Prove the validity of the following gray-scale morphology expressions. You may assume that b is a flat structuring element. Recall that fc(x, y) = −f(x, y)and that
.
(a) Duality of erosion and dilation:
.
(b)
.
(c)
and
. Assume a symmetric structuring element.
(d)
.
(e)
, where (f ⊕ nb)indicates n erosions of f by b. Also,
.
(f)
and
. Assume that the structuring element is symmetric with respect to its origin.
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