Image Understanding via Deformable Templates, Differomorphisms, Metrics and Geodesics: Applications to Computational Anatomy

Michael Miller, Johns Hopkins University

We shall describe spaces of images as Grenander deformable templates, orbits under mappings of transformations of prototypes. Both matrix groups from computer vision as well as infinite dimensional diffeomorphisms are examined for Biological shape. Metrics are introduced on the space of images for describing likeness and similarity. The metrics correspond to shortest length paths (geodesics) in the space of mappings. Applications to computational anatomy will be described.