New Morphological Operators On Structural Hypergraph

Mathematical morphology,an image processing subject with rigorous mathematical theory basis,is widely used in the fields of image processing.In mathematical morphology operation,the structure elements are used to analyze and deal with the morphological and structural features of the image.The results are different after morphology image processing with the difference in the selection of structure elements.Therefore,the selection of structure elements is very important in the image processing of mathematical morphology.In traditional morphological processing,structure elements are fixed,which is not suitable for every region of the image and can lead to the loss of details.Therefore,it is necessary to improve the structure elements of the traditional morphology.As hypergraphs have good performance in structuring information,new morphological operators on structural hypergraph are proposed to avoid the loss of details caused by fixed structure element in traditional morphological operators effectively.In this paper,a new grayscale morphological model on structural hypergraph is proposed and applied to the edge extraction of grayscale image.At the same time,based on the distance of grayscale image and connected domain,the hypergraph model in gray image is established.The concept of structural hypergraph in grayscale image is also proposed by dividing the structure of hypergraph.Then,the grayscale morphological operators on structural hypergraph are defined.Experiments show that the new operators can not only achieve the effect of image morphological processing,but also effectively solve the serious problem of missing plenty of details and preserve more image information.Meanwhile,the processed image is soft and conform to the visual characteristics of human eyes.As the new operators are applied to the grayscale image edge extraction,new edge extraction operators on structural hypergraph are defined.The experiments show that the new grayscale morphological edge extraction operators are better in processing the edge of the local detail.Then,as the grayscale morphology on structural hypergraph is extended to color image,a new color morphology on structural hypergraph is proposed and applied to the edge extraction of color images.By introducing the concept of color image distance,color ordering relations and connected domain,the hypergraph model is established in color image.The concept of the structure hypergraph in the color image is also proposed.On this basis,new color morphological operators on structural hypergraph are defined,and their properties are also analyzed.Experiments show that the new operators not only achieve the effect of color image morphological processing,but also effectively protect the texture and detail information of the image.Meanwhile,using the new operators can avoid the destruction of the color topological structure,which make the results have strong relevance with the original image.Then,as the new operators are applied to the edge extraction of color images,new color morphological edge extraction operators based on structural hypergraph is proposed.Compared with the existing color morphological edge extraction operator,the new operators can effectively protect and extract the local edge of the image,which shows the effectiveness and innovation of the edge extraction operator proposed in this paper.