  Organoids are multi-cellular structures which are cultured in vitro from stem
cells to resemble specific organs (e.g., brain, liver) in their
three-dimensional composition. Dynamic changes in the shape and composition of
these model systems can be used to understand the effect of mutations and
treatments in health and disease. In this paper, we propose a new technique in
the field of topological data analysis for DEtecting Temporal shape changes
with the Euler Characteristic Transform (DETECT). DETECT is a rotationally
invariant signature of dynamically changing shapes. We demonstrate our method
on a data set of segmented videos of mouse small intestine organoid experiments
and show that it outperforms classical shape descriptors. We verify our method
on a synthetic organoid data set and illustrate how it generalises to 3D. We
conclude that DETECT offers rigorous quantification of organoids and opens up
computationally scalable methods for distinguishing different growth regimes
and assessing treatment effects.
