[论文解读] Topological shape transform for thymus structures

Haochen Yang, Vadim Lebovici+6 more|arXiv (Cornell University)|Feb 21, 2026

Topological and Geometric Data Analysis被引用 0

一句话总结

SampEuler，一种基于欧拉特征变换的鲁棒形状描述符，用于量化胸腺结构；它优于一些基于拓扑的方法，并能在胸腺组织中提供随年龄变化的结构洞见。

ABSTRACT

The Euler characteristic transform (ECT) is an emerging and powerful framework within topological data analysis for quantifying the geometry of shape. The applicability of ECT has been limited due to its sensitivity to noisy data. Here, we introduce SampEuler, a novel ECT-based shape descriptor designed to achieve enhanced robustness to perturbations. We provide a theoretical analysis establishing the stability of SampEuler and validate these properties empirically through pairwise similarity analyses on a benchmark dataset and showcase it on a thymus dataset. The thymus is a primary lymphoid organ that is essential for the maturation and selection of self-tolerant T cells, and within the thymus, thymic epithelial cells are organized in complex three-dimensional architectures, yet the principles governing their formation, functional organization, and remodeling during age-related involution remain poorly understood. Addressing these questions requires robust and informative shape descriptors capable of capturing subtle architectural changes across developmental stages. We develop and apply SampEuler to a newly generated two-dimensional imaging dataset of mouse thymi spanning multiple age groups, where SampEuler outperforms both persistent homology--based methods and deep learning models in detecting subtle, localized morphological differences associated with aging. To facilitate interpretation, we develop a vectorization and visualization framework for SampEuler, which preserves rich morphological information and enables identification of structural features that distinguish thymi across age groups. Collectively, our results demonstrate that SampEuler provides a robust and interpretable approach for quantifying thymic architecture and reveals age-dependent structural changes that offer new insights into thymic organization and involution.

研究动机与目标

• 基于欧拉特征变换（ECT）构建一个鲁棒、等距不变的形状描述符，用于量化复杂的3D/2D生物形状。
• 通过引入新的离散采样器（SampEuler）和向量化框架，提升ECT对噪声和错位的鲁棒性。
• 在标准形状数据集上对SampEuler与基于持续同调的方法、DETECT以及深度学习进行基准比较。
• 将SampEuler应用于小鼠胸腺图像，检测随年龄变化的结构变化并将形态与细胞组成相关联。

提出的方法

• 将SampEuler定义为从ECT推动测度中采样曲线得到的离散、等距不变描述符，通过ECCs采样曲线构建。
• 证明当离散化趋于精细时，SampEuler收敛至ECT推动测度，并使用 Wasserstein 距离来刻画连续性。
• 开发SampEuler的向量化与可视化框架，以支持解释和机器学习应用。
• 在合成网络和MPEG-7数据集上对SampEuler进行基准，比较现有的TDA方法和深度学习基线。
• 将SampEuler应用于不同年龄组的2D胸腺上皮细胞（TEC）网络图像，以进行年龄分类并可视化基于形状的特征。

Figure 1 : MOTIVATION FOR NEW PUSHFORWARD MEASURE on ECT. We apply ECT, DETECT, SampEuler, and vectorization of SampEuler to aligned toy simplicial complexes(Left) and randomly rotated simplicial complexes (right).( A ) Representations of simplicial complexes from the two classes. Each class shares

实验结果

研究问题

• RQ1 SampEuler 是否可以在旋转和扰动下提供对形状的鲁棒、等变表示，而ECT在这些情形下敏感？
• RQ2 与持续同调和DETECT在标准基准上的比较，SampEuler 是否提供更高的分类准确性和更短的计算时间？
• RQ3 SampEuler 是否能够揭示胸腺TEC网络中随年龄相关的结构变化，并将形态与细胞组成相关联？

主要发现

• SampEuler及其向量化能区分扰动与对齐的形状，在信息保留方面优于DETECT。
• 在MPEG-7数据集上，SampEuler的分类准确率高于若干传统的TDA方法。
• 基于SampEuler的胸腺象限年龄分类在计算成本低于深度学习模型的同时达到有竞争力的准确度。
• 基于SHAP的解释识别驱动年龄组分类的欧拉特征曲线区域，将形态学与皮质/髓质胸腺结构联系起来。
• 随年龄变化的形态差异在胸腺被包膜附近最为显著，而在皮髓交界处趋于减弱，老胸腺可能存在额外待证的差异。

Figure 2 : CLASSIFICATION STUDY on MPEG7 DATASET. We compare SampEuler with conventional shape analysis methods using the MPEG7 dataset [ 43 ] . ( A ) Examples of the MPEG7 dataset images, one sample from each of the 10-class subset used in previous studies [ 33 , 44 ] . ( B ) The barplot of the acc