The suffix “-ology” means “study of-,” so obviously, “morphology” is the study of morphs; answering critical questions like: “How come they only come out at night, and then fly toward the light?” and “Why is it that bug zappers only toast the harmless critters, leaving the 'skeeters alone?” and – HOLD IT! That's MORPH-ology, the study of SHAPE, not moths! Try again …

Binary morphology

We begin by considering ONLY BINARY images. That's important, remember it! Only binary! We will discuss a couple of operators first. Then, once you understand how they work, we'll explain how they are used in binary images. As an extension to binary morphology, we also describe gray scale morphology operations and the corresponding operators.

Dilation

First, the intuitive definition: The dilation of a (BINARY) image is that same image with all the foreground regions made just a little bit bigger.

Now, formally: We consider two images, fA and fB, and let A and B be sets of ordered pairs, consisting of the coordinates of each foreground pixel in fA and fB, respectively.

Consider one pixel in fB, and its corresponding element (ordered pair) of B, call that element b ∈ B.