论文标题
关于形态开放和关闭的吸收特性的条件
On the Conditions of Absorption Property for Morphological Opening and Closing
论文作者
论文摘要
本文旨在为数学形态中的转移纳入理论基础。在本文中，我们证明了有关移动包容性属性的结构元素的形态开放和闭合将保留图像的排序，而此属性在粒度分析和相关图像处理任务中很重要。此外，我们提出了一种系统的方式，称为移动包含的分解定理，以构建具有移位包含属性的结构元素序列。此外，讨论了图像域的影响，并定义了指定的弱移位包含条件，这被证明是确保订单保留属性的等效条件。
This paper aims to establish the theoretical foundation for shift inclusion in mathematical morphology. In this paper, we prove that the morphological opening and closing concerning structuring elements of shift inclusion property would preserve the ordering of images, while this property is important in granulometric analysis and related image processing tasks. Furthermore, we proposed a systematic way, called the decomposition theorem for shift inclusion, to construct sequences of structuring elements with shift inclusion property. Moreover, the influences of the image domain are discussed and the condition named weak shift inclusion is defined, which is proved as an equivalent condition for ensuring the order-preserving property.
