Pseudo-Boolean Polynomials Approach To Edge Detection And Image Segmentation

We introduce a deterministic approach to edge detection and image segmentation by formulating pseudo-Boolean polynomials on image patches. The approach works by applying a binary classification of blob and edge regions in an image based on the degrees of pseudo-Boolean polynomials calculated on patches extracted from the provided image. We test our method on simple images containing primitive shapes of constant and contrasting colour and establish the feasibility before applying it to complex instances like aerial landscape images. The proposed method is based on the exploitation of the reduction, polynomial degree, and equivalence properties of penalty-based pseudo-Boolean polynomials.