where ∅ is the empty set and B is the structuring element. In words, the dilation of A by B is the set consisting of all the structuring element origin locations where the reflected and translated B overlaps at least some portion of A. The translation of the structuring element in dilation is similar to the mechanics of spatial convolution discussed in Chapter 3. Figure 9.4 does not show the structuring element's reflection explicitly because the structuring element is symmetrical with respect to its origin in this case. Figure 9.5 shows a nonsymmetric structuring element and its reflection.
Dilation is commutative; that is, A ⊕ B = B ⊕ A. It is a convention in image
processing to let the first operand of A ⊕ B be the image and the second