# Selective metamorphosis for growth modelling with applications to landmarks

## TL;DR

This paper introduces a shape matching framework in computational anatomy that allows localized control of deformations, enabling growth modeling in specific image regions with applications to landmarks.

## Contribution

It develops a mathematical model for localized template deformation in shape matching, incorporating control over growth regions, and analyzes its well-posedness and geodesic equations.

## Key findings

- Preliminary numerical results demonstrate the framework's potential.
- The model allows specifying or learning growth locations in images.
- Analysis confirms the mathematical well-posedness of the approach.

## Abstract

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.