Granulometry in image processing

Hi - I am trying to interpret the 'first derivative of the object distribution' in an image as is mentioned in the Matlab tutorial of granulometry.

What is a good way to explain this in simple terms?

http://www.mathworks.com/products/image/examples.html?file=/products/demos/shipping/images/ipexsnow.html

I am specifically trying to interpret what the plot tells us about the image. The explanation from the link is not very intuitive to me.

Thanks Nad