Why is the structuring element asymmetric in OpenCV?

Question

Why is the structuring element asymmetric in OpenCV?

cv2.getStructuringElement(cv2.MORPH_ELLIPSE, ksize=(4,4))

returns

array([[0, 0, 1, 0],
       [1, 1, 1, 1],
       [1, 1, 1, 1],
       [1, 1, 1, 1]], dtype=uint8)

Why isn't it

array([[0, 1, 1, 0],
       [1, 1, 1, 1],
       [1, 1, 1, 1],
       [0, 1, 1, 0]], dtype=uint8)

instead?

Odd-sized structuring elements are also asymmetric with respect to 90-degree rotations:

array([[0, 0, 1, 0, 0],
       [1, 1, 1, 1, 1],
       [1, 1, 1, 1, 1],
       [1, 1, 1, 1, 1],
       [0, 0, 1, 0, 0]], dtype=uint8)

What's the purpose of that?

Answer 1

There's no purpose for it other than it's one of many possible interpolations for such a shape. In the case of the ellipse with size 5, if it were full it would just be the same as the MORPH_RECT and if the same two were removed from the sides as from the top it would be a diamond. Either way, the way it's actually implemented in the source code is what you would expect---it creates a circle via the distance function and takes near integers to get the binary pixels. Search that file for cv::getStructuringElement and you'll find the implementation, it's nothing too fancy.

If you think an update to this function should be made, then open up a PR on GitHub with the implemented version, or an issue to discuss it first. I think a successful contribution would be easy here and I'd venture that the case for symmetry is strong. One would expect the result of a symmetric image being processed with an elliptical kernel wouldn't depend on orientation of the image.