2024/04/10 by Salem Mosleh, Gary P. T. Choi, Mosleh, Salem +3
Computer Science · Earth and Planetary Sciences · #Biological Physics (physics.bio-ph) #Computational Geometry (cs.CG) #FOS: Biological sciences #FOS: Computer and information sciences #FOS: Physical sciences #Geological Modeling and Analysis #Image Processing and 3D Reconstruction #Quantitative Methods (q-bio.QM) #Soft Condensed Matter (cond-mat.soft)
paper · pdf · doi:10.48550/arxiv.2404.07073
openalex publication_date 2024/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.