Theory Of Spatially-variant Gray-scale Morphology And Its Applications To Image Restoration And Target Detection

As a vital method of artificial vision,the mathematical morphology(MM)has powerful nonlinear image processing and analysis ability.The morphological operators using a probe called a structuring element(SE),to collect image information by the interaction between an image and the structuring element and becomes an important research area in digital image processing for the reason that its fundamental laws and methods have greatly influenced the theory and techniques of image processing.But it still can't describe the meaning of natural scenes and the symbol of human's thoughts effectively and need be further developed.The original theory of MM is set-oriented,and is applied to binary images.Then it is extended to gray-scale images based on umbra theory.But now,there exists a very successful theoretical framework based on complete lattice for MM,and this laid a sound foundation for the characteristic analysis and system design of morphological filters.The works in this dissertation are focus on the theory of spatially-variant(SV)MM in the framework of complete lattice to compensate the inadequacy of classical gray-scale morphological operators and enrich SVMM theory system.First,this work begin with a discussion about the theory of classical gray-scale MM and SVMM and their corresponding typical design methods,and on this basis,adaptive SEs used in SV morphological operators and operator algorithm(or called the operator form)are deeply discussed and researched,the major contributions in this dissertation are as follows:(1)We examine existing adaptive SEs construction methods based on local similarity,and propose a new one,called nonlocal amoeba SE,which have the needed algebraic properties to induce a couple of adjoint dilation and erosion.This method takes the theory of amoeba morphology as a foundation and fused of nonlocal image processing method.By designing nonlocal amoeba SEs,a new family of SV morphological filters are derived that have better performance in removing the noise while adaptively preserving the main structures compared with traditional amoeba filters.(2)Combining subgradient algorithm and Bregman iteration technique,we model a reasonable adaptive morphological regularization method based on nonlocal amoeba kernel for general linear inverse problems in imaging(e.g.,denoising,deblurring and super resolution)and then solve the optimization problem using subgradient technique and Bregmanized operator splitting algorithm.It thus appears useful to build bridges between convex analysis and MM.The image restoration experimental results indicate that the proposed model produce excellent results.(3)Using nonlocal amoeba SEs,genetic programming as a supervised learning algorithm is employed for optimal morphological filter design,and this study offers a new approach for building optimal composite SV morphological filters.The proposed method is chosen because of its capability to easily fit extremely nonlinear morphological operators.Medical experimental results on MRI data sets show that the proposed filter produces excellent results.(4)Different from pixel-based morphological image processing techniques mentioned above,novel SV connected operators(a region-based morphological image processing techniques)are further proposed,and they are applied in image target detection problem.First,in view of the limitations of classical reconstruction operators we present attribute controlled reconstruction operators using the attribute operators filtered image as marker.Then,novel SV morphological reconstruction operators are proposed based on a new type of nonclassical connectivity,where the connectivity rely on nonlocal patch-wise path connectedness relation.This definition means that the reconstruction operators are SV and adaptive SE is defined computing the reconstruction propagation for each pixel on a pilot image.Experimental results on real remote sensing images show that our methods produce excellent results and this provides a possible way for the fusion of SVMM and connected MM.