Implicit Neural representations (INRs) are widely used for scientific data
reduction and visualization by modeling the function that maps a spatial
location to a data value. Without any prior knowledge about the spatial
distribution of values, we are forced to sample densely from INRs to perform
visualization tasks like iso-surface extraction which can be very
computationally expensive. Recently, range analysis has shown promising results
in improving the efficiency of geometric queries, such as ray casting and
hierarchical mesh extraction, on INRs for 3D geometries by using arithmetic
rules to bound the output range of the network within a spatial region.
However, the analysis bounds are often too conservative for complex scientific
data. In this paper, we present an improved technique for range analysis by
revisiting the arithmetic rules and analyzing the probability distribution of
the network output within a spatial region. We model this distribution
efficiently as a Gaussian distribution by applying the central limit theorem.
Excluding low probability values, we are able to tighten the output bounds,
resulting in a more accurate estimation of the value range, and hence more
accurate identification of iso-surface cells and more efficient iso-surface
extraction on INRs. Our approach demonstrates superior performance in terms of
the iso-surface extraction time on four datasets compared to the original range
analysis method and can also be generalized to other geometric query tasks.

通过改进范围分析技术，我们能够更准确地估计价值范围，从而更准确地识别等值面单元并在 INR 上实现更高效的等值面提取。

利用不确定性传播提高隐式神经表示的等值面提取效率

Improving Efficiency of Iso-Surface Extraction on Implicit Neural  Representations Using Uncertainty Propagation

In this paper, we propose a new method, called DoubleCoverUDF, for extracting
the zero level-set from unsigned distance fields (UDFs). DoubleCoverUDF takes a
learned UDF and a user-specified parameter $r$ (a small positive real number)
as input and extracts an iso-surface with an iso-value $r$ using the
conventional marching cubes algorithm. We show that the computed iso-surface is
the boundary of the $r$-offset volume of the target zero level-set $S$, which
is an orientable manifold, regardless of the topology of $S$. Next, the
algorithm computes a covering map to project the boundary mesh onto $S$,
preserving the mesh's topology and avoiding folding. If $S$ is an orientable
manifold surface, our algorithm separates the double-layered mesh into a single
layer using a robust minimum-cut post-processing step. Otherwise, it keeps the
double-layered mesh as the output. We validate our algorithm by reconstructing
3D surfaces of open models and demonstrate its efficacy and effectiveness on
synthetic models and benchmark datasets. Our experimental results confirm that
our method is robust and produces meshes with better quality in terms of both
visual evaluation and quantitative measures than existing UDF-based methods.
The source code is available at this https URL

本文提出了一种名为 DoubleCoverUDF 的新方法，用于从无符号距离场（UDF）中提取零水平集。该方法通过使用标准的 Marching Cubes 算法，使用学习得到的 UDF 和用户指定的参数 $r$ 提取具有等值 $r$ 的等值面。实验证明，计算得到的等值面是目标零水平集 $S$ 的 $r$- 偏移体的边界，而不管 $S$ 的拓扑结构。接下来，算法通过计算一个覆盖映射将边界网格投影到 $S$ 上，保持网格的拓扑结构并避免折叠。如果 $S$ 是一个可定向流形表面，我们的算法可以通过鲁棒的最小割后处理步骤将双层网格分割成单层。通过对开放模型的三维表面重建以及对合成模型和基准数据集的实验证明了我们算法的有效性和效果。实验结果表明，与现有的基于 UDF 的方法相比，我们的方法具有更好的视觉评估和定量指标。源代码可以在此 https URL 找到。