Paper 76: Expansion, corrosion, opening and closing operations--morphology in Digital image processing

Expansion, corrosion, opening and closing operations are the most basic transformations of mathematical morphology.
This paper mainly focuses on the morphology of binary image.
Expansion: The boundary of each 1-pixel connecting component of a two-value image is enlarged by one layer (the hole that fills the edge or 0 pixels inside);
Corrosion: To reduce the boundary point of each 1-pixel connecting component of a two-value image to narrow one layer (can extract the backbone information, remove the Burr, remove the isolated 0 pixels);
Open: First corrosion and then expansion, you can remove the target outside the isolated point
Closed: first expansion and then corrosion, you can remove the hole in the target.
The following reference papers: "The application of mathematical morphology in image processing"

Two-valued morphology
The morphological transformation of binary images in mathematical morphology is a processing process for sets. The essence of its morphological operator is to express the interaction between the set of object or shape and the structure element, and the shape of the structure element determines the shape information of the signal extracted by this operation. Morphological image processing is to move a structure element in the image, and then the structure element and the following two value image are intersection, and so set operation.
The basic morphological operations are corrosion and swelling.
In morphology, structural elements are the most important and basic concepts. The function of structural elements in morphological transformation is equivalent to the "filter window" in signal processing. Using B (x) to represent structural elements, the definition of each point x, Corrosion and expansion in Workspace E is:

The result of corrosion of E with B (x) is to translate the structural element B into a set consisting of all the points of E. The result of the expansion of E with B (x) is that the structure element B is translated to make the intersection of B and e a non-empty point of the set. The process of first corrosion and swelling is called open operation. It has the effect of eliminating small objects, separating objects in slender places and smoothing the boundaries of larger objects. The process of first swelling and corrosion is called closed operation. It has the function of filling the small hole inside the object, connecting the neighboring object and smoothing the boundary.
It can be seen that the two-value morphological expansion and corrosion could be transformed into a set of logical operations, the algorithm is simple, suitable for parallel processing, and easy to implement hardware, suitable for two-value image segmentation, refinement, extraction skeleton, edge extraction, shape analysis. However, in different applications, the choice of structural elements and their corresponding processing algorithms are not the same, the different target images need to design different structural elements and different processing algorithms. The size and shape selection of structural elements will directly affect the results of morphological operation of the image. Therefore, many scholars combine their own application practice, put forward a series of improved algorithms. As proposed by Liang Yong, the edge detection algorithm with multi-directional morphological structure elements has good edge location capability and excellent noise smoothing ability. Sipo proposed a design method combining the structure elements of a quasi-circular structure element or a sequence structure element with the shortest line segment structural elements, used for skeleton extraction, can greatly reduce the computational amount of the morphological operation, and can meet the scale, translation and rotation compatibility, suitable for the analysis and description of the shape.

The main applications of mathematical morphology in image processing include: edge detection, image segmentation, morphological skeleton extraction, noise filtering.
The method of selecting structural elements: Multi-structure element and genetic algorithm.

Paper 76: Expansion, corrosion, opening and closing operations--morphology in Digital image processing