Dilation (morphology)

Dilatation (from Latin: dilatare = to expand, extend ) is a morphological basis operation in digital image processing.

Dilation means be patterned element

In digital image processing is i.a. dilation applied by means be patterned element. Mathematically, these are in the case of binary images to the formation of the Minkowski sum of image and be patterned element. The dilation of an image with a structuring element is referred to as. Clearly, the means in the case of Binärbildmorphologie that it fits at each pixel of the entire element, the pixel virtually expands to the shape of the structuring element (dilated ).

Gray-scale image processing

On a grayscale image dilation interacts with a structuring element similar to a maximum filter. Light structures are enlarged, darker reduced. where the domain of definition of the structuring element represents. This clearly means the Grauwertdilatation that the gray value mountain man - the values ​​of the pixels are interpreted as height information - from above with a reference form ( the structuring element ) scans.

Generalization

Given a complete lattice. An operator on a dilation if it is distributive with respect to the Supremumsbildung, so the following applies:. Binary images represent the elements of a ( Boolean ) association; the Supremumsbildung is then the ORing of images ( one pixel is set when it is set in one of the output images ). In the case of gray-scale images, the maximum value is taken from the images at each location.

Adjunction of dilation and erosion

In mathematical morphology form dilations and erosions on a complete lattice itself again two mutually isomorphic associations. There is an erosion for each dilation and any erosion dilation with. Thus true for.

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