How do I edit movies taken with the iPad?

I recorded several movie segments using the camera mode of an iPad mini. Now I would like to edit the segments together, add music, transitions, photos and titles. What is the best software to use for that purpose? I tried importing the segments into iMovie and the formatting changed and cut off some of the video images at the top of the frames.

If iMovie doesn't do it for you there are multiple alternative apps for computers - just copy/move the raw video from the iPad to computer and use what works for you.