Erosion (morphology)

Erosion ( from Latin: erodere = nibble ) is a basic operation of the morphological image processing.

Binary image

The basic operation of erosion is implemented using a pattern mask. The structure mask is a small subset of the total image which is used for testing the image to be examined. For each mask, a reference point is defined, which allows placing the mask at a particular pixel location. The actual operation consists of the pixel-wise displacement of the structure mask over the entire image.

It is checked:

Can the question be answered with yes, as part of the pixels of the image, in which is the reference point of the mask structure at the point where the eroded amount.

The morphological erosion (with A as an image and X be patterned as an element ) is quoted as follows:

Gray-scale image processing

On a grayscale image erosion works with a structuring element similar to a minimum filter. Dark structures are larger, brighter reduced.

Where the domain of the mask represents.

Generalization

In the framework of the theory of mathematical morphology images are seen as elements of a dressing. Thus, the erosion can generally be prepared. An operator on a (complete) association is erosion when it is invariant with respect to the Infimumsbildung. Clearly this means that you disassemble an image into individual structures, respectively erode this and then can overlay the result images. The filter thus to any structure regardless of the context.

The dual to the erosion operator is the dilatation.