Abstract: In the pattern matching context, “metamorphosis” implement a compromise between template matching and interpolation. Under the umbrella of a general abstract theory, it can be declined in a series of modalities allowing for the comparison of landmarks, curves, images, densities or general measures. They always provide a Riemannian metric on the considered, generally infinite dimensional, space of deformable objects.
In this talk, we will describe the underlying theory, including the associated variational problems, Euler-Lagrange equations and relevant algorithms. Some cases (namely landmark, images and densities) will be illustrated by numerical experiments.