  A functional for joint variational object segmentation and shape matching is
developed. The formulation is based on optimal transport w.r.t. geometric
distance and local feature similarity. Geometric invariance and modelling of
object-typical statistical variations is achieved by introducing degrees of
freedom that describe transformations and deformations of the shape template.
The shape model is mathematically equivalent to contour-based approaches but
inference can be performed without conversion between the contour and region
representations, allowing combination with other convex segmentation approaches
and simplifying optimization. While the overall functional is non-convex,
non-convexity is confined to a low-dimensional variable. We propose a locally
optimal alternating optimization scheme and a globally optimal branch and bound
scheme, based on adaptive convex relaxation. Combining both methods allows to
eliminate the delicate initialization problem inherent to many contour based
approaches while remaining computationally practical. The properties of the
functional, its ability to adapt to a wide range of input data structures and
the different optimization schemes are illustrated and compared by numerical
experiments.
