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. 2019 Jun:11492:208-220.
doi: 10.1007/978-3-030-20351-1_16. Epub 2019 May 22.

Diffeomorphic Medial Modeling

Paul A Yushkevich  1 , Ahmed Aly  1 , Jiancong Wang  1 , Long Xie  1 , Robert C Gorman  2 , Laurent Younes  3 , Alison M Pouch  1
Affiliations

Diffeomorphic Medial Modeling

Paul A Yushkevich et al. Inf Process Med Imaging. 2019 Jun.

Abstract

Deformable shape modeling approaches that describe objects in terms of their medial axis geometry (e.g., m-reps [10]) 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.

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Figures

Fig. 1.
Fig. 1.
Template generation and shape matching in the toy example. (a) Manual template construction by sampling tuples from the skeleton of the source shape. (b) Medial-preserving diffeomorphic flow between the template and a target shape. The deforming medial scaffold of the template (ϕtMO) is in close agreement with the Voronoi skeleton of the deforming template (MϕtO), which illustrates that medial preservation constraints are working. (c) When analogous same shape matching (between BO and Bϕ1O) is performed using point set geodesic shooting without medial preservation constraints, the Voronoi skeleton of the deforming object changes structure and bifurcates (yellow arrows)
Fig. 2.
Fig. 2.
Data attachment, kinetic energy, and constraints over the course of AL optimization for synthetic shape matching.
Fig. 3.
Fig. 3.
Data attachment, kinetic energy, and constraints over the course of AL optimization for the 14 LV wall matching cases.
Fig. 4.
Fig. 4.
Example of shape matching in the LV wall dataset. The top row shows the deforming medial scaffold (colored by thickness = 2× MIB radius) and the deforming boundary as a white wireframe. The bottom row shows the Voronoi skeleton of the deforming boundary, again emphasizing the preservation of medial scaffold structure during deformation.
See this image and copyright information in PMC

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