We propose a model for segmentation problems
involving an energy concentrated on the vertices of an unknown
polyhedral set, where the contours of the images to be recovered
have preferred directions and focal points.
We prove that such an energy is obtained as a Γ-limit of
functionals defined on sets with smooth boundary that
involve curvature terms of the boundary.
The minimizers of the limit functional are polygons with
edges either parallel to some prescribed directions or pointing to some
fixed points, that can also be taken as unknown of the problem.