Gaussian radial growth

Abstract

The growth of planar and spatial objects is often modelled using one-dimensional size parameters, e.g., volume, area or average width. We take a more detailed approach and model how the boundary of a growing object expands in time. We mainly consider star-shaped planar objects. The model can be regarded as a dynamic deformable template model. The limiting shape of the object may be circular but this is only one possibility among a range of limiting shapes. An application to tumour growth is presented. A 3D version of the model is presented and an extension of the model, involving time series, is briey touched upon.