# Diffeomorphic Medial Modeling

## TL;DR

This paper introduces a new shape analysis method combining medial shape modeling with diffeomorphic flows, enabling accurate shape correspondence while preserving medial axis geometry, demonstrated on cardiac ventricular wall data.

## Contribution

It presents a novel diffeomorphic medial modeling approach that maintains medial axis correspondence during shape deformation, improving shape analysis accuracy.

## Key findings

- Successfully modeled left ventricular shape from 3D echocardiography.
- Preserved medial axis geometry during shape matching.
- Enhanced shape correspondence accuracy.

## Abstract

Deformable shape modeling approaches that describe objects in terms of their medial axis geometry (e.g., m-reps [Pizer et al., 2003]) yield rich geometrical features that can be useful for analyzing the shape of sheet-like biological structures, such as the myocardium. We present a novel shape analysis approach that combines the benefits of medial shape modeling and diffeomorphometry. Our algorithm is formulated as a problem of matching shapes using diffeomorphic flows under constraints that approximately preserve medial axis geometry during deformation. As the result, correspondence between the medial axes of similar shapes is maintained. The approach is evaluated in the context of modeling the shape of the left ventricular wall from 3D echocardiography images.