New Morphological Operators Based On Formal Concept Analysis

Mathematical morphology is a nonlinear methodology for image analysis based on rigorous mathematical theories,which has been found applications in a broad range of neighboring fields,including image enhancement,image restoration and image filtering.The main idea of mathematical morphology is the structuring element with certain shape and size which is used to detect and extract the corresponding geometric shape for image recognition and analysis.The selection of structuring element is very crucial because different shape and size of structuring element lead to totally different results.However,following the development of color images,the disadvantages of classic structuring element appears.The structuring element with fixed shape and size ignore the local characteristics of images so that it could not adapt to the images which have complex content.Thus,new mathematical morphology operators are proposed to address above problem based on formal concept analysis which provides a systematic way of structuring information.Firstly,a new color ordering,i.e.improved W ordering,is proposed to address the problem of vector sorting and to get a more intuitive morphological result.Then,a mapping algorithm from color image to formal context is proposed based on the fundamental theory of formal concept analysis.The formal concept is extracted from formal context which can be used to analysis and obtain the structural information in color images.This kind of formal concept is regarded as the structuring element,namely concept structuring element,for constructing the basic morphological operators,including dilation,erosion,opening and closing.Experimental results are provided to show the practical behavior of new operators.And discusses on the properties of new operators are also given showing the feasibility and rationality of operators.Next,the proposed method is compared against the state-of-the-art morphology framework i.e.color soft morphology,and the classic one to give an insight into the superiority in preserving structural information of the proposed method.The images are carried out under different color space and the results are compared comprehensively through qualitative and quantitative way.Experimental results show that the operators based on formal concept analysis outperform other kind of operators in preserving image topology and detail information.Finally,a group of new morphological gradient operators are developed to achieve the task of edge extraction based on proposed operators.The experimental results show that the novel gradient operators are more effective than the classic method in preserving important detail and structural information.