Uninitialized, globally optimal, graph-based rectilinear shape segmentation - the opposing metrics method

We present a new approach for the incorporation of shape information into a segmentation algorithm. Unlike previous approaches to the problem, our method requires no initialization, is non-iterative and finds a steady-state (i.e., global optimum) solution. In the present work, we are specifically focused on the segmentation of rectilinear shapes. The key idea is to use the fact that certain shape classes optimize the ratio of specific metrics, which can be expressed as graph Laplacian matrices applied to indicator vectors. We show that a relaxation of the binary formulation of this problem allows a global solution via generalized eigenvectors. The approach is tested on both synthetic examples and natural images.