# Granulometry by morphological opening and closing

I am trying to understand granulometry. I understand that it deals with determining the size distribution of particles in an image and uses the principles of opening and closing.

I have a smoothed image with marbles in different sizes and call it A and a structuring element B, which is a disk with variable radii. I get that when opening the image with the structuring element B, smaller marbles disappear and by increasing the radius of B, bigger marbles start to disappear.

What I do not understand is what will happen if I use closing instead of opening. Do the bigger marbles disappear with a smaller radius B? So, does the exact opposite happen with closing?

You can think of closing as the dual operator to opening; while opening the image using structuring elemnts $B$ at different sizes gives you values for the Pattern Spectrum $P(k)$ at $k >= 0$, closing will give you values at $k < 0$. These give you an idea of the sizes of "holes" present in the image, rather than the actual objects.