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.

基于伪布尔多项式的图像碎片的边缘检测方法。

基于伪布尔多项式的图像边缘检测方法

A Pseudo-Boolean Polynomials Approach for Image Edge Detection

We introduce usage of a reduction property of penalty-based formulation of
pseudo-Boolean polynomials as a mechanism for invariant dimensionality
reduction in cluster analysis processes. In our experiments, we show that
multidimensional data, like 4-dimensional Iris Flower dataset can be reduced to
2-dimensional space while the 30-dimensional Wisconsin Diagnostic Breast Cancer
(WDBC) dataset can be reduced to 3-dimensional space, and by searching lines or
planes that lie between reduced samples we can extract clusters in a linear and
unbiased manner with competitive accuracies, reproducibility and clear
interpretation.

通过惩罚项形式的拟布尔多项式的减法性质，我们在聚类分析过程中引入了一种不变维数减少机制。在我们的实验中，我们展示了多维数据，如 4 维的鸢尾花数据集可以被减少到 2 维的空间，30 维的威斯康星州诊断性乳腺癌数据集可以被减少到 3 维的空间，并且通过搜索位于减少样本之间的线或平面，我们可以以线性、无偏的方式提取出具有竞争准确性、可重复性和清晰解释的聚类。

使用伪布尔多项式进行聚类分析的降维

Dimensionality Reduction Using pseudo-Boolean polynomials For Cluster  Analysis

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.

通过在图像块上构建伪布尔多项式，我们介绍了一种确定性的边缘检测和图像分割方法，该方法基于计算提取图像块上的伪布尔多项式的度数，对图像中的斑点和边缘区域进行二分类。我们在包含基本形状的简单图像上测试了该方法的可行性，并将其应用于复杂的景观图像等复杂情况。该提议方法基于基于惩罚的伪布尔多项式的简化、多项式度数和等价性属性的利用。