Pseudo-Boolean Polynomials Approach To Edge Detection And Image Segmentation

TL;DR

This paper presents a deterministic method for edge detection and image segmentation using pseudo-Boolean polynomials to classify image regions based on polynomial degrees, tested on simple and complex images.

Contribution

It introduces a novel pseudo-Boolean polynomial-based approach for edge detection and segmentation, leveraging polynomial properties for image analysis.

Findings

Feasibility demonstrated on primitive shape images

Effective classification of blob and edge regions

Potential application to complex aerial images

Abstract

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.