Erosion and Dilation

Many operators in mathematical morphology are based on the use of a small "test-set" B called structuring element (SE). Its shape and size can be chosen in accordance with the segmentation or filtering task.

In order to calculate the morphological erosion of a binary image A, we test for each point x if the structuring element centered in x fits completely into A. If this is the case, x belongs to the eroded set e A. The dilation can be seen as an erosion of the background.

(a) Original (b) Erosion (c) Dilation

Figure 7.5: Erosion and dilation with a circular SE of a retinal image (detail).

(a) Original (b) Erosion (c) Dilation

Figure 7.5: Erosion and dilation with a circular SE of a retinal image (detail).

The gray level dilation/erosion substitutes the value f (x) by the maximum/minimum of f for all the pixels contained in the translated SE Bx:

In Fig. 7.5, the effect of these operations are shown. We see that the erosion enlarges dark details and reduces bright ones and the dilation enlarges bright details and reduces dark ones.

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