How to fill gaps in object to make complete silhouette without white lines going through

Hello All,
Can someone tell me how I can fill in the lines of my object and still be able to export it with transparent background? I've tried to use the section tools but they all make select the background when i try to select the spaces between the puzzle pieces. As you can see the lines go all the way through the object. Though not actually connected or touching, the pieces still move as one object.
thank you for you help in advance!
