用神经元结构直接提取高精度3D表面，不依赖传统采样网格。
Marching Neurons: Accurate Surface Extraction for Neural Implicit Shapes
- 基于神经元分割空间的特性，设计深度优先遍历法提取表面。
- 在多种模型上实现比传统方法更高的几何保真度，精度显著提升。
- 适合需要高精度3D重建的研究者，尤其适用于复杂神经隐式模型。
精确的三维表面几何表示在3D视觉计算中至关重要。显式表示（如多边形网格）与隐式表示（如符号距离函数）各有优势，二者之间的高效转换日益重要。传统的隐式表示表面提取方法（如广泛使用的Marching Cubes算法）依赖于空间分解和采样，受限于固定且有限的分辨率，导致精度不足。本文提出一种从神经隐式函数中解析提取表面的新方法。该方法原生支持并行计算，可处理大型神经网络。利用每个神经元对空间进行划分的特性，我们设计了一种深度优先遍历策略，以高效追踪编码的表面。生成的网格能忠实还原网络中的全部几何信息，无需人为的空间离散化，在多种形状和网络架构下均实现前所未有的精度，同时保持竞争力的运行速度。
原文摘要 · Abstract (English)
Accurate surface geometry representation is crucial in 3D visual computing. Explicit representations, such as polygonal meshes, and implicit representations, like signed distance functions, each have distinct advantages, making efficient conversions between them increasingly important. Conventional surface extraction methods for implicit representations, such as the widely used Marching Cubes algorithm, rely on spatial decomposition and sampling, leading to inaccuracies due to fixed and limited resolution. We introduce a novel approach for analytically extracting surfaces from neural implicit functions. Our method operates natively in parallel and can navigate large neural architectures. By leveraging the fact that each neuron partitions the domain, we develop a depth-first traversal strategy to efficiently track the encoded surface. The resulting meshes faithfully capture the full geometric information from the network without ad-hoc spatial discretization, achieving unprecedented accuracy across diverse shapes and network architectures while maintaining competitive speed.
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