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 simple neural network is trained on the input planes to receive a 3D coordinate and return an inside/outside estimate for the query point. This prior is powerful in inducing 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 focusing on high frequencies at later stages. In addition, we identify and analyze a common 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, cutting 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：从平面截面重建3D形状这一挑战性任务源于医学成像与地理信息学等下游应用需求。输入数据为空间稀疏平面上完全定义的内部/外部指示函数，输出则是将该指示函数插值至整个体空间。针对这一稀疏且病态的重建问题，现有方法或重建质量低下，或需依赖目标拓扑、外观信息、输入法向方向等额外先验。本文提出OReX方法，仅通过截面数据即可实现3D形状重建，其核心创新在于采用神经场作为插值先验。通过在输入平面上训练简单神经网络，为查询点提供内/外估计。该先验能有效驱动平滑性与自相似性特征。方法面临的主要挑战在于高频细节的保持——神经先验存在过度平滑倾向。为此，我们提出迭代估计架构与分层输入采样方案，通过粗到细的训练策略在后期阶段聚焦高频特征。此外，我们识别并分析了网格提取步骤中常见的涟漪效应，通过约束输入内外边界处指示函数的空间梯度从根源缓解该问题。大量定性与定量实验表明，本方法兼具鲁棒性与精确性，且能随输入规模扩展。与现有方法及近期潜在解决方案相比，我们取得了最优结果，并通过消融实验验证了各创新点的有效性。