用深度符号距离函数与马尔可夫链蒙特卡洛方法，实现心脏形状重建的不确定性量化。
Uncertainty Quantification for Cardiac Shape Reconstruction with Deep Signed Distance Functions via MCMC methods
- 将心脏形状建模为神经网络的零水平集，通过潜在空间的贝叶斯推断生成多表面重构。
- 在公开数据集上实现高精度重建，并获得校准良好的不确定性估计。
- 适用于需要可信形变分析的临床场景，如心脏手术规划与随访评估。
基于图谱的方法能够从稀疏或噪声较大的数据（如点云）中实现高质量、个性化的心脏解剖结构重建。然而，这些方法主要依赖先验信息，不确定性影响较大，限制了其临床可靠性。本文提出一种概率框架，结合深度符号距离函数（DeepSDFs）与马尔可夫链蒙特卡洛（MCMC）采样，实现不确定性感知的心脏形状重建。心脏几何体被隐式建模为条件于学习到的潜在码的神经网络的零水平集，支持左右心室的多表面重构。通过将重建损失解释为对数似然，我们在潜在空间中进行贝叶斯推断，获得最大后验（MAP）及后验采样重构结果。在公开心脏数据集上的实验表明，该方法能生成准确的重构结果，并提供校准良好的不确定性估计。
原文摘要 · Abstract (English)
Atlas-based approaches allow high-quality, patient-specific shape reconstructions of cardiac anatomy from sparse and/or noisy data such as point clouds. However, these methods are mainly prior-driven, so the impact of uncertainty can be large, limiting their clinical reliability. We propose a probabilistic framework for uncertainty-aware cardiac shape reconstruction that combines Deep Signed Distance Functions (DeepSDFs) with Markov Chain Monte Carlo (MCMC) sampling. Cardiac geometries are modeled implicitly as zero-level sets of a neural network conditioned on learned latent codes, enabling multi-surface reconstruction of the left and right ventricles. By interpreting the reconstruction loss as a log-likelihood, we perform Bayesian inference in the latent space to obtain both maximum a posteriori (MAP) and posterior-sampled reconstructions. Experiments on a public cardiac dataset show that our approach produces accurate reconstructions and well-calibrated uncertainty estimates.
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