Bridging islands in my stencil I am using the MatterHackers MatterControl software. MatterControl has an option to convert an image into a 3d object. The image converter converts any image into an STL. I was wondering what program would work for bridging the islands? I tried SOLIDWORKS and I think the export messed up the file.
You should know that there will be no such functionality anywhere because "make a bridge between islands" causes some questions:


what do you mean be bridge
where this bridge should be
how it should look like


Application cannot answer these questions automatically. 
Conver image to 3D object is (almost) only to create logo-like-objects or text-like-objects.

If your image will consist more than one separate elements then MC will convert it into separate objects and these objects will be treated as separate islands. There will be no way to bridge them on certain level/layer. The only thing you can achieve is a solid "connection" between islands if they will be connected with line on the image. I'm sure it's not what you expect.

Almost all 3D apps have a functionality to create 3D obj out of image but it will always be a perimeter or surface which you can extrude.

You can create bridges in your app by creating additional 3D object according to your expectations or you can use sculpting app to extend a form. It means you won't add extra object but sculpt existing objects by  extruding/extending/pulling faces.

For such sculpting you can use Meshmixer for example.