If you get the chance - rephotograph the hat with a better contrast between the fur and the background. If not you could try using a copy of the blue channel with a curves adjustment to make an initial mask.
Then use a brush to ensure the centre is solid white and the select and mask refine edge tool on the fur edges
My reply was similar to the above. Its really a job for the channels and refine mask command. I see you wanted to keep the styrofoam base. This is totally achievable. Since the hat is principally dark, and you ought to shoot against a light background, there are still ways to manually select the base, but I was still able to keep it with channels. Here's how I achieved it:
I duplicated the blue channel, since it was a good base to begin a mask. I multiplied green channel via the calculations command to darken the image.
I multiplied the resulting alpha channel onto itself with the apply image command.
After that I used the calculations command set to overlay to increase the difference between the lights and darks (its a contrast mode). It created a new channel which is the one I focused on from here on out (Alpha 2).
With the lasso tool, I selected the most important area of the image. Then inverted it and filled it with white.
With the Dodge tool set as you see, I was able to get rid of the highlight areas. With a black brush set to overlay, I filled in the darker areas.
Next I used levels to squash some of the grays. After hitting ok, I inverted the Alpha 2 channel with Command + I (Invert). I command clicked the Alpha 2 channel to make it a selection and clicked the mask button at the bottom of the layers palette.
There were some rough edges as you can see above. To soften those harsh edges on the back of the styrofoam neck, I used the pen tool to delicate trace a smooth transition on the mask. Command + clicking a path makes it a selection. I filled it with while. Remember, white reveals, black conceals.
Once I had the mask there, to soften it I invoked the gaussian blur command.
I then fade the blur with the fade command (command shift + f, immediately). I set the fade to multiply. It brings some of the contrast back into the mask.
You can further refine the mask by double-clicking it and using the refine mask command. I used roughly these values:
And this is what I would up with:
Here is the image masked and the mask itself. With fuzz and low contrast on the bottom, its not as easy as a selection tool. Channels usually (not always) have a mask hiding in them. Used in conjunction with calculations and a good overlay brush, those are your weapons for attacking fuzzy beasts like this. It took me longer to write this out than to actually do the task. I hope this helped! Cheers!
I've also read the answer by mozgod. I don't know Pshop well enough to comment on it other than that I can be persuaded that it will work, but I think elders12 might be seeking something less daunting. Mostly, I just give up on difficult subjects. I've had some success with the quick select tool, but I'm not convinced I show a profit on the deal. I use it to do a rough selection then, more or less at random depending on how I feel on the day, I use the polygon select tool, and/or a more complicated: select and mask, then a brush to edit the resulting mask. I suspect that the quick select tool saves almost none of the time I spend on the polygon select tool and/or brush, but I live in optimism. It is useful to know that holding down alt while clicking the mask displays it in black and white. This helps a little, but only a little. It is also useful to remember that if Load Selection is used to check where the mask is and isn't, it isn't possible to change bits of the mask outside the selected area. And it is useful to understand the clever Add to selection, Subtract from selection, and Intersect with selection options of the Load Selection command. I get these options wrong quite often and often need to draw Venn diagrams to work out what I should have done. I'm sure that I stumbled over a way to display the mask as a colour overlaying my image, but I haven't been able to rediscover what I did. Help on this subject is spectacularly unhelpful. I'm tempted to buy the AddOn: FluidMask. That might automate the steps suggested by mozgod, or something equivalent. Why the polygon, not the lasso? It seems to be a rough and ready tool, not a precision tool, and amplifies mistakes I make.
I guess it all boils down to proficiency in Photoshop (and I respect all levels). If you are running a business/own a shop, than learning tricks in channels may not be prudent for you. If you think an add-on is what ultimately will turn you a profit, by all means. I am not familiar with the add on you speak of, as I've never needed it, but if you are primarily not a retoucher/etc., it might behoove you to purchase it. To do what you are asking with out sacrificing quality in one step though, takes effort. All in all it took me less than 10 minutes to accomplish what I did above. I've been using Photoshop since 1996 however. The quick selection tool would give you grief in the styrofoam base (I have wigs I use as disguises, so I'm familiar with them, lol). Quick selection can be good with the hairy parts used in conjunction with the refine selection command. That is a good place to start. As for the more contrasted edges, you can trace them with pen or magnetic lasso to add to the selection.
Down and dirty? I'd select the background with the magic wand, tolerance set to 50 and mask it out (make the selection & option click the mask button at the bottom of the layers palette). Paint back the missing neck with a white brush on the mask. You can invoke the red "rubylith" overlay you are seeking by clicking the mask and hitting the "\" (forward slash key). This way you can edit in real time. I wish there was an easier 1 or 2 step way to do this, but the fuzziness & lack of contrast on the bottom make it not so straightforward.
Mostly just to say "thanks". "Rubylith" was the word I was trying to think of. I can't imagine why I couldn't remember that "/" meant "Rubylith". As for "respect", I didn't mean to seem disrespectful, and mostly I view people who can beat Pshop into submission with admiration. From what I've read, I gather that some experts can play the commands almost the way a pianist plays a Chopin Mazurka. Meanwhile, I use a tool, wonder why it did that, search help, become even more confused, become very grateful for the History panel, quit without saving, and start again. I hope you've helped elders12 as much. Again, thanks.
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Fix the white point and the color cast first!
Then you'll discover that there isn't all that much masking needed. It just makes life a lot easier. Besides, if you're going to put something on a white background, it needs to look credible. Muddy highlights don't.
As a matter of fact, you don't need any selection/masking at all here. Just lift the whites all around the object. Only the base needs an active selection if you want it prominently visible.
I know I sound like a broken record on this, I keep repeating it. Don't reach for the selection tools until the global adjustment options are exhausted!