一个具有附益性及保序性算子的形态学非局部拓展

近年，形态学非局部拓展工作在图像处理领域受到众多关注.而附益性算子是经典形态学的最基本形式，也是形态学分析方法最重要的变换工具.为此，一些研究者就形态学非局部拓展中如何保持算子的附益性开展工作.本文从理论及实例两个方面说明，相关拓展工作为保持算子的附益性而丢失了保序性的不足；进一步，通过设计非局部权值的获取过程，并结合现有工作，本文提出了一个新的形态学非局部拓展，并定理证明了所得算子同时具备附益性及保序性两个重要性质；人工合成图像及自然图像上的仿真实验也表明了本文所提算法的有效性.

A Nonlocal Extension of Morphology with Adjunction and Order-Preservation Operators

Due to the success in image denoising,the nonlocal strategies have recently been introduced to extend morphology from local to nonlocal.And the operators with adjunction property (adjunction operators for short) are the basic operator form in traditional morphology,which are fundamental in morphological analyzing.However,the adjunction property of operators has usually been missed in the extended works.To overcome the problem,some extensions for nonlocal morphology with adjunctions operators have been provided.Unfortunately,as declared in this paper,another important property,i.e.,order-preservation,has been lost in these extensions.To make up the defect of losing order-preservation,by adapting the nonlocal weights acquisition,a novel nonlocal morphology is proposed in this study.Meanwhile,it has been proved that adjunction and order-preservation properties are both kept in the proposed extension.Finally,the experimental results on synthetic and natural images validate its feasibility and effectiveness.