| A toy model for a shape recognition problem in computer vision is studied within the framework of the Monge-Kantorovich optimal transport problem with a view to understand the underlying geometry of boundary matching. This formulation generates an optimal transport problem between measures supported on the boundaries of two planar domains O, Λ ⊂ R2 ---with optimality measured against a cost function c(x, y) that penalizes a convex combination of distance |x - y|2 and a relative change in local orientation |nO( x) - nΛ(y)| 2. The questions addressed are the existence, uniqueness, smoothness and geometric characterization of the optimal solutions. |
