Given a sample of an abstract manifold immersed in some Euclidean space, we describe a way to recover the singular homology of the original manifold. It consists in estimating its tangent bundle -- seen as subset of another Euclidean space -- in a measure theoretic point of view, and in applying measure-based filtrations for persistent homology. The construction we propose is consistent and stable, and does not involve the knowledge of the dimension of the manifold. In order to obtain quantitative results, we introduce the normal reach, which is a notion of reach suitable for an immersed manifold.

翻译：给定嵌入欧几里得空间的抽象流形样本，本文提出一种恢复原始流形奇异同调的方法。该方法从测度论视角出发，将流形切丛（视为另一欧几里得空间的子集）作为估计对象，并应用基于测度滤波的持续同调技术。我们构建的框架具有一致性与稳定性，且无需预知流形维度。为获得定量结果，我们引入法向到达距离——这一适用于浸没流形的到达距离概念。