A Pseudo-Boolean Polynomials Approach for Image Edge Detection

TL;DR

This paper presents a new edge detection method using pseudo-Boolean polynomials that distinguishes edge regions from blobs by analyzing polynomial degrees, offering a novel mathematical approach to image processing.

Contribution

The paper introduces a pseudo-Boolean polynomial-based technique for edge detection, highlighting degree reduction and polynomial properties as key innovations.

Findings

Edge patches produce higher-degree pseudo-Boolean polynomials

Degree reduction correlates with blob regions

Method effectively differentiates edges from blobs

Abstract

We introduce a novel approach for image edge detection based on pseudo-Boolean polynomials for image patches. We show that patches covering edge regions in the image result in pseudo-Boolean polynomials with higher degrees compared to patches that cover blob regions. The proposed approach is based on reduction of polynomial degree and equivalence properties of penalty-based pseudo-Boolean polynomials.