New Grayscale Morphology Operator Based On The Hypergraph And The Mathematical Morphology

Mathematical morphology has been widely used in various fields of image processing which has a strict mathematical theory and simple thought. Structural elements, the different shape and size of which would lead to different results, play an important role in the processing of mathematical morphology, therefore, choosing and designing the suitable structural elements is crucial. In the use of mathematical morphology for image processing, the designers can only base on personal experience in determining the size and shape characteristics of structural elements and roughly estimate the basic characteristics of the target images, which makes the processed image difficult to achieve the desired effect.The appearance of hypergraph helps people better use the theory of mathematical morphology for image processing in a certain extent. Hypergraph, the most general structure in discrete mathematics, is a subset system of a finite set. Image is a structured representation of information. Based on this reason, the ordinary image can be transformed to a hypergraph model, which can integrate hypergraph theory and mathematical morphology theory, so as to expand the application range of the two theories.Because hypergraph can better express the characteristics of structured information, first of all, this paper designs a reasonable algorithm of gray image turning into hypergraph, then based on the concept of the super sides in hypergraph theory, puts forward corrosion expansion as well as the opening and closing operation of the new operator in the grayscale morphology. Experiments show that using the new operator, can effectively solve the serious problem of image detail information loss in traditional gray-scale morphological operator in image processing, fully retaining more image information, thus improving the precision of the image processing.However, the new operator still has a problem of selecting structural elements in dealing with a gray image. In order to overcome this defect, this paper based on the hypergraph model, using the hyperedge operation between the set, puts forward a new operator of union and intersection operation. This paper selects the results of union and intersection operation as structural elements, and proposes the new operator of expansion, corrosion, opening and closing based on the union and intersection operation of hyperedge in gray image processing. The structural elements in the new operator is changed based the relationships of each pixel and its neighboring pixels, which makes the new operators have more advantages than traditional gray-scale morphological operator. Experiments show that the use of the results of the union and intersection operation as structural elements, not only can make the automation of the selection of structure elements, solving the difficulties of traditional morphological structure elements in the selection, but also can effectively avoid the problem of serious details loss caused by fixed structure element in the part of the image area.On this basis,IC defect image edge extraction is tested by using the new operator. The result turns out that, compared with the edge extraction based on the traditional gray-scale morphological operator and the gray-scale morphological operator based on the super edge, the edge extraction based on the new operator results in more accurate test results.