Research On Nonlocal Extension Of Mathematical Morphology

As a traditional nonlinear tool for image processing,mathematical morphology(MM)is yet applied widely.Based on set theory,it focuses on the geometric structure of images.The key idea is to design different structuring elements and operators to measure images according to different task requirements.Because of the rigorous theoretical basis and various operators,mathematical morphology can be applied to a variety of application scenarios.However,the traditional mathematical morphology(TMM)is still belonged to local operations,and thus nonlocal extensions have been studied due to their advantages of adaptivity and nonlocal self-similarity.However,the nonlocal extensions faced with several challenging tasks such as difficult to hold the theoretical properties,gray value deviation,noise sensitivity,high algorithm complexity and poor reliability of structuring element.This thesis studies these drawbacks in the nonlocal extensions profoundly.The main contents and contributions are as follows:1)A novel nonlocal mathematical morphology(RNLMM)is proposed.The reliability of structuring elements is improved by k-reciprocal nearest neighbors(KRNN).To improve the robustness to noise effectively,the traditional(local)operators and nonlocal ones are serially combined in the operator implementation.Theoretical proofs indicate that the operators of RNLMM keep the important mathematical properties successfully.2)A local-nonlocal mathematical morphology(LNLMM)is proposed.In LNLMM,we use flat structuring element to avoid gray value deviation and introduce local information to suppress noises,and thus the performance has been improved.Moreover,to speed up the nonlocal computation involved,we construct the structuring element in low-dimensional space.Benefiting from the constraint of KRNN,the operators of LNLMM theoretically inherit the important mathematical properties from traditional mathematical morphology,that gives solid supports in applications.