Pseudo-Boolean Polynomials Approach To Edge Detection And Image Segmentation
Tendai Mapungwana ChikakeThe Sci- entific and Educational Mathematical Center " Sofia Kovalevskaya Northwestern Center for Math- ematical Research " in Pskov State University , Sovetskaya Ulitsa , 21 , Pskov , Pskovskaya oblast' , 180000 , Russian FederationBoris GoldengorinDepartment of Mathematics , New Uzbekistan University , Tashkent , 100007 , UzbekistanAlexey SamosyukDepartment of Discrete Mathematics , Phystech School of Applied Mathematics and Informatics , Moscow Institute of Physics and Technology , Institutsky lane 9 , Dolgoprudny , Moscow region , 141700 , Russian Federation ,
2023en
ABI
Annotatsiya
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.
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