A BIOLOGICAL GROWTH METRIC FOR 3D SHAPE REGISTRATION
Mike Syn and Richard Prager
We review the Turing and Oster-Murraym models of biological morphogenesis. From the latter we apply primary mechanisms of extracellular-matrix (ECM) deformation, cell mitosis, cell diffusion and ECM-cell interaction to a model of biological growth, and derive the principal modes of mass flux from the linear eigenmodes of each mechanism. The assumption of uniform mass distribution means that the eigenmodes are the same for elastic, diffusive and convective modes.
We derive a metric of biological growth using the Gompertz function and show that it can also be arrived at from a thermodynamic model of growth inhibition. This metric is to be used in 3D shape registration, and can be computed for partial local registrations using a linear sum of eigenmode projections.
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