It tells you exactly how to compute the bottom hat transform(sort of looks like an inverted graduated threshold transform to me).
First thing to do is implement the two morphology functions dilation and erosion.
To do this you need your f and b then you compute the function over a small region of the image at a point keeping the largest value found.
(f ⊕ b)(s, t) = max{f (s − x, t − y) + b(x, y)
|(s − x), (t − y) ∈ Df ; (x, y)∈Db}
What this says is, take the maximum of the expression over all points in the domain region(such as a small rectangle centered at your point (s,t).
simple pseudo code would be
max = -infinity // for the point (s,t) on the image, must compute this for all points
for(x = -5 to 5)
for(y = -5 to 5)
max = Max(max, f(s - x, t - y) + b(x,y))
effectively we now have a new image of the max values.
It's actually quite simple so don't make it harder than it is(we are simply adding b(x,y) to each point in the region and finding out which one gives the maximum value).
you do the same for the erosion(very similar to above)
Now the opening and closing is the composition of the two
You can think of it first as performing a dilation and then an erosion for an opening.
It says finally subtract the closing from the original image and you should have your transform.
