用概率方法融合观测与形状先验，实现噪声下3D形状高精度重建。
Generative Shape Reconstruction with Geometry-Guided Langevin Dynamics
- 基于扩散模型的Langevin动力学，每步保持观测一致性
- 在缺失数据下几何精度优于现有方法，鲁棒性显著提升
- 适合需要真实感且需对齐观测数据的3D重建任务
从不完整或噪声观测中重建完整的3D形状是一个根本上病态的问题，需在测量一致性与形状合理性之间取得平衡。现有形状重建方法在理想条件下可实现强几何保真度，但在存在缺失数据或噪声时表现不佳；而近期的3D生成模型虽能合成高度逼真、细节丰富的形状，却难以与观测数据一致。本文提出GG-Langevin：一种几何引导的Langevin动力学方法，通过遍历由扩散模型诱导的Langevin轨迹，在每一步均保持测量一致性，从而生成既符合观测又满足数据先验的形状。大量实验证明，相较于现有表面重建方法，GG-Langevin在几何准确性与对缺失数据的鲁棒性方面均有显著提升。
原文摘要 · Abstract (English)
Reconstructing complete 3D shapes from incomplete or noisy observations is a fundamentally ill-posed problem that requires balancing measurement consistency with shape plausibility. Existing methods for shape reconstruction can achieve strong geometric fidelity in ideal conditions but fail under realistic conditions with incomplete measurements or noise. At the same time, recent generative models for 3D shapes can synthesize highly realistic and detailed shapes but fail to be consistent with observed measurements. In this work, we introduce GG-Langevin: Geometry-Guided Langevin dynamics, a probabilistic approach that unifies these complementary perspectives. By traversing the trajectories of Langevin dynamics induced by a diffusion model, while preserving measurement consistency at every step, we generatively reconstruct shapes that fit both the measurements and the data-informed prior. We demonstrate through extensive experiments that GG-Langevin achieves higher geometric accuracy and greater robustness to missing data than existing methods for surface reconstruction.
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