We propose a model for segmentation problemsinvolving an energy concentrated on the vertices of an unknownpolyhedral set, where the contours of the images to be recoveredhave preferred directions and focal points.We prove that such an energy is obtained as a Γ-limit offunctionals defined on sets with smooth boundary thatinvolve curvature terms of the boundary.The minimizers of the limit functional are polygons withedges either parallel to some prescribed directions or pointing to somefixed points, that can also be taken as unknown of the problem.
