Reconstructing 3D shapes from planar cross-sections is a challenge inspired by downstream applications like medical imaging and geographic informatics. The input is an in/out indicator function fully defined on a sparse collection of planes in space, and the output is an interpolation of the indicator function to the entire volume. Previous works addressing this sparse and ill-posed problem either produce low quality results, or rely on additional priors such as target topology, appearance information, or input normal directions. In this paper, we present OReX, a method for 3D shape reconstruction from slices alone, featuring a Neural Field as the interpolation prior. A modest neural network is trained on the input planes to return an inside/outside estimate for a given 3D coordinate, yielding a powerful prior that induces smoothness and self-similarities. The main challenge for this approach is high-frequency details, as the neural prior is overly smoothing. To alleviate this, we offer an iterative estimation architecture and a hierarchical input sampling scheme that encourage coarse-to-fine training, allowing the training process to focus on high frequencies at later stages. In addition, we identify and analyze a ripple-like effect stemming from the mesh extraction step. We mitigate it by regularizing the spatial gradients of the indicator function around input in/out boundaries during network training, tackling the problem at the root. Through extensive qualitative and quantitative experimentation, we demonstrate our method is robust, accurate, and scales well with the size of the input. We report state-of-the-art results compared to previous approaches and recent potential solutions, and demonstrate the benefit of our individual contributions through analysis and ablation studies.

翻译：从平面切片重建三维形状是一个受医学影像与地理信息学等下游应用启发的挑战。输入是定义在空间稀疏平面集合上的完整内外指示函数，输出则是将该指示函数插值至整个三维体空间。现有方法在处理这一稀疏且病态的问题时，要么产生低质量结果，要么依赖目标拓扑结构、外观信息或输入法线方向等额外先验。本文提出OReX方法——一种仅依赖切片进行三维形状重建的技术，其核心将神经场作为插值先验。通过在输入平面上训练一个轻量神经网络，使其能够返回给定三维坐标的内外估计值，从而构建一个兼具平滑性与自相似性的强先验。该方法的主要挑战在于高频细节的丢失，因为神经先验倾向于过度平滑。为解决该问题，我们提出迭代估计架构与分层输入采样方案，通过引导从粗到精的训练过程，使模型在后期阶段专注于高频信息学习。此外，我们识别并分析了网格提取步骤中产生的涟漪效应，通过在网络训练中对输入内外边界附近指示函数的空间梯度施加正则化，从根源上缓解该问题。大量定性与定量实验表明，本方法具有鲁棒性、准确性，且能随输入规模有效扩展。与现有方法及近期潜在解决方案相比，我们取得了最先进的成果，并通过消融研究与分析验证了各项独立贡献的有效性。