  Continuous image morphing is a classical task in image processing. The
metamorphosis model proposed by Trouv\'e, Younes and coworkers casts this
problem in the frame of Riemannian geometry and geodesic paths between images.
The associated metric in the space of images incorporates dissipation caused by
a viscous flow transporting image intensities and its variations along motion
paths. In many applications, images are maps from the image domain into a
manifold (e.g. in diffusion tensor imaging (DTI) the manifold of symmetric
positive definite matrices with a suitable Riemannian metric). In this paper,
we propose a generalized metamorphosis model for manifold-valued images, where
the range space is a finite-dimensional Hadamard manifold. A corresponding time
discrete version was presented by Neumayer et al. based on the general
variational time discretization proposed by Berkels et al. Here, we prove the
Mosco--convergence of the time discrete metamorphosis functional to the
proposed manifold-valued metamorphosis model, which implies the convergence of
time discrete geodesic paths to a geodesic path in the (time continuous)
metamorphosis model. In particular, the existence of geodesic paths is
established. In fact, images as maps into Hadamard manifold are not only
relevant in applications, but it is also shown that the joint convexity of the
distance function which characterizes Hadamard manifolds is a crucial
ingredient to establish existence of the metamorphosis model.
