How can I compute closure/morphology and dilution for an image using math?

Question

Suppose we have image A and the structuring element B from figure 2. How can I compute A dilated by B and A closed(or can be called morphology) by B? How can I apply math on paper for this?

Answer 1

To dilate image A by structuring element B, place the center of (a copy of) B over each pixel in A, and set all of the pixels under all of (each copy of) B.

To compute the closure of A by B, first dilate A by B, then erode the result by B (actually, by the transpose of B, but as this B is symmetrical, it amounts to the same thing. If, e.g, the bottommost pixel were removed from B, then it would matter). To erode an image by B, place (a copy of) B -completely- inside the image at every pixel where it will fit like that, and mark the center of (each copy of) B.