Page 123 -

Chapter 3 ■ Digital Morphology 97

In more or less plain English, this says that the complement of an erosion is
the same as a dilation of the complement image by the reflected structuring
element. If the structuring element is symmetrical, reflecting it does not change
it, and the implication of Equation 3.12 is that the complement of an erosion
of an image is the dilation of the background, in the case where simple is the
structuring element.

The structuring element is translated to the position Now the structuring element is translated to the next
of a black pixel in the image. In this case all members black pixel in the image, and there is one pixel that
of the structuring element correspond to black image does not match. The result is a white pixel.
pixels, so the result is a black pixel.

At the next translation there is another match so, The final translation is not a match, and the result is a
again, the pixel in the output image that corresponds white pixel. The remaining image pixels are white and
to the translated origin of the structuring element is could not match the origin of the structuring element;
set to black. they need not be considered.
Figure 3.7: Binary erosion using a simple structuring element.