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no, the radius is (size-1)/2 .

here is the 3x3 disk kernel, as you can see, it's pretty much the same as the MORPH_CROSS one, because it's so small:

Mat k = getStructuringElement(MORPH_ELLIPSE,Size(3,3));
cerr << k << endl;


[  0,   1,   0;
   1,   1,   1;
   0,   1,   0]

ofc., it gets more "disk-like" with larger size (like 11):

[  0,   0,   0,   0,   0,   1,   0,   0,   0,   0,   0;
   0,   0,   1,   1,   1,   1,   1,   1,   1,   0,   0;
   0,   1,   1,   1,   1,   1,   1,   1,   1,   1,   0;
   1,   1,   1,   1,   1,   1,   1,   1,   1,   1,   1;
   1,   1,   1,   1,   1,   1,   1,   1,   1,   1,   1;
   1,   1,   1,   1,   1,   1,   1,   1,   1,   1,   1;
   1,   1,   1,   1,   1,   1,   1,   1,   1,   1,   1;
   1,   1,   1,   1,   1,   1,   1,   1,   1,   1,   1;
   0,   1,   1,   1,   1,   1,   1,   1,   1,   1,   0;
   0,   0,   1,   1,   1,   1,   1,   1,   1,   0,   0;
   0,   0,   0,   0,   0,   1,   0,   0,   0,   0,   0]

please also see MORPH flags and tutorials