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Grayscale dilation

Regards.
I have recently started to learn about digital image processing, I'm currently reading on mathematical morphology.
Use the book Digital Image Processing, second edition.
I have several questions and I need some help:
Does the equation 9.61 represents the dilation for the point (s, t) of the output image or represents dilatation for the entire image (such as Equation 9.22)?.
If the answer is yes, this means that: for full dilatation of the image 'f' should apply Equation 9.61 for each possible value (s, t) or not?.
I'm also a bit confused with respect to equation 9.61:
It represents the image displacement is 'f' for all the structuring element and not the other? ...
can someone explain (at least somewhat) this.Thanks in advance for any help.

I'm afraid I don't have that book on my bookshelf today. Must have loaned it to a friend.
Would be helpful if you would post equations 9.61, 9.22, et al.