提出可微分的形态度量方法，用于精准量化生物形状动态变化。
A Continuous and Interpretable Morphometric for Robust Quantification of Dynamic Biological Shapes
- 基于前向传播符号距离构建平滑可微的几何拓扑编码
- 在小鼠原肠胚类器官中预测体轴形成，精度与速度均超卷积网络
- 适合需要解释性与动态建模的生物图像分析任务
我们提出推向前符号距离形态度量（PF-SDM），用于生物医学影像中的形状量化。该方法紧凑编码闭合形状的几何与拓扑特性，包括骨架和对称性，提供鲁棒且可解释的形状比较与机器学习特征。PF-SDM具备数学光滑性，可计算梯度与微分几何量，并能扩展至时间动态建模，支持融合空间强度分布（如基因标记）与形状演化。我们阐述了PF-SDM理论，在合成数据上进行基准测试，并应用于小鼠原肠胚类器官的体轴形成预测，其准确率与速度均优于卷积神经网络基线。
原文摘要 · Abstract (English)
We introduce the Push-Forward Signed Distance Morphometric (PF-SDM) for shape quantification in biomedical imaging. The PF-SDM compactly encodes geometric and topological properties of closed shapes, including their skeleton and symmetries. This provides robust and interpretable features for shape comparison and machine learning. The PF-SDM is mathematically smooth, providing access to gradients and differential-geometric quantities. It also extends to temporal dynamics and allows fusing spatial intensity distributions, such as genetic markers, with shape dynamics. We present the PF-SDM theory, benchmark it on synthetic data, and apply it to predicting body-axis formation in mouse gastruloids, outperforming a CNN baseline in both accuracy and speed.
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