Is there a way to do a perfect die cut on a person's hair or on dog's fur or others like difficult hair styles?
Similar to this:
1 - Make a quick selection with
2 - Edit your selection
3 - Choose
4 - Define
6 - Use
6 - Sometimes, you will need to refine edge several times to have perfect select
Personally I would normally put a background color that stands out and by hand remove the background elements.
This is a personal option as it comes out better than any select tool.
To allow you more information on the way I would do this I shall do a step by step. Sorry im at work so Images will have to come later.
Hope that updated edit helped more.
There's a lot of techniques for this, the secret to find them is a thing called Google :)
To remove a monochrome background we can add an alpha layer replacing the background color by transparency.
To leave the foreground objects non-transparent we may have to make a selection of the background by fuzzy select (magic wand tool) or by color selection. Hair may need to be unselected manually in addition. It is also a good idea to generously feather the selection.
The point of this approach is to have some of the background shine through by transparency on the hair or on other fuzzy regions in the foreground objects.
We can see that the image grain noise from the example source will be preserved. This may be a wanted effect to better merge the foreground and background image qualtity. If not this noise has to be removed beforehand.