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.

翻译：我们提出了一种确定性方法，通过构建图像块上的伪布尔多项式来实现边缘检测与图像分割。该方法基于从输入图像提取的局部图像块上计算的伪布尔多项式次数，对图像中的斑点区域与边缘区域进行二分类判别。我们首先在包含恒定色与对比色基本形状的简单图像上测试该方法，在验证其可行性后将其应用于诸如航拍景观图像等复杂场景。本方法的核心在于利用基于惩罚项的伪布尔多项式所具有的约简、多项式次数及等价性特征。