An Easier Way? [ How to extract image of diamond crown from black background?]

I had planned to do this in Illustrator but maybe there is an easier way in Photoshop? I am creating a tshirt design for a pageant. I have attached the exact crown for this year and want to put it on the shirt. I was going to use the pen tool in Illustrator to trace out each gem. Would this be easier in Photoshop or do you think there is an even easier way?

Thanks!!