Selective metamorphosis for growth modelling with applications to landmarks

We present a framework for shape matching in computational anatomy allowing users control of the degree to which the matching is diffeomorphic. This control is given as a function defined over the image and parameterises the template deformation. By modelling localised template deformation we have a mathematical description of growth only in specified parts of an image. The location can either be specified from prior knowledge of the growth location or learned from data. For simplicity, we consider landmark matching and infer the distribution of a finite dimensional parameterisation of the control via Markov chain Monte Carlo. Preliminary numerical results are shown and future paths of investigation are laid out. Well-posedness of this new problem is studied together with an analysis of the associated geodesic equations.