How can I merge multiple sets of morphological components (perhaps selected using different metrics)?

Question

Let's say I use SelectComponents to select morphological components in an image according to some criterion, like "Elongation". Then let's say, I pull out a different set of morphological components using another criterion like "Area".

m1 = SelectComponents[testImage, "Elongation", # == 1 &];
m2 = SelectComponents[testImage, "Area", # > 42 &];

How can I properly merge m1 and m2 into a single set of non-intersecting morphological components?

Answer 1

You can combine the outputs of SelectComponents in a straightforward way. Let's take a test image from the docs:

c=Import["https://i.sstatic.net/gSXIj.png"]

and select two conditions on the components:

m1 = SelectComponents[c, "Elongation", # > 0.5 &];
m2 = SelectComponents[c, "Area", # < 1000 &];

These m1 and m2 are binary images with 1's where the criterion is fulfilled and 0's where it fails.

{m1,m2}

You can find the intersection of the two components by multiplying

ImageMultiply[m1,m2]

You can find the union of the two selected components by adding (for binary images, ImageAdd is essentially the logical OR of the two images)

ImageAdd[m1, m2]

Answer 2

From the Mathematica documentation:

Selecting components based on multiple properties:

SelectComponents[image, {"Count", "AdjacentBorderCount"}, #1 > 100 && #2 == 0 &]

So instead of calling SelectComponents twice and somehow merge the output, you can just call it once with any logical combination of your criteria.