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Organoids are multi-cellular structures which are cultured in vitro from stemcells to resemble specific organs (e.g., brain, liver) in theirthree-dimensional composition. Dynamic changes in the shape and composition ofthese model systems can be used to understand the effect of mutations andtreatments in health and disease. In this paper, we propose a new technique inthe field of topological data analysis for DEtecting Temporal shape changeswith the Euler Characteristic Transform (DETECT). DETECT is a rotationallyinvariant signature of dynamically changing shapes. We demonstrate our methodon a data set of segmented videos of mouse small intestine organoid experimentsand show that it outperforms classical shape descriptors. We verify our methodon a synthetic organoid data set and illustrate how it generalises to 3D. Weconclude that DETECT offers rigorous quantification of organoids and opens upcomputationally scalable methods for distinguishing different growth regimesand assessing treatment effects.

Detecting Temporal shape changes with the Euler Characteristic Transform