Moving templates

Laurent Younes
Ecole Normale Supérieure, France

Many situations in image analysis model a set of visual objects, like images,
shapes, patterns of points, which can be affected by "deformations". Following
the seminal approach of Grenander's deformable template theory, we have designed
during the last decade, theoretical and numerical methods to analyze the action
of diffeomorphisms on geometric structures, like landmarks, shapes and images.
The basic assumption of the theory of deformable templates is that observable
objects are belong to the orbit of a fixed template, under the action of a group
of diffeomorphisms. In this talk, following the point of view is slightly
different, because the basepoint of the deformation (the template) is allowed to
vary during a process called a metamorphosis. We show how to design these
"deformable templates with moving templates", and study their metric and
geometric properties in several cases of interest.

Presentation Files (Zip Archive)

Back to Graduate Summer School: Mathematics in Brain Imaging