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Example of dilation on a grayscale image using a 5x5 flat structuring element. The top figure demonstrates the application of the structuring element window to the individual pixels of the original image. The bottom figure shows the resulting dilated image. It is common to use flat structuring elements in morphological applications.
A shape (in blue) and its morphological dilation (in green) and erosion (in yellow) by a diamond-shaped structuring element. Mathematical morphology (MM) is a theory and technique for the analysis and processing of geometrical structures, based on set theory, lattice theory, topology, and random functions.
In morphological opening (), the erosion operation removes objects that are smaller than structuring element B and the dilation operation (approximately) restores the size and shape of the remaining objects. However, restoration accuracy in the dilation operation depends highly on the type of structuring element and the shape of the restoring ...
In mathematical morphology, a structuring element is a shape, used to probe or interact with a given image, with the purpose of drawing conclusions on how this shape fits or misses the shapes in the image. It is typically used in morphological operations, such as dilation, erosion, opening, and closing, as well as the hit-or-miss transform.
The closing of the dark-blue shape (union of two squares) by a disk, resulting in the union of the dark-blue shape and the light-blue areas. In mathematical morphology, the closing of a set (binary image) A by a structuring element B is the erosion of the dilation of that set,
In binary morphology, an image is viewed as a subset of a Euclidean space or the integer grid , for some dimension d.Let us denote this space or grid by E.. A structuring element is a simple, pre-defined shape, represented as a binary image, used to probe another binary image, in morphological operations such as erosion, dilation, opening, and closing.
Erosion (usually represented by ⊖) is one of two fundamental operations (the other being dilation) in morphological image processing from which all other morphological operations are based. It was originally defined for binary images , later being extended to grayscale images, and subsequently to complete lattices .
Examples of such operations are thinning, dilating, finding branch points and endpoints, removing isolated pixels, shifting the image a pixel in any direction, and breaking H-connections. Conway's Game of Life is also an example of a 3×3 window operation. Another class of operations is based on the notion of filtering with a structuring element.