Morphological Operations

Every operation here tests how a small shape, the structuring element (StrataQuest calls it the kernel), meets the foreground. The Engines Reference gives the picture: dilation is the set of points the kernel covers as its center moves inside an object, and erosion is the set of points its center can reach while the kernel stays inside. So a 10-pixel square dilated by a disk of radius 2 becomes a 14-pixel square with rounded corners, and eroded it becomes a 6-pixel square.

Each operation is its own entry under Morphological:

In image processing generally, two more transforms are common: the morphological gradient (dilation minus erosion) and the bottom-hat (closing minus the image). The Morphological list has neither, nor a hit-or-miss transform. You can assemble the first two from Dilate, Erode, Close and Subtract images in the arithmetic operationsLoading..., because the module lets each operation use the outputs of earlier ones.

In image processing generally, mathematical morphology was formalized by Matheron and Serra in the 1960s, and many elaborate procedures reduce to sequences of dilations and erosions. Treat the structuring element as a coin. Slide it around inside an object: everything it can cover is the opening, so spikes and threads too narrow for the coin are lost. Roll it around the outside: notches and gaps it can't enter are filled, and that is the closing.

Dilation and erosion are duals, not inverses. An object that erosion removes completely is gone, and no dilation brings it back. The Grow (global)Loading... engine has a mode built around this: Shrink (retain last pixel) keeps the last pixel of each event when the shrink size is larger than the event.

On a grayscale image the same operations act on intensity. The reference ties them to two filters: Filter max has the same effect as Dilate and Filter min the same effect as Erode, a local maximum and minimum over the kernel. That makes the Top-hatLoading... easy to read: the opening is a background estimate that can't follow bright details narrower than the kernel, so the image minus its opening keeps those details and attenuates high background.

Kernel shape matters too. In general a disk treats every direction alike, while a square reaches farther along its diagonals than along its sides, so it reshapes objects unevenly. StrataQuest's default Kernel shape is Disk; the reference names no other shape.

There is no operation selector: you pick the entry. Kernel radius (px) defaults to 0 for Dilate, Erode, Open and Close, so nothing happens until you set it. A rule that follows from the coin picture: choose the radius larger than the specks or holes you want gone and smaller than the narrowest part of the objects you want to keep. Results are usually judged on the maskLoading... that comes out.

Source: StrataQuest 8.1 Engines Reference, ch. 6.8 (pp. 227–283), ch. 6.3 (Filter max and Filter min pp. 101–104), ch. 6.1 (Subtract images p. 69), ch. 6 (p. 19) and ch. 24 (p. 438).