Research On Self-dual Morphological Filter With Idempotence Based On Kernel Elements

As an important nonlinear filter,morphological filter has been widely used in the fields of image processing and analysis,computer vision and pattern recognition.The construction problem of morphological filter mainly involves the selection of structural elements and morphological transformations.Aiming at the construction problem of self-dual morphological filter with idempotence,this paper proposes a design method of this type of filter based on the kernel elements of morphological operators.The main content is divided into the following three parts:Firstly,the related theories of translation-invariant binary morphology and the translation-invariant kernel elements of the morphological operators are described.On this basis,the general properties of the kernel elements of translation-invariant binary morphological operators and the properties of some special operators are studied.Secondly,based on the basic knowledge of SV morphology,the above-mentioned properties of the kernel elements of translation-invariant binary morphological operators are extended to the SV morphology,and the basic properties of the kernel elements of the SV morphology in the case of binary and gray-level are studied respectively,and gave several methods of generating new kernel elements based on the known kernel elements.Finally,according to the kernel representation theorem in SV binary morphology,through SV erosion and dilation,union and intersection operations,operators ? and ? are constructed,and on the basis of studying the morphological center of operators? and ?,the necessary and sufficient conditions for the idempotence of morphological operators are characterized.Furthermore,based on the kernel elements of morphological operators,the construction method of self-dual morphological filter with idempotence and the sufficient conditions for the morphological operators to be strong filter are proposed.