Deformable modeling using a 3D boundary representation with quadratic constraints on the branching structure of the Blum skeleton.

We propose a new approach for statistical shape analysis of 3D anatomical objects based on features extracted from skeletons. Like prior work on medial representations, the approach involves deforming a template to target shapes in a way that preserves the branching structure of the skeleton and provides intersubject correspondence. However, unlike medial representations, which parameterize the skeleton surfaces explicitly, our representation is boundary-centric, and the skeleton is implicit. Similar to prior constrained modeling methods developed 2D objects or tube-like 3D objects, we impose symmetry constraints on tuples of boundary points in a way that guarantees the preservation of the skeleton's topology under deformation. Once discretized, the problem of deforming a template to a target shape is formulated as a quadratically constrained quadratic programming problem. The new technique is evaluated in terms of its ability to capture the shape of the corpus callosum tract extracted from diffusion-weighted MRI.