根据柔性形态学单调性、扩展性、和反扩展性等基本理论,讨论了柔性形态学在边缘检测中的应用.柔性形态变换是在经典形态变换基础上提出的一类非线性算子.它放宽了经典形态变换的定义,以获得一定程度的鲁棒性,但是,还保留了经典形态算子的优良特性.进而从理论上和几何意义上讨论了其进行边缘检测的原理,及算子的选择.另外,还与标准形态算子及Robert算子的处理结果进行了比较.通过计算机模拟实验表明:基于柔性形态学的边缘检测方法,不但几何意义明确,易于构造,而且性能也优于传统检测算子,尤其是具有去噪声的功能.

In this paper,the basic theory of the soft morphology is presented and the soft morphology applied to detecting edge is discussed by its monotonicity, extensibility and anti-extensionality. The soft morphology is a non-linear operations based on standard morphological operations. The idea of soft morphological operations is to relax the standard definitions a little, in such a way that a degree of robustness is achieved while most of the desirable properties of standard morphological operations are maintained. The traditional edges detection methods are compared with the algorithms based on the soft morphological operators after analyzing their geometrical properties and the effects of the structuring element. The simulation results, which are better than the traditional operators illustrate the attractive property of the method. Especially, in the noising condition the method can detect edges without filtering.