Maximum-Likelihood Estimation of Biological Growth Variables
Shapes of biological objects, such as anatomical parts, have been studied intensely in recent years. An emerging need is to model and analyze changes in shapes of biological objects during, for example, growths of organisms. A recent paper by Grenander et al.  introduced a mathematical model, called GRID, for decomposing growth induced diffeomorphism into smaller, local deformations. The basic idea is to place focal points of local growth, called seeds, according to a spatial process on a time-varying coordinate system, and to deform a small neighborhood around them using radial deformation functions (RDFs). In order to estimate these variables – seed placements and RDFS – we first estimate optimal deformation from magnetic resonance image data, and then utilize an iterative solution to reach maximum-likelihood estimates. We demonstrate this approach using MRI images of human brain growth.
KeywordsRadial Displacement Grid Model Biological Object Magnetic Resonance Image Data Seed Location
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