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Data-driven quasiconformal morphodynamic flows
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Paper
Data-driven quasiconformal morphodynamic flows
2024
Overview
Temporal imaging of biological epithelial structures yields shape data at discrete time points, leading to a natural question: how can we reconstruct the most likely path of growth patterns consistent with these discrete observations? We present a physically plausible framework to solve this inverse problem by creating a framework that generalises quasiconformal maps to quasiconformal flows. By allowing for the spatio-temporal variation of the shear and dilatation fields during the growth process, subject to regulatory mechanisms, we are led to a type of generalised Ricci flow. When guided by observational data associated with surface shape as a function of time, this leads to a constrained optimization problem. Deploying our data-driven algorithmic approach to the shape of insect wings, leaves and even sculpted faces, we show how optimal quasiconformal flows allow us to characterise the morphogenesis of a range of surfaces.
Publisher
Cornell University Library, arXiv.org
Subject
