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Cases where Morphological Opening and Closing yields the same results?

Yes, there are such images. One of the properties of opening (it's mentioned in wiki article, for example) is that it is an anti-extensive operation, i.e. if Y is opening of X, then Y ⊆ X. Similarly, closing is an extensive operation (i.e. X ⊆ Y), therefore for any such image X = Y. Any image invariant to both opening and closing will satisfy your requirement (and, as I have just shown, only such images will).

Concrete examples depend on structuring element used when performing erosion or dilation. For example, if it is a square n x n matrix with all elements equal to 1, then any rectangle with both height and width greater than n (and located far enough, i.e. at least n/2 pixels, from image edges) will satisfy this requirement.

Categories : Python

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