Effectiveness the Optimized Trajectory: We now demonstrate that the optimized trajectory ?*( superior in capturing geometric details while ensuring smoothness. The curvature constraint ensures:
Ax x(7 (t))dt 2
k(7)aas(t))
(46)
This implies that:
xx a
(t) 2 a J." (()) I.a
(47)
For the smoothness constraint, have:
23

---

Published as conference paper ICLR 2026
dN JAL ln (t)) dt (1 (1/bbsst)11 dt.
(48)
Thus, the overall objective function satisfies:
J(7") 1,²²' AN
(am((ranas()) (ll (t)ll) dt.
(49)
Final Inequalities and Conclusion:
Combining the above results, obtain:
J( S (r9DGs),
(50)
IN
/
pNN (1 di,
(1) < 1h
(51)
J1
/ fr
2 (t)
x(rrsos(t))dds
(52)
These inequalities confirm that the optimized trajectory > not only improves the smoothness and stability of the path but also enhances the capture of critical geometric details.
ADDITIONAL EXPERIMENTS AND RESULTS
C.I SPARSE VIEW RECONSTRUCTION RESULTS ON BLENDER DATASET
As shown in Table 6. method surpasses 3DGS with average PSNR of 24.98 (+6.33) for the 6-image set and 27.72 (+5.08) for the 9-image set. It excels in challenging scenes like "Ficus" (47.58) and "Hot Dog" (+9.44), proving its effectiveness sparse views. Even with just images, achieves a PSNR of 25.59, improving by +8.23 over 3DGS.
Table 6: Quantitative comparison on Blender dataset Mildenhall al. (021). We compare our method with 3DGS, and reconstruct scenes using 3, 6, or 9 images. The table shows the PSNR on each reconstructed scene and the overall average PSNR for both the sets of images. The blue text indicates the increase PSNR compared to 3DGS.
Mothod
Chair
Drums
Ficus
Hot Dog
Lego
Materials
Mic
Ship
Average
3DGS. images
22.52
14:03
30.94
19.92
18.52
15.48
21.57
16.25
18.65
3IXGS, images
16.25
3DGS.
images
23.43
17:22
23.16
27.80
24.22
19.15
26.03
20.07
22.61
Ours. 3 images
27.24 (+1.72)
19.62 (+5.59)
28.52 (+7.58)
29. (+9.44)
26.04 (+7.52)
20.13 (+1.65)
27.04 (+5.47)
21.85 (45.00 60)
24.98 (+6.35
Ours,
images
28.21 (+5.69) 69)
21.04 (+7.29)
28.97 (49.33)
30.15 (+11.82)
27.05 (49.93)
21.09 (47.08)
28.47 (47.43)
23.57 (48.43)
25.59
(-8.24822 (-8.25)
images
(+6.055
(+6.37)
(-3.6)))3
(+5.68))
(+1.30)
(+1.68)
C.2 ABLATION STUDY OF CURVATURE WEIGHT
We vary the curvature weight and baseline coverage term which together define w(+(tt) (t))
3. We observe from Table that moderate curvature weighting (our default, a = 0.3, $ = 0.7) achieves the best balance.
24

---

Published as conference paper ICLR 2026
Table 7: Ablation on trajectory optimization hyperparameters (a, B).
Hyperparams
a PSNRT
C
0.3
a PSNR1
0.4
(a,, 3)
CD1
PSNR1
CD
CD
(1.0, 0.0)
26.07
3.64
26.71
3.29
26.98
3.25
(0.5, 0.5)
26.84
3.56
27.06
3.21
27.32
3.19
(0.2, 0.8)
27.05
3.51
27.29
3.15
27.56
3.09
(0.3, 0.7) 27.05
3.49
27.38
3.07
27.89
3.01
C.3 QUANTIFYING THE IMPACT OF CURVATURE COVERAGE ON SPARSE- VIEW 3DGS
Clondare
94.66
94.5%
12.0%
06.7%
14
2838
21.0
21:11
19-11
27/3
11
KREAT
0.54
6.55
6.4
30
141
921
1211
Figure 5: Average novel-view and geometry quality w.. curvature coverage C' on four scenes. Higher image scores and lower geometry errors are better.
We use four representative scenes (Garden, Kitchen, Stump, Bicycle) from the MIP-NERF 360 benchmark (Barron et al. 2022). Starting from the fully-optimised trajectory r", we progressively drop every second B-spline control point to create four sub-trajectories [7x)*=) with strietly lower curvature coverage C (see appendix A.2 for full description). All other training byper-parameters are kept identical. Quality is measured on the official test split using PSNR, SSIM, LPIPS and two geometry scores- -ymemerrymetric Chamfer Distance (CD) and point-to-surface error (P2S). Each model is trained from 12 real input views.
Figure reveals an almost monotonic relationship: increasing C from 55% to 89% lifts PSNR by +3.9 dB, raises SSIM by +0.067, reduces LPIPS by -0.048, and halves Chamfer Distance. The consistent im- provement across both photometric and geometric metrics indicates that curvature coverage is a dominant explanatory variable for sparse-view 3DGS performance.
Table Per-scene breakdown at the two extremes of curvature coverage.
C (%)
CD40-3 3
Scene
APSNR
low
high
low
high
Garden
$2.9
87.2
+3.4
5.12
3.28
Kitchen
57.8
89.1
+4.1
4.55
3.14
Stump
55,6
91.3
+3,9
4.86
3.37
Bicycle
53.0
88.0
+4.3
5.09
3.17
25

---

Published as conference paper ICLR 2026
Table 8 shows that every scene benefits similarly: PSNR gains of x 4 dB and CD reductions of 1.7 10 This uniform trend supports our claim in Sec. 3 that dense supervision of high-curvatrre surfaces is universally critical for accurate reconstruction under sparse inputs.
C.4 CURVATURE COVERAGE AND TRAJECTORY SMOOTHNESS ON LLFF
To complement the coverage analysis on Mip-NeRF 360, we perform a curvature-coverag sweep on two LLFF scenes (Fern, Room). For each scene, we construct three trajectories with low medium / high curvature coverage and train 3DGS from scratch. As shown in Table 9 leads to monotonic improvement high coverage yields gains of about +1.6-1.9
increasing curvature coverage C' both photometric and geometric quality on LLFF. Moving from low to 1.9 dB PSNR and noticeable SSIM improvements, while Chamfer- D consistently decreases. This mirrors the trends observed on Mip-NeRF 360, supporting curvature coverage generic explanatory variable rather than dataset-specific artifact.
Table 9: Curvature coverage vs. reconstruction quality on LLFF (Fern, Room). Higher coverage consistently improves both photometric and geometric metrics.
Scene
Coverage C
PSNR 1
SSIM t
Chamfer-D | (x10 3)
58%
20.4
0.812
4.85
Fern
72%
21.3
0.828
4.21
87%
22.0
0.839
3.97
57%
20.1
0,804
5.02
Room
73%
21.0
0,821
4.36
88%
21.7
0.832
4.10
To isolate the effect of trajectory smoothness, we construct two trajectories on the Mip-NeRF 360 Garden scene with nearly identical curvature coverage but different smoothness scores. In Table IO both paths see almost the same high-curvature regions (similar C), but the jittery trajectory loses 1.6 dB PSNR, 0.025 SSIM, and exhibits higher Chamfer-D. This confirms that, beyond coverage, the smoothness of the view- ing path is itself an implicit bias of sparse-view 3DGS: abrupt camera motion harms both appearance and geometry even under comparable coverage.
Table 10: Trajectory smoothness at nearly fixed curvature coverage on Mip-NeRF 360 Garden. Jittery paths significantly degrade reconstruction quality even when coverage C' is similar.
Trajectory
Coverage C Smoothness Sinj +
PSNR
SSIM 1 Chamfer-D 4 (x10~3)
Smooth (ours)
86.7%
0.98
26.1
0.579
3.28
Jittery (same C)
85.9%
0.71
24.5
0.554
3.92
C.5 ROBUSTNESS TO DEPTH NOISE, POSE NOISE, AND CURVATURE THRESHOLDING
Depth refinement and synthetic-view robusiness. On the Blender Lego scene (6 views), we compare synthetic views built from monocular depth only uncertainty-weiighedd fusion of monocular and 3DGSSconsistent depth yields s +0.5 dB PSNR, better SSIM, lower LPIPS, and improved Chamfer-D. This indicates that refinement only avoids amplifying monocular errors, but also stabilizes geometry.
refined depth fusion. Table I1 shows that
We further inject Gaussian noise into the refined depth:
26

---

Published as conference paper ICLR 2026
Table 11: Effect of depth refinement on synthetic views (Blender Lego, views). Refinement improves both photometric and geometric quality.
Variant
PSNR
SSIM t
LPIPS +
CD CD1(x10-))
Mono-only depth
26.8
0.934
0.044
3.40
Refined depth (ours)
27.3
0.939
0.040
3.25
Table 12:
Robustness of our synthetic-view construction to depth noise (Blender Lego, 6 views). is relative to the per-view depth range A
Emax
minn
Variant
PSNR t
SSIM f
LPIPS
CD CD4(x10
Refined depth (no noise)
27.3
0.939
0.040
3.25
noise, 2%
27.1
0.937
0.041
3.30
noise, = 5%
26.9
0.936
0.042
3.42
even with 2-5% relative depth noise, PSNR drops by at most 0.4 dB and changes in SSIM/LPIPS/CD remain small. Our method remains robust moderate depth inaccuracies, with perfor- mance still above a 3DGS baseline without synthetic views.
As seen in Table 12
Filtered unfiltered synthetic views. We compare our full visibility- and consistency-aware filtering a naive "unfiltered" variant:
Table 13:
Impact of filtering synthetic views (Blender Lego, 6 views). Unfiltered warps degrade both image and geometry quality.
Variant
PSNR
SSIM t
LPIPS 4
CD J (x10-²)
Unfiltered synthetic
26.2
0.931
0.048
3.45
Filtered synthetic (ours)
27.3
0.939
0.040
3.25
Table 13 demonstrates that naive reprojection (no Mij. no depth consistency, no pruning) hurts both PSNR and LPIPS and worsens Chamfer-D. Our filtering pipeline removes ghosting and misaligned warps, turning synthetic views into reliable supervision instead of noisy pseudo-labels.
Visibility tolerance in the z-buffer mask. We sweep the depth tolerance T = m/ in the visibility mask. Results in Table 14 show that varying by order of magnitude changes PSNR by most 0.1 dB and LPIPS/SSIM only minimally. This suggests our visibility criterion not a brittle byperparameter.
Sensitivity to COLMAP/SIM pose noise. On DTU COLMAP poses. Table 15 indicates that both methods degrade by x 0.6-0.7 dB under realistic pose noise, but our method maintains essentially the same margin over vanilla 3DGS. This suggests that curvature-aware trajectories and synthetic supervision do not make the system more fragile to pose errors.
0.3), we add small Gaussian perturbations
Curvature threshold sensitivity. We vary the high-curvature percentile used to define important regions Mip-NeRF 360 Garden. As seen in Table 16, changing the percentile from 3% 10% affects PSNR by at most 0.15 dB and Chamfer-D by less than 0.1 x 10 This supports our design choice of using curvature coarsely (to rank regions) rather than relying precise pointwise estimates.
27

---

Published as conference paper ICLR 2026
Table 14: Effect of the z-buffer tolerance т on synthetic views (Blender Lego, 6 views). Performance largely insensitive in wide range.
T/A= A= (%)
PSNR 1
SSIM
LPIPS &
0.3%
27.29
0.938
0.041
1.0% (default)
27.32
0.939
0.040
3.0%
27.24
0.937
0.042
Table 15: Sensitivity to pose noise on DTU (a = 0.3). Both vanilla 3DGS and our method degrade slightly, but our margin over the baseline remains.
Method
Poses
PSNR
SSIM
LPIPS 4
CD CD4(x107)
3DGS
clean
23.3
0.85
0.33
3.39
3DGS
noisy
22.6
0.83
0.35
3.62
Ours
clean
27.4
0.89
0.19
3.07
Ours
noisy
26.9
0.88
0.20
3.27
C.6 RUNTIME OVERHEAD BREAKDOWN
We report per-stage wall-clock time NVIDIA A100 for representative DTU and Mip-NeRF 360 scenes.
Table 17 shows that trajectory optimization and synthetic-view construction together contribute only ~ 3- 5 minutes of overhead per scene, i.e., typically < 5% of total training time. Thus, the geometry-awan improvements we obtain come at very modest additional computational cost.
D SUPPLEMENTARY VISUAL RESULTS
D.1 VISUALIZATION RESULTS ON DTU
Our method generates more natural and detailed images on DTU by optimizing camera trajectories for maxi- mal curvature coverage and smooth transitions. By carefully selecting camera paths and generating synthetic views, we capture essential scene geometries and estimate Gaussian parameters for improved reconstruction. This ensures geometric consistency, reducing artifacts and preserving spatial relationships for superior detail retention and visual coherence (Figure 6). As shown in the second row, method enhances brightness and completeness drum cymbals, closely matching the ground truth while reducing floating artifacts.
D.2 VISUALIZATION RESULTS ON TANKS & TEMPLES DATASETS
Fig shows qualitative comparisons on the large-scale indoor scenes Auditorium and Ballroom. Our method produces renderings that visually closest to the ground truth, preserving both the global illumination and fine structures such as the rows of seats, cciling details, and carpet patterns. In contrast, MAtCha Gaussians (Guédon et al. 2025) and Difix3D++ (Wu et al. 2025) exhibit more blur and geometric distortions, particularly for distant regions and high-frequency textures, indicating that our approach better handles the long-range, cluttered environments in Tanks & Temples.
28

---

Published as conference paper ICLR 2026
Table 16: Sensitivity to curvature threshold on Mip-NeRE 360 Garden. Performance is stable across a broad range of thresholds.
High-curvature threshold
PSNR
SSIM
Chamfer-D & (x10-3)
top 3%
26.05
0.576
3.33
top 5% (default)
26.13
0.579
3.28
top 10%
25.98
0.574
3.35
Table 17:
Runtime breakdown per scene. Our trajectory optimization and synthetic-view generation add only small overhead compared to 3DGS training.
Pipeline
Traj. opt (CPU)
Synth. views (CPU/GPU)
3DGS training (GPU)
Total wall-clock
Vanilla 3DGS
70-80 min
70-80 min
Ours (full)
2-3 min
1-2 min
70-80 min
73-85 min
D.3 VISUALIZATION RESULTS FOR ABLATION STUDY
Fig 8 shows that our full method ("Ours") outperforms the ablated versions by producing the most accu- rate and coherent reconstructions. Without optimizing camera trajectories, the results show distortions and artifacts, particularly at object bases. The absence of synthetic view construction leads to incomplete recon- structions with missing details. Skipping the trajectory smoothness constraint introduces minor inconsisten- cies, especially in high-curvature areas. Overall, the complete framework best balances detail, accuracy, and coherence.
D.4 VISUALIZATION RESULTS FOR MESH RECONSTRUCTION
Figure 9h demonstrates the reconstructed mesh with detailed geometry. Our method can generate a clean mesh outperforming the performance of naive 3DGS.
D.5 VISUALIZATION RESULTS FOR DEPTH MAP AND FOREGROUND MASK
Figure Pa confirms that our method can provide accurate depth reconstruction, and precise foreground masks that segment objects reconstruct from the scene background.
E
LLM USAGE
We used large language model for minor English editing (gramnar/wordingllarity) and small, localized code fixes (e.g., resolving syntax errors, adding missing imports). The LLM did not contribute to research ideation, experimental design, data processing, analysis, figure generation. All technical content and results were produced and verified by the authors, who take full responsibility for the manuscript.
29

---

Published as a conference paper ICLR 2026
SpaneNouS Sparsefi
Chair (Bkakke)
Dome
500 40
Son
TRS (3T1))
Figure 6: Qualitative results of novel view synthesis on DTU dataset and Blender dataset. We train the model using 30% images for real scenes in DTU dataset, and 6% for synthetic scenes in Blender dataset.
30

---

Published as a conference paper ICLR 2026
GT
Ours
Auditorium
Gaussians
MAtCha
Difix3D+
GT
Ours
Ballroom
MAtCha Gaussians
Difix3D+
Figure 7: The visualization results on the Tanks & Temples dataset. We visualize the reconstruction results
with 20 total views.
31

---

Published as a conference paper ICLR 2026
w/o Optimal Camera Trajectory Gemeration
GT
Synthetic Camera View Construction
Trajectory Smoothness Constraint
Ours
Figure 8: Ablation Study of Our Framework (NeRF-Synthetic dataset, 10views). Comparison of 3D re- construction results across different configurations: Ground Truth (GT), w/ Optimal Camera Trajectory Generation, Synthetic Camera View Construction, Trajectory Smoothness Constraint, and Our complete method.
2002
Pongrant (a) Reconstructed depth and foreground mask. Figure 9: Qualitative comparison of reconstruction resuuts(NRRF-SSnnheee dataset, 10views).
CreatTaah
Berwetrated
Vion
Daph
(b) Qualitative comparison of mesh reconstruction.
32


Reviews:
[{"review_id": "0FUqB3cqaq", "reviewer": "Reviewer_8JLf", "summary": "This paper identifies two implicit biases limiting 3D Gaussian Splatting (3DGS) under sparse-view conditions: a geometric detail bias, where high-curvature regions require denser supervision, and a trajectory smoothness bias, where irregular camera paths degrade reconstruction. To mitigate these, the authors propose a curvature-aware trajectory optimization framework that maximizes curvature coverage and enforces smooth motion, coupled with synthetic view generation along optimized paths to enrich supervision. Using B-spline–based optimization, the method achieves consistent gains of  PSNR across DTU, Mip-NeRF360, LLFF, Blender, and Tanks & Temples, reaching state-of-the-art sparse-view performance. This could be potentially used for path planning.", "questions": "1. How do you ensure that synthetic views generated along the optimized trajectory do not introduce photometric or geometric artifacts that might bias the training of 3DGS?\n2. Does the proposed optimization generalize across scenes with very different geometric complexity (e.g., indoor vs. outdoor, man-made vs. natural environments)?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1. The first work to identify and thoroughly validate previously unrecognized implicit biases in 3DGS, namely curvature prioritization and trajectory smoothness.\n\n2. The paper is well written, clearly structured, and enjoyable to read.\n\n3. It suggests a promising direction for optimizing camera path planning to improve 3DGS performance, with potential applications in interactive or guided data collection for building high-quality 3DGS datasets.", "weaknesses": "1. The current analysis is conducted primarily on synthetic datasets. It would strengthen the paper if the authors could include a real-world evaluation—capturing scenes with different camera trajectories, then re-capturing them using the proposed optimized paths. Such a practical comparison would better demonstrate the method’s effectiveness and validate its impact under real capture conditions.\n\n2. Synthetic-view generation may amplify rendering artifacts or propagate depth estimation errors, yet the paper does not analyze robustness under such noise.\n\n3. While the implicit bias analysis is insightful, parts of the implementation—trajectory smoothing and synthetic interpolation—rely on well-established engineering heuristics rather than fundamentally new learning paradigms.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "BNqqnMxtvK", "reviewer": "Reviewer_2dz9", "summary": "The paper investigates the behavior of 3D Gaussian Splatting (3DGS) in sparse-view settings and reports that performance degradation is linked to geometric and trajectory-related factors. The authors identify two types of implicit bias—dependence on curvature coverage and sensitivity to camera trajectory smoothness—and propose an optimization framework that adjusts camera paths and augments supervision through synthetic views. Experiments on multiple benchmarks show consistent improvements in both visual quality and geometric accuracy.", "questions": "1 How sensitive is the proposed optimization to errors in initial camera poses obtained from SfM or COLMAP?\n\n2 Does the method depend heavily on accurate curvature estimation, and how robust is it in low-texture or noisy regions?\n\n3 Could the synthetic view generation module be integrated into an end-to-end differentiable pipeline in future work?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1 The paper explores a relevant and timely topic in the area of 3D reconstruction and view synthesis. The problem of sparse-view degradation is practically important and underexplored.\n\n2 The analysis of geometric and trajectory effects provides a new perspective on 3DGS behavior and contributes useful insights to understanding implicit bias in reconstruction models.\n\n3 The proposed optimization framework is technically sound and well motivated, combining curvature-aware path planning with synthetic view construction in a coherent manner.\n\n4 Experimental results are extensive and demonstrate consistent improvements over several recent baselines on diverse datasets. The ablation study also supports the contribution of individual components.\n\n5 The paper is clearly written and well organized, making the methodology and findings easy to follow.", "weaknesses": "1 The analysis of implicit bias remains primarily empirical. Providing more formal or quantitative evidence could make the claims more rigorous and generalizable.\n\n2 The quality and reliability of the synthetic views are not deeply discussed. It would be helpful to include a brief evaluation or visualization to show their effect on reconstruction stability.\n\n3 The computational cost of trajectory optimization is not clearly presented. Additional runtime or complexity analysis would make the evaluation more complete.\n\n4 Some details in the appendix may be overly technical, while certain conceptual explanations in the main text (e.g., how curvature coverage improves supervision) could be emphasized more clearly.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "pb8L5Dlsql", "reviewer": "Reviewer_FqdL", "summary": "The paper explores implicit biases in sparse-view 3D Gaussian Splatting (3DGS): regions of high surface curvature need disproportionately more supervision, and the layout/smoothness of camera poses (summarized as a continuous trajectory) affects reconstruction accuracy. To address this, they (i) fit a B-spline camera path and optimize it to maximize curvature coverage under smoothness and proximity constraints to original camera poses, and (ii) synthesize intermediate views sampled along the optimized path using depth-based warping with a two-stage depth pipeline (COLMAP or monocular bootstrap; then 3DGS-consistent fusion). On Mip-NeRF 360 and DTU/LLFF/Tanks&Temples, they show consistent gains vs. recent sparse-view methods; they also correlate “curvature coverage” with PSNR/SSIM and geometric errors to justify the trajectory objective. Ablation analyses highlight the importance of proposed components.", "questions": "1. In the ‘w/o synthetic views’ row of ablation, do you keep trajectory optimization/smoothness? would this not be naive 3DGS in terms of reconstruction and accuracy (or do you change the previously sampled poses in any way)\n2. The blending uses a z-buffer mask “with a small tolerance.” How is the tolerance chosen, and how does it trade off ghosting vs. holes across datasets?\n3. Is there any analysis of the impact of the accuracy of novel view generation (for example, sensitivity to depth estimation accuracy) on final accuracy?\n4. What’s the wall-clock overhead for trajectory optimization and synthetic view generation compared to vanilla 3DGS training? The efficiency table is helpful but doesn’t isolate these stages.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper is well written overall, with the insights motivated upfront leading to the proposed method\n2. The insights pertaining to surface curvature and smoothness of pose trajectories affecting reconstruction accuracy is new and interesting\n3. The optimized trajectory leading to synthetic generation of views is a clean formulation\n4. Qualitative and quantitative results show superior performance over a broad range of baselines\n5. Ablation studies highlight the importance of the various proposed components", "weaknesses": "1. Given that the sparse views are combatted through synthetic view generation, it seems the proposed method trains a 3dgs with more views than other compared methods, potentially leading to an unfair comparison.\n2. The number of synthetic views generated per scene is not clearly specified: it is difficult to visualize the impact of the proposed method without this relevant information.\n3. The analysis in section 3 Figure 2 is done on only one scene, reducing the potential empirical validity of the insights", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "LGTNPB38wp", "reviewer": "Reviewer_QAJ4", "summary": "This work focuses on the reconstruction degradation issue of sparse-view 3DGS, and points out two implicit biases of it, i.e., \"stronger demand for supervision signal toward regions of high curvature\", and \"sensitive to the smoothness of the trajectory of the input views\". To this end, this work proposes a method to optimize the camera trajectory for maximizing curvature coverage. Experimental results on different datasets show that this work achieves improvements compared to several baselines.", "questions": "* I notice that the computatoinal costs in A.2. \"Training one model on an NVIDIA A100 takes ∼80 min; the entire sweep (5 trajectories × 4 scenes) required 2 GPU-days.\" I am confuse that why this work requires so much computational resources, because it seems that this work only optimizes the camera trjectories. If I misunderstand anything, please correct me.\n* I notice that this work has better reconstruction quality compared to the previous state-of-the-art methods, which often utilize the external pre-trained priors, like DUST3R/MAST3R for InstantSplat, monocular depth predictors for DNGaussian, etc. I also want to figure out that what external pre-trained priors this work utilizes. I only notice that this work utilizes the monocular depths on the LLFF/Mip-NeRF 360/Blender dataset, as demonstrated in A.4. I hope the authors can provide more clarity on the use of external pre-trained models.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "* This paper is well-written, and the readers can easily get the points this work aims to propose.\n* The perspective of optimizing the camera trajectory of this work is interesting to me. However, I still have some questions for it. See more details in the Questions part.\n* The experimental results show that this work has better reconstruction quality compared to the previous methods.", "weaknesses": "* More detailed ablations are required, like the ablations of different components in Table 4(a).\n* It is recommended to report the SSIM of Table 2 at the same time.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "SETLKLBgAj", "reviewer": "Reviewer_cTEf", "summary": "The paper proposes a framework to improve 3D Gaussian Splatting (3DGS) under sparse-view inputs. By maximizing curvature coverage while maintaining smooth camera motion, and synthesizing new views along the optimized path via depth-guided parallax-based interpolation, it improves the rendering quality and geometry fidelity of 3DGS under sparse-view inputs.", "questions": "As noted in the weaknesses, I strongly encourage the authors to include additional qualitative results in the main paper for all datasets reported with quantitative metrics. Each figure should include clear captions indicating the number of input views. In addition, I recommend the authors to provide a side-by-side video comparison against all competitive baselines to better access the rendering qualities. Furthermore, I recommend adding both qualitative and quantitative comparisons with MAtCha Gaussians and DIFIX3D+, which are highly relevant recent methods for sparse-view novel view synthesis. I would consider raising my score if these added results and visualizations demonstrate clear and consistent improvements over the baselines.\n\nI also have two additional questions:\n- Would the proposed method benefit further from an iterative, on-the-fly pseudo-view generation strategy similar to DIFIX3D+ (CVPR 2025)? In DIFIX3D+, the authors progressively (over several iterations) render intermediate novel views from the current 3D Gaussian Splats, enhance them using a single-step diffusion model, and then add these enhanced views back into the training set to improve under-constrained regions. Could a similar iterative scheme, where synthetic views are dynamically regenerated and re-used throughout 3DGS training, instead of being pre-interpolated before training, further improve the performance of the proposed method?\n- Could the proposed method be formulated as a plug-in module applicable to any sparse-view Gaussian Splatting pipeline? For example, if integrated into more competitive baselines such as MVPGS or SCGaussian, would it yield a comparable relative improvement over those baselines as it does over vanilla 3DGS? Demonstrating such consistency in quantitative gains across different pipelines would make the contribution far more convincing, showing that the method benefits a broad class of Gaussian-based pipelines in a plug-and-play manner.", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 1, "contribution": 2, "strengths": "- The paper proposes a methodical camera path optimization problem which seems effective and significantly enhances the performance of vanilla 3DGS in sparse-view settings.\n- The algorithm is clearly explained and easy to reproduce.\n- The ablation studies show the benefits of each of the proposed components.", "weaknesses": "- Insufficient qualitative results: Apart from the toy examples in Figures 1 and 2, the main paper includes only a single set of qualitative comparisons (Figure 4) on LLFF and Mip-NeRF 360, without specifying the number of input views used. While additional qualitative results are provided in the supplementary material, comparisons on the Tanks & Temples dataset are still missing, leaving an incomplete qualitative evaluation.\n\n- Limited quantitative gains: The main issue I see in this paper is that the reported improvements over other sparse-view baselines appear marginal or inconsistent. For example, in the 3-view DTU results (Table 3), the proposed method performs slightly better than SCGaussian on PSNR (20.56 vs. 20.65) and SSIM (0.86 vs. 0.89), and significantly worse on LPIPS (0.12 vs. 0.24). Similarly, in the 3-view LLFF comparison, the method performs slightly better than MVPGS on PSNR (20.65 vs. 20.93), but performs notably worse on SSIM (0.88 vs. 0.78) and LPIPS (0.10 vs. 0.23). On 12-view Mip-NeRF360 comparison, the proposed method also only achieves very marginal improvement over MVPGS. These quantitative results make it unconvincing that the proposed approach consistently outperforms prior methods under sparse-view settings.\n\n- Missing baselines: Two strong and relevant baselines for sparse-view NVS are missing. (1) MAtCha Gaussians (CVPR 2025): this method integrates monocular depth priors to achieve high-quality novel view synthesis from sparse inputs. (2) Difix3D+ (CVPR 2025): this work tackles sparse-view NVS by progressively augmenting the training set using diffusion-based image enhancement. Including these baselines would provide a more complete and fair comparison of the proposed method’s effectiveness.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)