An Improved Estimator of GRID Model for Representing Large Diffeomorphic Deformations

The growth by random iterated diffeomorphisms (GRID) model seeks to decompose large deformations, caused by growth, anomaly, or anatomical differences, into smaller, biologically-meaningful components. These components are spatially local and parametric, and are characterized by radial deformation patterns around randomly-placed seeds. A sequential composition of these components, using the group structure of diffeomorphism group, models the cumulative deformation. The actual decomposition requires estimation of GRID parameters from observations of large growth, typically from 2D or 3D images. While past papers have estimated parameters under certain simplifying assumptions, including that different components are spatially separated and non-interacting, we address the problem of parameter estimation under the original GRID model that advocates sequential composition of arbitrarily interacting components. Using a gradient-based approach, we present an algorithm for estimation of GRID parameters by minimizing an energy function and demonstrate its superiority over the past additive methods.