Research On Morphological Adaptivity And Cross-modal Extension

As a traditional nonlinear image processing tool,mathematical morphology(MM)is still widely applied in many fields.Benefiting from the fixed structuring element,the theoretical foundation of traditional MM is solid.However,as a matter of fact,the individual pixels are usually not identical in the whole image under study.That means,the frozen implementation of structuring element is not always easy to meet the practice.Hence,it has been a constant topic to design the adaptive morphologies whose structuring elements can vary with different contents,and attracted a great amount of attention from the community.Traditional mathematical morphology(TMM)is not well in structure-preserving,and the existing adaptive morphologies usually miss important mathematical properties,have poor robustness to noise and are only limited to single mode image.To address these problems,in this work,two kinds of different adaptive mathematical morphologies are proposed,and proved and simulated.The research contents are as follows:(1)With the a-cut of a fuzzy set,this work gives an adaptive structuring element,and combines it with the fixed structural elements of TMM.By using serial forms to implement the dilation and erosion,a novel adaptive morphology is proposed.As expected,its operators are not only adaptive to image contents but also robust to noises.Meanwhile,the operators inherit the important properties from the traditional ones as many as possible.The theoretical proofs and simulated results both support the same conclusion.Experiments on edge detection and noise reduction further suggest that the proposed morphology achieves more powerful performances than the existing ones.(2)By introducing another more reliable image with different modes,the adaptive morphology is further extended and a guided adaptive mathematical morphology is proposed.By considering the joint information of the input and the guidance,the structuring elements are constructed and their members have stronger reliability.Furthermore,the members are dynamically filtered according to 3σ rule,so that the structuring elements became adaptive to the image content.Simultaneously,the symmetry constraints are successfully imposed on the structuring elements by using the mutual nearest neighbor modified product of sparse matrix.Mathematical proofs and simulated experiments both verify that the proposed operators hold important mathematical properties.Denoising experiments on multimodal images show the effectiveness of the proposed morphology in terms of visual quality in denoising and structure-preserving.