Although 3D Gaussian Splatting has been widely studied because of its
realistic and efficient novel-view synthesis, it is still challenging to
extract a high-quality surface from the point-based representation. Previous
works improve the surface by incorporating geometric priors from the
off-the-shelf normal estimator. However, there are two main limitations: 1)
Supervising normal rendered from 3D Gaussians updates only the rotation
parameter while neglecting other geometric parameters; 2) The inconsistency of
predicted normal maps across multiple views may lead to severe reconstruction
artifacts. In this paper, we propose a Depth-Normal regularizer that directly
couples normal with other geometric parameters, leading to full updates of the
geometric parameters from normal regularization. We further propose a
confidence term to mitigate inconsistencies of normal predictions across
multiple views. Moreover, we also introduce a densification and splitting
strategy to regularize the size and distribution of 3D Gaussians for more
accurate surface modeling. Compared with Gaussian-based baselines, experiments
show that our approach obtains better reconstruction quality and maintains
competitive appearance quality at faster training speed and 100+ FPS rendering.
Our code will be made open-source upon paper acceptance.

通过直接将法线与其他几何参数耦合，提出了一种深度法线正则化器以完全更新几何参数，并引入置信度项以减轻多视图法线预测的不一致性，同时通过密度化和分割策略对 3D Gaussians 的大小和分布进行正则化，实验结果表明该方法在更快的训练速度和 100+ FPS 渲染时获得更好的重建质量和竞争性外观质量。

VCR-GauS：用于高斯曲面重建的视角一致的深度 - 法线正则化方法

VCR-GauS: View Consistent Depth-Normal Regularizer for Gaussian Surface  Reconstruction

We consider the noise complexity of differentially private mechanisms in the
setting where the user asks $d$ linear queries $f\colon\Rn\to\Re$
non-adaptively. Here, the database is represented by a vector in $\Rn$ and
proximity between databases is measured in the $\ell_1$-metric.
We show that the noise complexity is determined by two geometric parameters
associated with the set of queries.
We use this connection to give tight upper and lower bounds on the noise
complexity for any $d \leq n$. We show that for $d$ random linear queries of
sensitivity~1, it is necessary and sufficient to add $\ell_2$-error
$\Theta(\min\{d\sqrt{d}/\epsilon,d\sqrt{\log (n/d)}/\epsilon\})$ to achieve
$\epsilon$-differential privacy. Assuming the truth of a deep conjecture from
convex geometry, known as the Hyperplane conjecture, we can extend our results
to arbitrary linear queries giving nearly matching upper and lower bounds.
Our bound translates to error
$O(\min\{d/\epsilon,\sqrt{d\log(n/d)}/\epsilon\})$ per answer. The best
previous upper bound (Laplacian mechanism) gives a bound of
$O(\min\{d/\eps,\sqrt{n}/\epsilon\})$ per answer, while the best known lower
bound was $\Omega(\sqrt{d}/\epsilon)$. In contrast, our lower bound is strong
enough to separate the concept of differential privacy from the notion of
approximate differential privacy where an upper bound of $O(\sqrt{d}/\epsilon)$
can be achieved.

本文研究了差分隐私机制在 $d$ 个非适应性线性查询的噪音复杂度，使用几何参数给出了噪音复杂度的上下界，并根据凸几何学中的超平面猜想证明了任意线性查询的结果，提高了先前的结果，揭示了差分隐私概念与近似差分隐私概念之间的分离。