  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.
