We describe a novel continuous medial repre- sentation for describing object geometry and a deformable templates method for tting the representation to images. Our representation simultaneously describes the boundary and medial loci of geometrical objects, always maintaining Blum's symmetric axis transform (SAT) relationship. Cu- bic b-splines dene the continuous medial locus and the as- sociated thickness eld, which in turn generate the object boundary. We present geometrical properties of the rep- resentation and derive a set of constraints on the b-spline parameters. The 2D representation encompasses branching medial loci; the 3D version can model objects with a sin- gle medial surface, and the extension to branching medial surfaces is a subject of ongoing research. We present prelim- inary results of segmenting 2D and 3D medical images. The representation is ultimately intended for use in statistical shape analysis.
['Paul A. Yushkevich', 'P. Thomas Fletcher', 'Sarang C. Joshi', 'Andrew Thall', 'Stephen M. Pizer']
Continuous Medial Representations for Geometric Object Modeling in 2D and 3D