project

Continuous Medial Representation

This project's goal is to extend and improve the medial modeling methodology on which some of PICSL's morphometry and functional imaging analysis projects are based. In the medial modeling technique, deformable templates are fitted to anatomical objects under constraints that preserve the geometrical structure of the template's medial axis. These constraints allow statistical morphometric analysis to leverage the rich set of shape features by the medial axes. In particular, medial axis explicitly describe the thickness of objects, and thickness is a feature of great interest in studies involving neurodegeneration and similar biological processes.

Deformable modeling with medial constraints presents a significant methodological challenge. The boundary of a 3D object and its medial axis are related by a set of non-linear equality constraints, which our models must satisfy throughout deformation. Our present solution to this problem is to define the medial model as a solution of Poisson equation whose boundary conditions embody the non-linear constraints. At present, this approach is limited to models whose medial axis is formed by a single manifold. Such models have been used successfully to answer hypotheses about the hippocampus in 3D and the corpus callosum in 2D.

aims

Automatic Segmentation
Many anatomical structures can not be delineated on the basis of intensity contrast with surrounding tissues. Segmentation of such structures can benefit from the Bayesian model-based approach, in which the shape and the appearance of the target structure are modeled as probability distributions. Medial models make it possible to use rich geometric features like thickness in shape priors. Furthermore, medial models offer an attractive way in which to sample appearance information: image values inside of the object can be sampled along vectors orthogonal to the model's boundary in a way that guarantees one-to-one and onto parameterization of the object's interior.

Medial Branching Representation
Not all structures can be modeled using a single medial manifold. We are working on extending our method to modeling branching of 3D medial manifolds. We indend to develop a model that circumvents having to satisfy the non-linear constraints of medial geometry in practice, while still allowing the attractive properties of continuous medial models to be leveraged. The initial application of this approach will be to modeling the myocardium.

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