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Cell biologists study in parallel the morphology of cells with the regulationmechanisms that modify this morphology. Such studies are complicated by theinherent heterogeneity present in the cell population. It remains difficult todefine the morphology of a cell with parameters that can quantify thisheterogeneity, leaving the cell biologist to rely on manual inspection of cellimages. We propose an alternative to this manual inspection that is based ontopological data analysis. We characterise the shape of a cell by its contourand nucleus. We build a filtering of the edges defining the contour using aradial distance function initiated from the nucleus. This filtering is thenused to construct a persistence diagram that serves as a signature of the cellshape. Two cells can then be compared by computing the Wasserstein distancebetween their persistence diagrams. Given a cell population, we then compute adistance matrix that includes all pairwise distances between its members. Weanalyse this distance matrix using hierarchical clustering with differentlinkage schemes and define a purity score that quantifies consistency betweenthose different schemes, which can then be used to assess homogeneity withinthe cell population. We illustrate and validate our approach to identifysub-populations in human mesenchymal stem cell populations.

Persistence diagrams as morphological signatures of cells: A method to measure and compare cells within a population