Embedded within this project is actually a process that warrants it's own Instructable. That is "How to make custom patterns for a router using a laser cutter" covered in steps 1, 2 , 3 ,4 ,5 and 8. Look for that Instructable coming soon.
Note - this project details some basic wood working processes that require some previous wood working experience. To simplify this project once could easily just glue the coral onto the base using epoxy and use a bit of quarter round molding from Home Depot to make a well for the smaller earrings and thus avoid several of the more challenging wood working steps.
Step 1: Scan coral
It's ok to leave the over open while you scan, it will still work fine.
Scan the image in greyscale and at a suitable resolution, like 300DPI.