Abstract: An improved method of graph-based segmentation of objects in images uses the property of rectilinear shape classes which optimize the ratio of specific metrics, that can be expressed as Laplacian matrices applied to indicator vectors. A relaxation of the binary formulation of this problem allows a solution via generalized eigenvectors. This segmentation algorithm incorporating shape information requires no initialization, is non-iterative and finds a steady-state (i.e., global optimum) solution. The method is generally applicable to segmentation of rectilinear shapes.